First Week School

Second Week School

Third Week Discussion Meeting



First Week School


Angelo Bassi

Introduction to collapse models

We will introduce the idea of spontaneous wave function collapse models and will present the Ghirardi-Rimini-Weber (GRW) model, the first model of this kind. We will discuss why and how nonlinear modifications to the Schrödinger equation have always to be accompanied by appropriate stochastic terms, in order to avoid superluminal signalling.

We will discuss in detail the amplification mechanism, which allows to describe both the quantum properties of microscopic systems and the classical properties of macroscopic objects within a single dynamical framework.

We will present the Continuous Spontaneous Localization (CSL) model, which somehow has become the reference model in the literature. We will also introduce gravity-related models, the most famous being the Diosi-Penrose (DP) model.

We will review the most promising tests of collapse models, which range from matter-wave interferometry to non-interferometric tests, to cosmological observations. We will show which region of the parameter space of the CSL model has been excluded by experimental data.

Useful references:

  • The GRW model: G. C. Ghirardi, A. Rimini, and T. Weber, Phys. Rev. D 34, 470 (1986).
  • The CSL model: G. C. Ghirardi, P. Pearle, and A. Rimini, Phys. Rev. A 
42, 78 (1990).
  • The DP model: L. Diosi, Phys. Rev. A 40, 1165 (1989).
 P. Penrose, Gen. Rel. Grav. 28, 581 (1996).

  • A review of collapse models: Bassi, K. Lochan, S. Satin, T. P. Singh, and H. Ulbricht, Rev. Mod. Phys. 85, 471 (2013). [arXiv:1204.4325]


Dustin Lazarovici

The measurement problem and some mild solutions

We shall introduce two solutions of the measurement problems of quantum mechanics, which do not change the Schrödinger evolution of the wave function: Bohmian Mechanics and Many Worlds. 

We shall explain on the basis of Bohmian Mechanics how randomness has to be understood in a deterministic theory of nature, since both Bohmian Mechanics and Many Worlds are deterministic. We shall further but shortly explain the emergence of operator observables and Heisenberg's uncertainty relation.

We shall also discuss Bell’s inequalities and the nonlocality of Nature, which has been firmly established by now.

If time permits, I shall touch upon so called on decoherent histories, which is another attempt to solve the measurement problem, but which is problematical with respect to the various no go theorems, like Kochen and Specker. 

Useful references:

  • Detlef Dürr, Stefan Teufel: Bohmian Mechanics, Springer, 2009.
  • John S. Bell: Speakable and Unspeakable in Quantum Mechanics (2nd Edition), Cambridge University Press, 2004.
  • Jean Bricmont: Making Sense of Quantum Mechanics, Springer, 2016.
  • Tim Maudlin: Three measurement problems, Topoi 14(1), 1995.
  • Sheldon Goldstein: Bohmian Mechanics, in: The Stanford Encyclopedia of Philosophy


Andrè Grossardt

Quantum mechanics and gravitation – what we know, what we don't know, and what we think we know

  1. Mechanics of a point mass – nonrelativistic to relativistic and classical to quantum
    We will briefly discuss the quantisation of the relativistic point particle and of the Klein-Gordon field. We will further discuss how the limit to nonrelativistic quantum mechanics can be obtained, and what issues arise with this step.
  2. Gravitation – from Newton to Einstein and back
    We will review the principles of general relativity and its Newtonian limit. Then we focus on the problems that arise when we try to couple classical gravity to quantum matter.
  3. What we know: nonrelativistic particles in a Newtonian gravitational potential
    We will discuss the experiments conducted with quantum matter in the gravitational field of the Earth.
  4. Equivalence principle in classical and quantum mechanics
    A brief review will be given on the equivalence principle in classical general relativity. We will discuss how questions arising when generalising the equivalence principle to quantum physics.
  5. What we don't know: a very brief history of quantum gravity
    In a short presentation an overview of the different approaches to quantum gravity will be given.
  6. What we think we know (I): perturbative quantum gravity vs. semiclassical gravity
    We will discuss the perturbative approach to quantum gravity as a quantum field theory, how it compares to a possible semiclassical alternative, and how it could be experimentally tested.
  7. What we think we know (II): Quantum mechanics in curved space-time beyond Newton
    We discuss what is known about the behaviour of quantum systems in a gravitational field beyond the nonrelativistic limit. We will review previously considered effects such as gravity-induced decoherence and discuss open questions and problems.


  • Wolfgang Rindler, Essential Relativity (second ed.), Springer, 1977
  • Thanu Padmanabhan, Gravitation, Cambridge University Press, 2010
  • Claus Kiefer, Quantum Gravity (third ed.), Clarendon Press, 2012
  • D. Giulini, C. Kiefer, C. Lämmerzahl (eds.), Quantum Gravity, Lecture Notes in Physics,
Springer, 2003
  • R. Colella, A.W. Overhauser, and S.A. Werner, Observation of Gravitationally Induced Quantum Interference, Physical Review Letters 34 (1975) 1472
  • Daniel M. Greenberger, The neutron interferometer as a device for illustrating the strange behavior of quantum systems, Reviews of Modern Physics 55 (1983) 875
  • Domenico Giulini, Equivalence principle, quantum mechanics, and atom-interferometric tests. In: F. Finster et al. (eds.), Quantum Field Theory and Gravity, pp. 345-370, Birkhäuser/Springer, 2012. arXiv:1105.0749 [gr-qc]
  • James Mattingly, Is Quantum Gravity Necessary? In: A.J. Kox and J. Eisenstaedt (eds.), The Universe of General Relativity, Einstein Studies 11, pp. 327-338, Birkhäuser/Springer, 2005.
  • Roger Penrose, On the Gravitization of Quantum Mechanics 1: Quantum State Reduction, Foundations of Physics 44 (2014) 557.


Alex Matzkin

Weak measurements

What is the value of a given physical property of a quantum system at some intermediate time between the system preparation in an initial state and its final detection ?  The answer to this question hinges on the peculiar status of quantum measurements. The standard answer according to standard quantum mechanics would be that this question is meaningless and leads at best to counterfactual paradoxes. Standard quantum mechanics affords nevertheless another answer, in the form of a minimally perturbing and experimentally feasible protocol known as “weak measurements”.

The aim of these lectures will be to introduce weak measurements  and  to appraise the relevance of the weak measurement protocol in order to shed light on the properties of evolving quantum systems. The lectures will be structured according to the following outline:

  1. Introduction: Properties and measurements
  2. Measurements in Quantum (and also in Classical) Mechanics
  3. Weak measurement protocol
  4. Weak values and properties of quantum systems


    Some References:
  • Y. Aharonov, D. Z. Albert, and L. Vaidman , How the result of a measurement of a component of the spin of a spin-1/2 particle can turn out to be 100, Phys. Rev. Lett. 60, 1351-1354 (1988)
  • Y. Aharonov and D. Rohrlich, Quantum Paradoxes, Wiley, 2005
  • A. Danan, D. Farfurnik, S. Bar-Ad and L. Vaidman, Asking photons where they have been,  Phys. Rev. Lett. 111, 240402 (2013)
  • J. Dressel, Weak values as interference phenomena, Phys. Rev. A 91, 032116 (2015)
  • A. Matzkin, Observing trajectories with weak measurements in quantum systems in the semiclassical regime, Phys. Rev. Lett. 109, 150407 (2012)
  • S. Kocsis , B. Braverman, S. Ravets, M. J. Stevens, R. P. Mirin, L. K. Shalm, and A. M. Steinberg, Observing the average trajectories of single photons in a two-slit interferometer, Science 332, 1170 (2011).


Tejinder Singh

Trace Dynamics: Quantum theory as an emergent phenomenon

It has been suggested, for various reasons, that quantum theory maybe an approximation to a deeper theory. In these talks, we will begin by reviewing these reasons. We will then describe one concrete attempt to develop such an underlying theory, namely the theory of Trace Dynamics [TD], proposed by Stephen Adler and collaborators. TD is a classical dynamical theory of matrices, possessing an important global unitary invariance. It is shown how, as a result of coarse-graining, quantum theory emerges as the equilibrium statistical thermodynamics of the underlying microscopic TD. Statistical fluctuations about equilibrium can in principle result in a stochastic nonlinear modification of quantum theory, thus providing a theoretical underpinning for the phenomenological collapse model known as Continuous Spontaneous Localisation [CSL]. We will end by mentioning the outstanding unsolved problems of this program, and attempts to include gravitation.The tutorial will be used to present some ongoing research work in this context, and to have an open-ended discussion with the audience on the subject matter of these talks.

References that the students will find useful:


  • S. L. Adler, Quantum theory as an emergent phenomenon (Cambridge University Press, Cambridge, 2004) Available in part at arXiv:hep-th/0206120

Original Papers: 

  • S. L. Adler, Nucl. Phys. B 415, 195 (1994) [arXiv:hep-th/9306009]: Generalised quantum dynamics
  • S. L. Adler and A. C. Millard, Nucl. Phys. B 473, 199 (1996)  [arXiv:hep-th/9508076]: Generalised quantum dynamics as prequantum mechanics 

Condensed reviews:

  • P. Pearle, Stud. Hist. Philos. Mod. Phys. 36, 716 (2005) [arXiv:quant-ph/0602078]
  • Bassi, K. Lochan, S. Satin, T. P. Singh, and H. Ulbricht, Rev. Mod. Phys. 85, 471 (2013) [arXiv:1204.4325]



Rafael Sorkin

The quantum measure (and how to measure it)

When utilized appropriately, the path-integral offers an alternative to the ordinary quantum formalism of state-vectors, self-adjoint operators, and external observers - an alternative that seems closer to the underlying reality and more in tune with quantum gravity. The basic dynamical relationships are then expressed, not by a propagator, but by the quantum measure, a set-function μ that assigns to every (suitably regular) set E of histories its generalized measure μ(E). (The idea is that μ is to quantum mechanics what the Wiener-measure is to Brownian motion.) Except in the special case where E is an instrument-event, μ(E) cannot be interpreted as a probability, as it is neither additive nor bounded above by unity. Nor, in general, can it be interpreted as the expectation value of a projection operator (or POVM). Nevertheless, I will describe how one can ascertain μ(E) experimentally for any desired E, by means of an arrangement which, in a well-defined sense, filters out the histories that do not belong to E.


  1. Alvaro M. Frauca and Rafael D. Sorkin, ``How to Measure the Quantum Measure'', to appear on arXiv 2016 Oct 10, and in IJTP eventually.
  2. Sukanya Sinha and Rafael D. Sorkin, ``A Sum-over-histories Account of an EPR(B) Experiment'',  Found. of Phys. Lett. 4, 303-335 (1991).
  3. Rafael D. Sorkin, ``Quantum Mechanics as Quantum Measure Theory'', Mod. Phys. Lett. A 9, 3119-3127 (1994).  ArXiv: gr-qc/9401003.
  4. Rafael D. Sorkin, ``Quantum dynamics without the wave function'' J. Phys. A: Math. Theor. 40, 3207-3221 (2007). ArXiv: quant-ph/0610204.


Bassano Vacchini

Introduction to non-Markovian open quantum systems dynamics

The lectures will be devoted to introduce the basic ideas and formalism for the description of open quantum systems, namely quantum systems whose interaction with an external environment cannot be neglected. As a consequence the reduced system dynamics is irreversible and features typical phenomena such as dissipation and decoherence.  

We will introduce the notion of quantum dynamical map and the basic dynamical equations governing the time evolution of an open quantum system, considering both the fundamental Gorini-Kossakowski-Sudarshan-Lindblad master equation and more general time evolutions including time-convolutionless and memory kernel master equations. 

We will further consider recent developments pointing to possible definitions of memory effects in a quantum reduced dynamics. In particular we will explore a recently introduced notion of quantum non-Markovianity based on the distinguishability of quantum states as quantified by the trace distance and connecting memory effects with an information flow between system and environment. 

We will consider the connection of this approach with the divisibility of quantum dynamical maps. Finally we will show how this strategy leads to the actual measurement of non-Markovianity and also allows for the detection of initial system-environment correlations.

The structure of the lectures will be as follows:

  • Lecture 1: Foundations of open quantum system theory. 
  • Lecture 2: Lindblad theory and generalized master equations
  • Lecture 3: Definitions and measure of non-Markovianity
  • Lecture 4: Detections of non-Markovianity and of initial correlations


Lecture 1+2
General references: [1, 2, 3]
Seminal papers: [4, 5] 
Collisional decoherence: [6] 
Memory kernels: [7, 8] 
Lecture 3+4
General references: [9, 10, 11] 
Seminal papers: [12, 13, 14] 
Classical-quantum connection: [15] 
Dynamics with initial conditions: [16] 

  [1]  H.-P. Breuer and F. Petruccione, The Theory of Open Quantum Systems (Oxford University Press, Oxford, 2002) 
  [2]  A. Rivas and S. F. Huelga, Open Quantum Systems: An Introduction (Springer, 2012) 
  [3]  B. Vacchini, Lecture notes on advanced quantum mechanics 
  [4]  V. Gorini, A. Kossakowski, and E. C. G. Sudarshan, J. Math. Phys. 17, 821 (1976) 
  [5]  G. Lindblad, Rep. Math. Phys. 10, 393 (1976) 
  [6]  B. Vacchini and K. Hornberger, Phys. Rep. 478, 71 (2009) 
  [7]  H.-P. Breuer and B. Vacchini, Phys. Rev. Lett. 101, 140402 (2008) 
  [8]  B. Vacchini, Phys. Rev. Lett. xx, xxxxxx (2016) 
  [9]  H.-P. Breuer, E.-M. Laine, J. Piilo, and B. Vacchini, Rev. Mod. Phys. 88, 021002 (2016) 
[10]  A. Rivas, S. F. Huelga, and M. B. Plenio, Rep. Prog. Phys. 77, 094001 (2014) 
[11]  I. de Vega and D. Alonso, Rev. Mod. Phys. (2016) 
[12]  H.-P. Breuer, E.-M. Laine, and J. Piilo, Phys. Rev. Lett. 103, 210401 (2009) 
[13]  A. Rivas, S. F. Huelga, and M. B. Plenio, Phys. Rev. Lett. 105, 050403 (2010) 
[14]  E.-M. Laine, J. Piilo, and H.-P. Breuer, EPL 92, 60010 (2010) 
[15]  B. Vacchini, A. Smirne, E.-M. Laine, J. Piilo, and H.-P. Breuer, New J. Phys. 13, 093004 (2011)
[16]  B. Vacchini and G. Amato, Sci. Rep. 6, 37328 (2016)


Apoorva Patel

Quantum Trajectory formalism for Weak Measurements

Projective measurement is used as a fundamental axiom in quantum mechanics, even though it is discontinuous and cannot predict which measured operator eigenstate will be observed in which experimental run. The probabilistic Born rule gives it an ensemble interpretation, predicting proportions of various outcomes over many experimental runs. Understanding gradual weak measurements requires replacing this scenario with a dynamical evolution equation for the collapse of the quantum state in individual experimental runs. We revisit the quantum trajectory framework that models quantum measurement as a continuous nonlinear stochastic process. We describe the ensemble of quantum trajectories as noise fluctuations on top of geodesics that attract the quantum state towards the measured operator eigenstates. Investigation of the restrictions needed on the ensemble of quantum trajectories, so as to reproduce projective measurement in the appropriate limit, shows that the Born rule follows when the magnitudes of the noise and the attraction are precisely related, in a manner reminiscent of the fluctuation-dissipation relation. That implies that the noise and the attraction have a common origin in the measurement interaction between the system and the apparatus. We analyse the quantum trajectory ensemble for the dynamics of quantum diffusion and quantum jump, and show that the ensemble distribution is completely determined in terms of a single evolution parameter, which can be tested in weak measurement experiments. We comment on how the specific noise may arise in the measuring apparatus.


Second Week School


Daniele Faccio

Optical Models for Gravity

In 1981 Unruh published a paper that initiated the field of Analogue Gravity. Originally just a theoretical endeavour, this is now involves a remarkably broad range of research areas such as Bose-Einstein condensates, optics, nonlinear optics, superfluids and hydrodynamics. More than that, and possibly the main legacy of the field, these different field often come together and find an overlap or common inspiration through the ideas of analogue gravity. In a nutshell, Analogue gravity refers to the attempt to reproduce certain aspects of the quantum field theory in specific curved spacetime geometries.

Einstein’s theory of general relativity can be seen to be composed of two parts: the first is essentially a theory of geometry, i.e. the geometry of curved spacetimes. The second part are the Einsteina equations that describe how mass or the energy stress tensor modifies the surrounding spacetime metric and how this in turn modifies the mass distribution. A full quantum gravity theory must necessarily account for the full nonlinear dynamics of the Einstein equations - this level of quantisation is the main challenge of contemporary physics and is even celebrated in Hollywood movies.

However, a semi-classical approach is also possible whereby one quantizes the fields, e.g. the electromagnetic field and studies the evolution of these fields on a classical spacetime metric. Such classical spacetime metrics, whilst usually considered to be the result of mass or exotic oject such as balck holes, may actually be encountered in very trivial situations and therefore easily controllable on Earth-based laboratories.

The first model investigated by Unruh was simply a flowing body of water. He showed that it is possibly, by controlling the flow, to create a horizon for acoustic waves propagating inside the flow. Even more interestingly, he discovrered that the same mathematical procedures applied by hawking to predict the quantum-vacuum seeded blackbody emission from black holes also applies to these lab systems.

The implications of this is that whilst it is not possible to directly verify if a black hole emits Hawking radiation, we may certainly verify in the lab if the mathematical model that predicts this emission is indeed correct.

Recent results have provided possible evidence of Hawking emission from analogue black holes or horizons created in a BEC, a flowing body of water and an optical light pulse propagating in a dielectric medium.

We will take a closer look at these effects, starting from a basic overview of the main curved spacetimes that are being studies, or could be studies using analogue gravity. We will look at the basic mathematical tools used to predict particle emission from a curved or time dependence spacetime metric and then apply this to a few simple cases.

We will then use this to look in detail at how optical models for gravity work with some working examples.

Note: this will be an experimentalist’s view of the topic. Equations will be infrequent and incomplete with more weight given to intuitive understanding of the physics at play.

Lecture 1:

Optical Models for Gravity, part I - optical media that change in time

Contents: General overview of analogue gravity, why analogue gravity?, the “one trick pony” approach to QFT in curved spacetimes, Unruh and Hawking radiation, negative frequencies, zero-permittivity media and expanding cosmologies

Lecture 2:

Optical Models for Gravity, part II - superfluids made of light and rotating spacetimes

Contents: Photon fluid basics, spacetime structures in photon fluids, hydrodynamic turbulence in photon fluids, Penrose superradiance from rotating black holes, Zel’dovich superradiance

Lecture 3:

Optical Models for Gravity, part III - Newton-Schrodinger equation in optics

Contents: NSE basics, Boson stars, quantum droplets of light



  • S. Hawking, Nature (London) 248, 30 (1974).
  • S. Hawking, Commun. Math. Phys. 43, 199 (1975).
  • W. G. Unruh, Phys. Rev. Lett. 46, 1351 (1981).
  • C. Barcelo, S. Liberati, and M. Visser, Living Rev. Relativity 8, 12 (2005)
  • Analogue Gravity Phenomenology, D. Faccio, F. Belgiorno, S. Cacciatori, V. Gorini, S. Liberati, U. Moschella eds., Springer (2013)
  • T. Philbin et al., Science 319, 1367 (2008)
  • Measurement of Stimulated Hawking Emission in an Analogue System, S. Weinfurtner et al., Phys. Rev. Lett. 106, 021302 (2010)
  • Laser pulse analogues for gravity and analogue Hawking radiation, D. Faccio, Contemp. Phys., 53, 97 (2012)
  • Optical Black Hole Lasers, D. Faccio, T. Arane, M. Lamperti, U. Leonhardt, Class. Quant. Gravity 29, 224009 (2012)
  • Negative frequency resonant radiation, E. Rubino et al., Phys. Rev. Lett., 108, 253901 (2012)
  • Hawking radiation from ultrashort laser pulse filaments, F. Belgiorno et al., Phys. Rev. Lett., 105, 203901 (2010)
  • Observation of self-amplifying Hawking radiation in an analogue black-hole laser, J. Steinhauer, Nat. Phys  10, 864–869 (2014)
  • Observation of quantum Hawking radiation and its entanglement in an analogue black hole, J. Steinhauer, Nat. Phys  12, 959–965 (2016)
  • Ya. B. Zel'dovich, Pis'ma Zh. Eksp. Teor. Fiz. {14, 270 (1971); Zh. Eksp. Teor. Fiz. 62, 2076 (1972); [JETP Lett. 14}, 180 (1971)][Sov. Phys. JETP 35, 1085 (1972)].
  • Ya. B. Zel'dovich, L. V. Rozhanskii, A. A. Starobinskii, Izvestiya Vysshikh Uchebnykh Zavedenii, Radiofizika, 29, I008-I016 (1986).
  • R. Penrose, General Relativity and Gravitation, 34, 1141 (2002) [reprinted from Rivista del Nuovo Cimento, Numero Speziale I, 257 (1969)].
  • ``Superradiance'', R. Brito, V. Cardoso, P. Piani, Springer (2015)
  • J. D. Beckenstein and M. Schiffer,  Phys. Rev. D, 58, 064014 (1998).



Nikolai Kiesel

Quantum Cavity Optomechanics


At first glance, the minute momentum of photons seems an unlikely candidate to provide control over the motion of massive objects. Yet, today on-chip mechanical oscillators can be manipulated with only a few photons and momentum transfer from lasers can manipulate the mechanical properties of gram-scale mirrors. The relevance of this reasearch covers new approaches to answer fundamental questions about the quantum behaviour of massive objects, applications in quantum information science, and novel methods for sensing of forces and acceleration.

All of this is part of cavity quantum optomechanics [1, 2, 3], where methods from quantum optics are employed to taylor the interaction between light and mechanical resonators. Theory on the subject has been investigated already over a rather long time and soon after the millenium first ground-breaking experiments have been conducted. However, only the last seven years have witnessed experimens that unambiguously demonstrate optomechanics at the quantum level. A few examples are the demonstration of entanglement between a microwave field and a mechanical resonator [4], the generation of squeezed mechanical states [5], and non-classical correlations between single photons and phonons [6].

In this lecture, we will understand the underlying principles of quantum cavity-optomechanical interaction, some of the common methods to measure its effects and examples of broadly used cavity-optomechanical systems . We will furthermore look exemplarily at a selection of the recent ground-breaking experiments to illustrate solutions and challenges in the field.

  1. M. Aspelmeyer, T. J. Kippenberg, F. Marquardt, Cavity Optomechanics, Rev. Mod. Phys. 86, 1391 (2014).
  2. M. Aspelmeyer, S. Gröblacher, K. Hammerer, and N. Kiesel, Quantum optomechanics - throwing a glance, JOSA B 27 A189 (2010).
  3. T. J. Kippenberg and K. Vahala, “Cavity optomechanics: back-action at the mesoscale,” Science 321, 1172 (2008).
  4. T. A. Palomaki, J. D. Teufel, R. W. Simmonds, K. W. Lehnert, Entangling Mechanical Motion with Microwave Fields, Science 342, 710 (2013).
  5. E. E. Wollman, C. U. Lei, A. J. Weinstein, J. Suh, A. Kronwald, F. Marquardt, A. A. Clerk, K. C. Schwab, Quantum squeezing of motion in a mechanical resonator, Science  349, 952 (2015).
  6. R. Riedinger, S. Hong, R. A. Norte, J. A. Slater, J. Shang, A. G. Krause, V. Anant, M. Aspelmeyer, S. Gröblacher, Nonclassical correlations between single photons and phonons from a mechanical oscillator, Nature 530, 313-316 (2016).


Markus Arndt

These lectures will cover methods to perform matterwave interferometry experiments. The students will gain an insight into the complexity of such experiments, such as how to coherently split matterwaves. The second lecture will give a overview of experiments done on atom and molecule matterwave interferometry, while lecture three is focusing on applications of atom and molecule interferometry for metrology and sensing.


  1. Lecture 1: Realizations and ideas around coherent Matter-Wave beam splitters

    1. Amplitude beam splitters:

      1. Atom optics realizations of the Hadamard Gate using Rabi cycles

      2. Atom optics realizations using Raman transitions

    2. Wave front beam splitters:

      1. nanomechanical gratings, the role of van der Waals forces

      2. phase gratings, the role of the dipole force

      3. photo-depletion gratings, many ways to knock it out

      4. wires, discs and algae: many ways are leading to Rome

    3. Far-field diffraction: experiments with

      1. Atoms and dimers

      2. small clusters

      3. large molecules

    4. Wide angular momentum beam splitters:

      1. High order Bragg diffraction

      2. Bloch oscillations

    5. Coherent atom optics in the time domain

      1. Phase modulation

      2. Slits and double slits in the time domain


  1. Lecture 2: Concepts and realization of matter-wave interferometers with atoms and molecules

    1. Mechanical interferometer for atoms

    2. Ramsey-Bordé Interferometer for atoms and molecules

    3. Kasevich Chu interferometer for atoms

    4. Near-field interferometry with atoms and molecules

      1. Talbot-diffraction of light

      2. Talbot diffraction of atoms

      3. Talbot-Lau interferometry with light

      4. Talbot-Lau interferometry with atoms and fullerenes

      5. Kapitza-Dirac Talbot-Lau interferometry with complex molecules

      6. OTIMA interferometry in the time domain

    5. An introduction to theoretical concepts of matter-wave interferometry


  1. Lecture 3: Applications of matter-wave interferometers with atoms and molecules

    1. Atoms:

      1. Gravity sensing and the equivalence principle

      2. Measuring the gravitational constant G

      3. Rotation sensing

      4. measurement of h/m and the fine structure constant


    1. Molecules:

      1. polarizability and structural conformers

      2. dipole moments

      3. optical spectroscopy


Andrea Vinante

Detection of weak forces and quantum foundational problems


Detection of small forces is at heart of many fundamental physics experiments. Here, we are primarily interested in understanding how experiments detecting weak classical forces using mechanical systems can be used to test modifications of quantum mechanics, such as spontaneous collapse models. These techniques are often regarded as non-interferometric, as opposed to direct tests making use of quantum superposition states. I will introduce the general features of weak force detection experiment, and illustrate the main sources of noise and dissipation in relevant experiments, including and ultrasensitive force microscopy and gravitational wave detectors. Finally, we will discuss the state of the art in testing collapse models using mechanical systems.




Hendrik Ulbricht

Testing fundamental physics with table-top experiments


We will discuss trapping and cooling experiments of optically levitated nanoparticles [1]. We will report on the cooling of all translational motional degrees of freedom of a single trapped silica particle to 1mK simultaneously at vacuum of 10-5 mbar using a parabolic mirror to form the optical trap. We will further report on the squeezing of a thermal motional state of the trapped particle by rapid switch of the trap frequency [2].

We will further discuss ideas to experimentally test quantum mechanics by means of collapse models [3] by both matter-wave interferometry [4] and non-interferometric methods [5]. While first experimental bounds by non-interferometric tests have been achieved during the last year by a number of different experiments according to non-interferometric experiments [4], we shall also report on different matterwave interferometry experiments to test the quantum superposition principle directly for 1 million atomic mass unit (amu) particles.

We will further discuss some ideas to probe the interplay between quantum mechanics and gravitation by (levitated) optomechanics experiments. One idea is to seek first experimental evidence about the fundamentally quantum or classical nature of gravity by using the torsional motion of a non-spherical trapped particle, while a second idea is to test the effect of the gravity related shift of energy levels of the mechanical harmonic oscillator, which is predicted by semi-classical gravity (the so-called Schrdinger-Newton equation) [6]. The idea is to complement topic covered during the first week of this school from the experimental perspective.


  1. Vovrosh, J., M. Rashid, D. Hempston, J. Bateman, and H. Ulbricht, Controlling the Motion of a Nanoparticle Trapped in Vacuum, arXiv:1603.02917 (2016).
  2. Rashid, M., T. Tufarelli, J. Bateman, J. Vovrosh, D. Hempston,M. S. Kim, and H. Ulbricht, Experimental Realisation of a Thermal Squeezed State of Levitated Optomechanics, arXiv:1607.05509 (2016).
  3. Bassi, A., K. Lochan, S. Satin, T.P. Singh, and H. Ulbricht, Models of Wave-function Collapse, Underlying Theories, and Experimental Tests, Rev. Mod. Phys. 85, 471 - 527 (2013);
  4. Bateman, J., S. Nimmrichter, K. Hornberger, and H. Ulbricht, Near-field interferometry of a free-falling nanoparticle from a point-like source, Nat. Com. 5, 4788 (2014); Wan, C., et al. Free Nano-Object Ramsey Interferometry for Large Quantum Superpositions, Phys. Rev. Lett. 117, 143003 (2016).
  5. Bahrami, M., M. Paternostro, A. Bassi, and H. Ulbricht, Non-interferometric Test of Collapse Models in Optomechanical Systems, Phys. Rev. Lett. 112, 210404 (2014); Bera, S., B. Motwani, T.P. Singh, and H. Ulbricht, A proposal for the experimental detection of CSL induced random walk, Sci. Rep. 5, 7664 (2015).
  6. Grossardt, A., J. Bateman, H. Ulbricht, and A. Bassi, Optomechanical test of the Schroedinger-Newton equation, Phys. Rev. D 93, 096003 (2016).


Saikat Ghosh

Feeback Control: taming atoms and nano-drums with electronic feedback

Over last few decades, spectacular sophistication has been achieved in experiments involving macroscopic systems that behave quantum mechanically. These include laser-cooled and trapped atoms, ions and condensates, artificially fabricated mesoscopic quantum circuits, micro and nano-mechanical as well as a myriad of hybrid systems with a mixed combination. Experimentally, a skeletal structure that guides almost all these experiments is provided by control theory, which explains how to observe fluctuations (mostly classical) and compensate for it in real time. In this short lecture, I will pick up examples to explain the basics of control theory, as applicable to experiments with quantum systems. In particular, I will talk about how feedback control is used in widely different cases, for experiments pursued in our laboratory, with cold atoms, cavities and graphene resonators. The tutorial problems will mostly consists of understanding few simple op-amp circuits, debugging and interpreting them in the language of feedback control. We will end with a short overview of how these ideas extend to quantum feedback control.


Urbasi Sinha

Experimental Quantum Measure: Connection with the Superposition principle and the Born Rule

These two lectures will deal with the experimental attempts at measuring the Quantum Measure. [1]. There have been several attempts at experimentally bounding the Quantum Measure using photons, atoms, NMR among others [2–6] . Recently, it has been measured to be a definite non-zero for the first time [7]. These lectures will discuss these experiments, the usual difficulties faced in such precision experiments and future experiments which could be attempted in this genre. We will also discuss the implications of such experiments in measuring the deviation from the Superposition principle in interference experiments [8, 9] as well as the Born Rule for probabilities.

  1. R. D. Sorkin, Quantum mechanics as quantum measure theory. Mod. Phys. Lett. A. 9, 3119 (1994).
  2. U.Sinha, C.Couteau, T.Jennewein, R.Laflamme, G.Weihs, Ruling out multi-order interference in quantum mechanics. Science 329, 418-421 (2010).
  3. S¨ollner, I. et al. Testing born’s rule in quantum mechanics for three mutually exclusive events. Found Phys. 42, 742-751 (2012).
  4. Park, D. K. Moussa, O. Laflamme, R. Three path interference using nuclear magnetic resonance: a test of the consistency of Born’s rule. New J. Phys. 14, 113025 (2012).
  5. T.Kauten, R.Keil, T.Kaufmann, B.Pressl, C.Brukner, G.Weihs, Obtaining tight bounds on higher-order interferences with a 5-path interferometer. arXiv :1508.03253v3
  6. Markus Arndt: Private communication
  7. G.Rengaraj, U.Prathwiraj, Surya N.Sahoo, R.Somashekhar and U.Sinha, Experimental measure of the correction term in the Superposition Principle, arXiv:1610.09143.
  8. R.Sawant, J.Samuel, A.Sinha, S.Sinha, U.Sinha, Non classical paths in quantum interference experiments. Phys.Rev.Lett.113, 120406 (2014).
  9. A.Sinha, Aravind H.V., U.Sinha, On the Superposition principle in interference experiments. Scientific Reports 5, 10304 (2015).


Gregor Weihs

Sources of nonclassical light

Applications of nonclassical states of light in quantum optics,foundational tests, metrology, and quantum communication requireappropriate, tailored sources. The typically desired states are singlephotons, entangled photon pairs, multiphoton states, or squeezed statesof light. Various techniques have been used to produce these states. Iwill speak about sources using nonlinear optics in dielectrics andsemiconductors as well as sources based on single semiconductor quantumemitters.




Third Week Discussion Meeting



Markus Arndt

A tale of two limits: Quantum interferometry exploring the limits of high mass and biological complexity

"Quantum mechanics and its relativistic brother, quantum field theory, have remained the uncontested winners of theoretical physics throughout the last century, with surprising accuracy and experimental confirmation in the microscopic world. The basic concepts of quantum physics seem however to challenge our philosophical notions that we grew up to like in our everyday world.

It is therefore legitimate to ask whether quantum mechanics is a universal theory or rather the limit of something more universal. How will quantum physics behave in a limit where the mass is sufficiently big to feel the warp of space-time? How will quantum physics affect the constituents of life? What fundamental or technological challenges do we face and what progress can we foresee in exploring these two interfaces to the macroscopic world? I will explore these two questions from an experimental and a conceptual viewpoint."



Tjerk Oosterkamp

A clock containing a massive object in a superposition of states; what makes Penrosian wavefunction collapse tick?

Penrose has been advocating the view that the collapse of the wave function is rooted in the incompatibility between general relativity and quantum mechanics. On the basis of conceptual analysis, he arrived at an estimate for the collapse time. To better understand his estimate, in this paper we present a thought experiment, which singles out the role of time-dilations in massive superpositions. First we investigate the behavior of a hypothetical clock containing a component which can be in a superposition of states. The clock contains a massive object, whose only purpose is to introduce a curvature of space time into the problem. We find that a state of this massive object with a smaller radius, but with the same mass, experiences a larger time dilation. Considering a coherent superposition of the large and small object, introduces an ambiguity in the definition of a common time for both states. We assert that this time ambiguity can be thought to affect the time evolution of a state in different ways and that the relative phase difference between these different interpretations can be calculated. We postulate that the wave function collapse will occur when this phase difference becomes of order unity. An absolute energy scale enters this equation and we recover Penrose's estimate for the collapse time by equating the absolute energy scale to the rest mass of the object.



Daniele Faccio

Optical simulations of problems in quantum cosmology

I will give a brief overview of ongoing research endeavours aimed at reproducing basic QFT predictions that are relevant to cosmology. Examples are photon production from expanding spacetimes (e.g. cosmological expansion), Penrose superradiance from a rotating black hole and recent experiments showing an optical analogue of the Newton-Schrodinger equation.



Urbasi Sinha

Quantum Superposition, Weak measurements and Higher dimensional quantum systems

This talk will give a general overview of experiments in different genres that are being performed in the Quantum Information and Computing lab at RRI, Bengaluru.

We will discuss an experiment which deals with measuring the deviation from the naive application of the Superposition Principle in interference experiments [1–3]. Our recently concluded experiment [4] reports the first successful measurement of the non-zero Sorkin parameter (which is commonly used in Quantum Measure Theory).

Next, we will discuss an ongoing experiment involving higher dimensional quantum systems. Maximally entangled qudits are subjects of interest in many quantum information protocols and fundamental tests of quantum mechanics. Transverse spatial correlation obtained from spontaneous parametric down converted photons is one of the simplest methods that could be readily implemented using slit based interferometric systems. Recently, it was shown that, the angular spectrum of the incident pump can be transferred to the signal-idler bi-photon pair in SPDC process. Tapping on to this, we attempt to harness qutrit- qutrit correlations in spatial degrees of freedom by making the pump have a profile of a triple slit [5]. This experiment could pave the way for using the spatial degree of freedom in experiments based on long distance Quantum Communication.

Finally, we will discuss an ongoing experiment which aims to infer the expectation value of Non Hermitian operators using weak measurements [6]. Weak values of Pauli operators acting on polarization state vectors are traditionally measured from the shift of the position pointer states which gets coupled to polarization degree of freedom due to the birefringent crystal, in a pre and post selected ensemble. Here, we present an alternative way to infer weak values that takes advantage of an interferometric setup.

  1. R.Sawant, J.Samuel, A.Sinha, S.Sinha, U.Sinha, Non classical paths in quantum interference experiments. Phys.Rev.Lett.113, 120406 (2014).
  2. U.Sinha, C.Couteau, T.Jennewein, R.Laflamme, G.Weihs, Ruling out multi-order interference in quantum mechanics. Science 329, 418-421 (2010).
  3. A.Sinha, Aravind H.V., U.Sinha, On the Superposition principle in interference experiments. Scientific Reports 5, 10304 (2015).
  4. G.Rengaraj, U.Prathwiraj, Surya N.Sahoo, R.Somashekhar and U.Sinha, Experimental measure of the correction term in the Superposition Principle, arXiv:1610.09143.
  5. Surya N. Sahoo, D.Ghosh, E.Kaur, T.Jennewein, P.Kolenderski and U.Sinha, Measuring Spatial Correlations in qutrits, to be submitted,(2016).
  6. A.Pati, U.Singh and U.Sinha, Measuring Non-Hermitian operators via weak values, Physical Review A 92 052120, (2015)



Nikolai Kiesel

Levitated Cavity Optomechanics

Cavity Optomechanics with clamped devices has been tremendously successful in the control of massive mechanical oscillators at the quantum level. However, isolating clamped microfabricated devices from their environment is an extremely hard task. Levitating mesoscopic objects has been suggested as a route to enable orders of magnitude improvement in thermal isolation compared to clamped devices. Experimentally, optically levitated resonators are already en par with the best clamped mechanical resonators in that respect. Levitated cavity optomechanics combines ultimate isolation from the environment with the full toolbox of cavity optomechanics available to control the quantum state of motion. The approach thus provides a route to combine the quantum state preparation techniques offered by quantum optics with the option for free-fall experiments that enable matter-wave interferometry. I will present the state of the art in the field and results from our ongoing experiments. The latter include studies of nanoparticles in hollow-core photonic crystal fibers and cavity-optomechanical control of nanoparticles. Finally, I will discuss some of the ideas how to exploit levitated cavity optomechanics in the context of stochastic thermodynamics and for fundamental tests of quantum physics



Tom van der Reep

Smoothly breaking unitarity

One of the remaining issues in quantum mechanics is the apparent discrepancy between this theory and our classical world. To probe the boundary between the two realms, we propose to build a microwave interferometer that contains a travelling wave parametric amplifier (TWPA) in each of its arms. Feeding the interferometer with a single photon source and studying its output radiation while varying the amplification of the TWPAs might provide more insight on the quantum-classical transition as the unitary amplifiers smoothly turn into unitarity-breaking detectors with increasing gain.

In this talk we will share our results on the expected output of the interferometer and, correspondingly, how to observe a collapse of the wavefunction within the experiment. 



Joseph Cotter

In search of multi-path interference using large m

I will present results from recent experiments where we search for multi-path interference using a far-field molecule interferometer by comparing the diffraction patterns arising from single, double and triple slits. Using a beam of phthalocyanine molecules, with a mass of 514amu, we have directly bounded the Sorkin-parameter using massive particles.



Jamie Vovrosh

Controlling the Motion of a Nanoparticle Trapped i

Optomechanics in the macroscopic regime has great potential as a platform for testing fundamental principles of quantum physics, in addition to creating a new range of ultra-sensitive sensors. In this work we demonstrate a simple and robust geometry for optical trapping in vacuum of a single nanoparticle based on a parabolic mirror and the optical gradient force. In this trap we demonstrate rapid parametric feedback cooling of all three motional degrees of freedom from room temperature to a few mK. A single laser at 1550nm, and a single photodiode, are used for trapping, position detection, and cooling for all three dimensions. Particles with diameters from 26nm to 160nm are trapped without feedback to 10^?5mbar and with feedback engaged the pressure is reduced to 10^?6mbar. Modifications to the harmonic motion in the presence of feedback is studied, and an experimental mechanical quality factor >4├Ý10^7 is demonstrated.



Thomas Durt

Non-Linear Quantum Mechanics and de Broglie's Double Solution Program

Recently, non-linear modifications of Schroedinger equation, like e.g. the Schroedinger-Newton equation have been studied in relation with the measurement problem.

In particular, the presence of a non-linearity would explain why the wave packet associated to a quantum particle does not spread with time.

In other words, particles behave as solitons, which is strongly reminiscent of de Broglie's Double Solution Program, elaborated by Louis de Broglie in the twenties, of which the de Broglie-Bohm pilot wave dynamics is a simplified version. It is also reminiscent of Poincare's pressure, invoked by Poincare in 1905 in order to solve the wave-particle duality in the context of classical field theory.

We shall describe recent attempts to derive the de Broglie-Bohm pilot wave dynamics from non-linear wave dynamics, and to apply them to quantum corpuscles at one side, and to so-called bouncing oil droplets at the other side.



Nalini Gurav

Zeno and Anti-Zeno effects in Quantum Mechanics

"Schrödinger equation gives us the time evolution operator (unitary) which tells us the dynamics of any quantum mechanical system. We can categorize this evolution with time in three different regimes. For the intermediate time interval, quantum system decays exponentially, whereas for very short or very long time intervals, decay is not exponential. Among them a short time regime is the most interesting because, if the time interval (of the observation) is too short, it never decays! One can completely halt the system from evolving.This is called as Quantum Zeno effect. The ""collapse of wave function"" playing very peculiar role here. Also, it has recently been pointed out that by exploiting the short-time features of the quantal evolution, one can also accelerate the decay. This phenomenon is known as ""Inverse or Anti Zeno effect (IZE).""

However, these effects cannot work macroscopically, because continuous or infinite measurements are physically unattainable. But we can still use it under finite number of measurements."



Gregor Weihs

Multipath Interference Experiments Probe the Foundations of Quantum Physics

Born's rule, the superposition principly, higher-order interference, and hypercomplex representations of quantum mechanics have one thing in common: They can be tested using multipath interference experiments. Going beyond the traditional double slit or interferometer we use sensitive free-space and waveguide multipath interferometers to investigate the foundations of quantum mechanics and generalized probabilistic theories.



Ashutosh Singh

Manipulation of entanglement sudden death in an all-optical experimental set-up

The unavoidable and irreversible interaction between an entangled quantum system and its environment causes decoherence of the individual qubits as well as degradation of the entanglement between them. En-tanglement sudden death (ESD) is the phenomenon wherein disentanglement happens in finite time even when individual qubits decohere only asymptotically in time due to noise. Prolonging the entanglement is essential for the practical realization of entanglement-based quantum information and computation proto-cols. For this purpose, the local NOT operation in the computational basis on one or both qubits has beenproposed. In this talk, I will briefly review the ESD followed by an all-optical implementation of the NOT operations such that it can hasten, delay, or completely avert ESD, all depending on when it is applied during the process of decoherence for the polarization entangled qubits as the system. The simulation results of such manipulations [1] of ESD will be presented with the experimental progress on the same.


1. Ashutosh Singh, Siva Pradyumna, A.R.P. Rau and Urbasi Sinha, “Manipulation of entanglement sudden death in an all-optical experimental set-up”, Submitted, 2016."



Sourav Dutta

Coupled atom-cavity system: a quantum sensor

A technique for non-destructive detection of trapped ions using a strongly coupled atom-cavity system will be discussed. Generalization of the technique to detect generic two-particle interactions will be suggested.



Som Kanjilal

Probing Aspects of Quantum Non-Locality using Weak Interaction and Post-Selection

"A novel application of weak measurement involving pointer state post-selection is proposed in order to study non-locality and its relationship with entanglement. Our scheme starts with Werner-like states( non-maximally entangled state mixed with white noise )which satisfy Bell-CHSH inequality and introduce, in one of the parties, weak interaction involving a coupling between the particle momentum and position. The position acts like a pointer coordinate. The pointer position is then post-selected, which would mean selecting or filtering the particles corresponding to a particular value of the weakly interacting particleΓÇÖs position. The resulting two-party state is in general a mixed entangled state, and its entanglement is more or less than the unfiltered state, depending on what position of the pointer is post-selected.

What is particularly interesting is that in the same spirit, we can post-select states that violate the Bell-CHSH inequalities, even though the unfiltered state may not. Hence, this constitutes a demonstration of what has been called ΓÇýhidden non-localityΓÇÖ. Furthermore, we probe, using the filtered states, the relationship between entanglement and non-locality. This is done by comparing the concurrence versus the Bell-CHSH operator as functions of the filtered states corresponding to different values of the post-selected pointer coordinates. It is found that among this set of filtered states, the one that corresponds to maximum concurrence (hence, maximum entanglement) is not the one that displays maximum violation of the Bell-CHSH inequalities ( hence, maximum non-locality) . This demonstrates that maximum entanglement does not necessarily imply maximum non-locality."



Fatemeh Ahmadi

On a New Formulation of Microphenomena and Relativ

"We develop a new formulation of microphenomena based on the principles of reality and causality. This theory provides us with a new formulation of quantum phenomena based on a unified concept of information, matter and energy. We suppose that in a definite microphysicsl context, each particle is enfolded by a probability field whose existence is contingent on the existence of the particle, but it can locally affect the physical status of the particle in a context-dependent manner. The dynamics of the whole particle-field system (PF system) obeys deterministic equations in a manner such that when the particle is subjected to a conservative force, the form of which is determined by the dynamics of the particle.

Here, by using Newtonian-like equation for a one-particle system, we show how quantum dynamics will be reconciled with classical rules and find the trajectory of a PF system in terms of the particleΓÇÖs location and time. At last we will talk about the relativistic generalization of the theory. We are going to formulate the equation of motion for PF system in a form which is Lorentz-invariant. This means the description should not allow one to differentiate between frames of reference which are moving relative to each other with a constant uniform velocity."



Miles Blencowe

An Investigation of the Influence of Gravity on Macroscopic Mechanical Quantum Superpositions

We describe our work in progress to address theoretically the influence of gravity on spatial and energy quantum superposition states of macroscopic mass systems. One relevant problem concerns whether it is possible to consistently describe a ‘quantum Cavendish’ type thought experiment where a macroscopic mass in a spatial superposition state is a source for a gravitational field. Another problem concerns whether gravity as an environment causes unavoidable decoherence of such superposition states. We argue that a quantitative analysis can be brought to bear on these two related problems by applying perturbative quantum general relativity as an effective field theory, and by also invoking analogue mechanical, quantum non-inertial reference frame systems as a guide.



Dipankar Home

Quantum mechanical violation of macrorealism for large spin and for large mass using the harmonic oscillator coherent state

This talk seeks to provide an overview of the core ideas and key results of two different types of recent studies concerning the quantum mechanical (QM) violation of macrorealism (MR):

(a) For multilevel spin systems, using two different necessary conditions of MR, namely, the Leggett-Garg inequality (LGI) and Wigner’s form of the Leggett – Garg inequality (WLGI), the extent to which the QM violation of MR can be demonstrated in the asymptotic limit of spin, even for arbitrary coarse-grained or unsharp (noisy) measurements, is investigated. It is shown that classicality in the sense of satisfying MR does not emerge in the asymptotic limit of spin, whatever be the unsharpness or coarse-grainedness of measurements.

(b) The QM violation of LGI or WLGI in the context of a linear harmonic oscillator is invoked to reveal non-classicality of the state which is considered the most “classical-like” of all quantum states, namely the Schrodinger coherent state. In the macrolimit, the extent to which such nonclassicality persists for large values of mass and classical amplitudes of oscillation is quantitatively investigated, and the relevant results will be presented, hinting a possible experimental setup using nano-objects.



Daniel Bedingham

Collapse models and spacetime symmetries

A relativistic and time-symmetric picture of dynamical collapse of the wave function is presented. The part of the model which exhibits these symmetries is the set of collapse outcomes. These play the role of matter distributed in space and time. It is argued that the dynamically collapsing quantum state, which is both foliation dependent and follows a time asymmetric dynamics, is not fundamental: it represents a state of information about the past matter distribution for the purpose of estimating the future matter distribution. It is also argued from the point of view of collapse models that both special and general relativistic considerations point towards a discrete spacetime structure and that gravity may not need to be quantised to give a theory that is consistent with quantum matter.



Apoorva Patel

Understanding the Born rule in weak measurements

"Projective measurement is used as a fundamental axiom in quantum mechanics, even though it is discontinuous and cannot predict which measured operator eigenstate will be observed in which experimental run. The probabilistic Born rule gives it an ensemble interpretation, predicting proportions of various outcomes over many experimental runs. Understanding gradual weak measurements requires replacing this scenario with a dynamical evolution equation for the collapse of the quantum state in individual experimental runs. We revisit the framework to model quantum measurement as a continuous nonlinear stochastic process. It combines attraction towards the measured operator eigenstates with white noise, and for a specific ratio of the two reproduces the Born rule. We emphasise some striking features this result, which would be important ingredients for understanding the origin of the Born rule in quantum measurements."



Suman Chand

Quantum Otto heat engine and refrigerator

We demonstrate how a quantum Otto engine (QOE) can be implemented how to implement a quantum Otto engine in trapped ion set-up. The existing proposals on implementing quantum heat engine consider `switching off' the interaction between the working fluid and the bath during the cycle. In a quantum system, it is quite challenging. In our work we show that one can implement the quantum Otto engine in a realistic trapped ion set up, without switching off the bath. The electronic state of the ion is chosen as the working fluid while its vibrational degree of freedom works as a cold bath. The adiabatic stages of the Otto cycle involve change in the local magnetic field, while a projective measurement of the electronic state of the ion leads to heat release to the cold bath. Further we are considering two trapped ions in the system. This gives an entanglement effect on the whole study. The the effect of entanglement in work-efficiency of the engine give many interesting results.



Shreya Banerjee

Quantum discord-tool for comparing collapse models

"The quantum to classical transition maybe caused by decoherence or by dynamical collapse of the wave-function. We propose quantum discord as a tool, 1) for comparing and contrasting the role of a collapse model (Continuous Spontaneous Localization) and various sources of decoherence (environmental and fundamental), 2) for detecting collapse model and fundamental decoherence for an experimentally demonstrated macroscopic entanglement (where the effect of environmental decoherence is negligible). We discuss the experimental times which will lead to the detection of either Continuous Spontaneous Localization or fundamental decoherence. We further put bounds on the collapse parameters from this experiment for quantum discord and compare them with those obtained by a similar study of quantum entanglement. [ arXiv:1604.05834]"



Ankur Mandal

Some importance of "time delay" in quantum theory

In general scattering processes involves a time delay to take place. Current state-of-the-art experimental techniques are capable of measuring the time delay in Photoionization, which can be described by the time reversed scattering process. This tiny time delay (of the order of attosecond) is very important, since the quantum description of the interaction of light and matter is to be understood clearly to derive the experimental results with better accuracy. In this presentation, a review of the recent works in this field will be given.



Adrian Kent

Quantum Reality via Late Time Photodetection

I investigate postulates for realist versions of relativistic quantum theory and quantum field theory in Minkowski space and other background space-times. According to these postulates, quantum theory is supplemented by local variables that depend on possible outcomes of hypothetical measurements on the late time electromagnetic field in spacelike separated regions. We illustrate the implications in simple examples using photon wave mechanics, and discuss possible extensions to quantum field theory.



Joseph Samuel

Exceptional Points and Quantum Information

"My talk will address the behaviour of quantum systems near an exceptional point. These are points in the space of Hamiltonians which show remarkable geometric and topological properties. Some of these properties have already been experimental realised in analog classical wave systems. My talk will concern the use of the geometry and topolgy near exceptional points of quantum systems to achieve a degree of control in manipulating quantum information."


Rafael D Sorkin

The quantum measure (and how to measure it)

When utilized appropriately, the path-integral offers an alternative to the ordinary quantum formalism of state-vectors, self-adjoint operators, and external observers - an alternative that seems closer to the underlying reality and more in tune with quantum gravity. The basic dynamical relationships are then expressed, not by a propagator, but by the quantum measure, a set-function μ that assigns to every (suitably regular) set E of histories its generalized measure μ(E). (The idea is that μ is to quantum mechanics what the Wiener-measure is to Brownian motion.) Except in the special case where E is an instrument-event, μ(E) cannot be interpreted as a probability, as it is neither additive nor bounded above by unity. Nor, in general, can it be interpreted as the expectation value of a projection operator (or POVM). Nevertheless, I will describe how one can ascertain μ(E) experimentally for any desired E, by means of an arrangement which, in a well-defined sense, filters out the histories that do not belong to E.


  1. Alvaro M. Frauca and Rafael D. Sorkin, ``How to Measure the Quantum Measure'', to appear on arXiv 2016 Oct 10, and in IJTP eventually.
  2. Sukanya Sinha and Rafael D. Sorkin, ``A Sum-over-histories Account of an EPR(B) Experiment'',  Found. of Phys. Lett. 4, 303-335 (1991).
  3. Rafael D. Sorkin, ``Quantum Mechanics as Quantum Measure Theory'', Mod. Phys. Lett. A 9, 3119-3127 (1994).  ArXiv: gr-qc/9401003.
  4. Rafael D. Sorkin, ``Quantum dynamics without the wave function'' J. Phys. A: Math. Theor. 40, 3207-3221 (2007). ArXiv: quant-ph/0610204.



Sumati Surya

Covariant Observables in Causal Set Quantum Gravity

The standard formulation and interpretation of quantum theory which depends crucially on the existence of external observers is inadequate to describe closed systems and in particular quantum cosmology. How then are we to understand quantum amplitudes and probabilities associated with the very early universe? The quantum measure formulation is an attempt to address this question, drawing on the close analogy between quantum theory and classical stochastic processes. At its most basic, it requires that events of zero quantum measure are ``precluded'' or do not occur. In this talk I will examine how these ideas can be used to find precluded covariant observables in a simple model of causal set quantum cosmology.



Lajos Diosi

Gravity-related alterations of non-relativistic quantum theory

Possible gravity-related limitations of standard quantum mechanics and a fundational role of gravity in quantum-classical transition have been under consideration for about three decades. Various concepts have been developped, leading to variants of non-linear and stochastic modifications of the standard Schrodinger equation by terms proportional to Newtons's G. Their status will be considered, also in the light of some particular tests, and their perspectives will be outlined."



Kinjalk Lochan

Quantum Correlations in curved spacetime

"Quantum correlations play very decisive role in characterizing a system classical or quantum. The role of correlations has been studied in various systems in standard laboratory settings. We will discuss applications of such quantum correlations in the curved spacetime, particularly in black hole settings, which gives rise to some (classically) counter intuitive phenomenon, such as Unruh radiation for inertial observers without any (classical) source.

Reference : arXiv:1603.01964"



Souradeep Sasmal

A proposed steering criterion using Generalised Uncertainty Relation​

"Reid steering criterion (Phys. Rev. A 40, 913 (1989)) based on Heisenberg uncertainty relation fails to detect steerability for the states having higher than second order correlation. Here, we have derived a new steering criterion using generalized uncertainty relation. Our steering criterion overcomes the limitation of Reid steering criterion and our derived steering inequality is tighter than Reid steering criterion. The proposed steering criterion is able to detect steerability of LG beam, NOPA state and photon annihilated NOPA states. Furthermore, the steerability of the two mode Werner state in continuous variable systems are investigated for all range of the mixedness parameter."



Debarshi Das

Probing quantum nonlocality of bipartite qutrits by generalising Wigner's argument

"Bell-type local realist inequalities are developed for demonstrating quantum nonlocality of bipartite entangled qutrit states by generalizing Wigner's argument that was originally formulated for the bipartite qubit singlet state. This treatment is based upon assuming existence of the overall joint probability distributions for the measurement outcomes pertaining to the relevant trichotomic observables, satisfying the locality condition, and yielding the measurable marginal probabilities. The salient features of the paper are as follows:

a) We first show that such generalised Wigner inequalities (GWI) are violated by quantum mechanics (QM) for both the bipartite qutrit isotropic and singlet states, thereby revealing their nonlocality.

b) The efficacy of GWI is then probed by comparing its QM violation with that obtained for the other two types of local realist inequalities that have been used for probing nonlocality of entangled bipartite qutrits. This is done in two differentways, (i) by employing unsharp measurements, and (ii) by incorporating white noise in the isotropic and singlet qutrit states.

c) It is shown that in both these cases, contingent upon using z-component spin-1 observables, GWI outperforms the other two types of local realist inequalities in terms of the respective QM violations, by being (i) more robust against the unsharpness of measurement, and (ii) more tolerant to the white noise incorporated in the states considered."



Shiladitya Mal

Sharing of Nonlocality of a single member of an En

We address the recently posed question as to whether the nonlocality of a single member of an entangled pair of spin 1/2 particles can be shared among multiple observers on the other wing who act sequentially and independently of each other [1]. We first show that the optimality condition for the trade-off between information gain and disturbance in the context of weak or non-ideal measurements emerges naturally when one employs a one-parameter class of positive operator valued measures (POVMs). Using this formalism we then prove analytically that it is impossible to obtain violation of the Clauser-Horne-Shimony-Holt (CHSH) inequality by more than two Bobs in one of the two wings using unbiased input settings with an Alice in the other wing.



Anirudh Reddy

Entropy and Geometry of Quantum States

We derive a metric on the space of density matrices using the relative entropy as the starting point. This metric enables us to distinguish nearby quantum states. We derive an explicit form in the context of a qubit. We notice that there is an advantage in using the quantum relative entropy over its classical counterpart in the context of measurements on quantum states.



T. Padmanabhan

GR And QG: The Next Hundred Years

It appears that the field equations of GR - which describe the dynamical evolution of the spacetime - have the same conceptual status as the equations of fluid mechanics or elasticity, suggesting a paradigm shift in our ubderstanding of gravity. In particular, it may be incorrect to think of Cosmology as a part of GR described by a specific solution to gravitational field equations. I will describe several aspects of these results and how it could lead to a solution of the cosmological constant problem.



Daniel Sudarsky

Dynamical Reduction in General Relativistic Contexts

Spontaneous collapse theories provide one of the most promising approaches to dealing with the measurement problem in Quantum Theory (QT) . Recent advances have provided versions of the theory that are compatible with special relativity. However for a theory to be truly viable, it should also be made compatible with General Relativity (GR). I will describe some of the issues that arise when attempting to follow that path, and discuss some ideas about how these might be addressed. I will then argue that , in fact, it is in various situations where GR and QT come together, that collapse theories exhibit their potential in the most spectacular manner, offering plausible resolutions to issues that have remained unresolved for a long time.



Ward Struyve

Must space-time be singular?

According to Einstein's theory of general relativity space-time singularities such as a big bang typically occur. It has been believed that a quantum theory for gravity might avoid such singularities. The answer will of course depend on which approach to quantum gravity one considers, such as e.g. loop quantum gravity or the Wheeler-DeWitt approach. It will also depend on which version of quantum theory one adopts. I will consider the Bohmian version of quantum mechanics, for which the question in the title is well-posed. For mini-superspace models I will show that there is no singularity for loop quantum gravity, while there may be a singularity in the Wheeler-DeWitt approach



Parampreet Singh

Consistent quantum histories and the probability for singularity resolution

"In this talk, we will apply the methods of generalized quantum mechanics to answer the questions about the fate of singularities in different quantum cosmological models. In particular, we will discuss the way consistent histories formalism can be applied in a rigorous way to extract consistent probabilities for singularities or bounce to occur. We will show that for Wheeler-DeWitt quantum cosmology, an arbitrary superposition of physical states result in probability of singularity to be unity. In loop quantum cosmology, the probability for singularity to occur turns out to be zero. We will also discuss a covariant generalization of these results."



Sumanta Chakraborty

Information Retrieval from Black Holes

"It is generally believed that, when matter collapses to form a black hole, the complete information about the initial state of the matter cannot be retrieved by future asymptotic observers, through local measurements. This is contrary to the expectation from a unitary evolution in quantum theory and leads to (a version of) the black hole information paradox. Classically nothing else, apart from mass, charge and angular momentum is expected to be revealed to such asymptotic observers after the formation of a black hole. Semi-classically, black holes evaporate after their formation through the Hawking radiation. The dominant part of the radiation is expected to be thermal and hence one cannot know anything about the initial data from the resultant radiation. However, there can be sources of distortions which make the radiation non-thermal. Although the distortions are not strong enough to make the evolution unitary, these distortions carry some part of information regarding the in-state. In this work, we show how one can decipher the information about the in-state of the field from these distortions. We show that the distortions of a particular kind --- which we call {\it non-vacuum distortions} --- can be used to \emph{fully} reconstruct the initial data. The asymptotic observer can do this operationally by measuring certain well-defined observables of the quantum field at late times. We demonstrate that a general class of in-states encode all their information content in the correlation of late time out-going modes. Further, using a $1+1$ dimensional CGHS model to accommodate back-reaction self-consistently, we show that observers can also infer and track the information content about the initial data, during the course of evaporation, unambiguously. Implications of such information extraction are discussed."



Antoine Tilloy

An alternative to the Schrodinger Newton approach

The Schrodinger-Newton (SN) equation is often used to model the gravitational interaction between quantum particles. It is well known that its non-linearity introduces fundamental problems such as faster than light signalling and Born rule breakdown. Starting from continuous dynamical reduction models like CSL, we show that it is possible to couple quantum matter and a classical gravitational field in a different way, formally inspired from quantum feedback. The resulting theory is fully explicit, linear at the master equation level, and suffers from no obvious inconsistency. Predictions include the usual Newtonian pair potential, additional gravitational decoherence and, importantly, no one particle self-interaction in contrast with what the SN approach predicts. We will argue that due to its increased consistency and comparable simplicity, our theory could be chosen as a reasonable alternative to the SN approach.



Sayantani Bera

A New Stochastic Schrodinger Newton equationn

We propose a modified stochastic Schrodinger-Newton equation which takes into account the effect of extrinsic spacetime fluctuations. We use this equation to demonstrate gravitationally induced decoherence of two gaussian wave-packets, and obtain a decoherence criterion similar to those obtained in the earlier literature in the context of effects of gravity on the Schrodinger equation.



Suratna Das

Cosmic inflation and the measurement problem

Cosmic inflationary paradigm beautifully explains the origin of the large structures, like galaxies and cluster of galaxies, we observe today in our universe. But the fluctuations during inflation, which seed these large scale structures, were quantum by origin, whereas the structures which were developed due to gravitational instability seeded by these quantum perturbations are all classical. Thus the persisting question of how and when these primordial quantum perturbations become classical still plagues the basic concept behind inflationary paradigm. In this talk we will seek for a plausible answer to this lingering issue by implementing collapse models of quantum mechanics in early universe.



Jaffino Stargen

Quantum-⁠to-⁠classical transition and imprints of wavefunction collapse in bouncing universes

Authors: D. J. Stargen, V. Sreenath and L. Sriramkumar

Abstract: The perturbations in the early universe are supposed to have originated due to quantum fluctuations, which turn classical as the universe evolves. The quantum-to-classical transition of the primordial perturbations have been studied to a good extent in the context of inflationary cosmology. A reasonably popular alternative to the inflationary paradigm are the bouncing scenarios, wherein the universe undergoes a phase of contraction until the scale factor reaches a minimum value, before it begins to expand. Such bouncing scenarios can provide well motivated initial conditions at early times during the contracting phase, as inflation does. In this talk, divided into two parts, we consider two issues related to the quantum-to-classical transition of tensor perturbations in bouncing universes. In the first part, we describe the evolution of the quantum state (specifically, the extent of the squeezing) of the tensor modes with the aid of the Wigner function. In the second part, we consider the evolution of the tensor perturbations from the perspective of the quantum measurement problem. In particular, we discuss the effects of wave function collapse, using a phenomenological model known as continuous spontaneous localization, on the tensor power spectra.



Madhavan Varadarajan

A note on entanglement entropy, coherent states and gravity

"We review two recent attempts to explain aspects of gravitational physics through changes in entanglement entropy of quantum fields. The first, due to Bianchi, builds on Sorkin's seminal ideas in the 80's and attempts to connect the change in black hole entropy with that of entanglement entropy without recourse to an explicit UV cutoff. The second, due to Jacobson, seeks to derive the equations of gravitational dynamics itself (which relate matter stress energy to spacetime curvature), through a certain maximal entanglement entropy hypothesis. Common to both attempts is the emergence, purely from quantum entanglement, of (changes in) stress energy. On the other hand, we note that the entanglement entropy of a free quantum field in a coherent state is {\em independent} of its stress energy content. We explore the tension between this fact and Bianchi's and Jacobson's ideas."



André Großardt

Quantum mechanics for non-inertial observers

I discuss the difficulties arising for the definition of centre-of-mass coordinates in a relativistic system. I will further consider how the centre-of-mass motion should be described from the point of view of accelerated observers. I will discuss consequences for alleged decoherence effects of the centre-of-mass of a complex quantum system in the presence of post-Newtonian gravitational forces.



Jerome Martin

Cosmic Inflation and Quantum Mechanics

According to cosmic inflation, the inhomogeneities in our universe are of quantum mechanical origin. This scenario was recently spectacularly confirmed by the data obtained by the European Space Agency (ESA) Planck satellite. In fact, cosmic inflation represents the unique situation in Physics where quantum mechanics and general relativity are needed to establish the predictions of the theory and where, at the same time, we have high accuracy data at our disposal to test the resulting framework. So inflation is not only a phenomenologically very appealing theory but it is also an ideal playground to discuss deep questions in a cosmological context. In this talk, I review and discuss those quantum-mechanical aspects of inflation. In particular, I explain why inflationary quantum perturbations represent a system which is very similar to systems found in quantum optics. But I also point out the limitation of this approach and investigate whether the large squeezing of the perturbations can allow us to observe a genuine observational signature in the sky of the quantum origin of the cosmological fluctuations.



Aephraim Steinberg

How to count one photon and get a(n average) result of 1000… (in binary)

I will present our recent experimental work using electromagnetically induced transparency in laser-cooled atoms to measure the nonlinear phase shift created by a single post-selected photon, and its enhancement through "weak-value amplification." Put simply, due to the striking effects of "post-selective" quantum measurements, a (very uncertain) measurement of photon number can yield an average value much larger than one, even when it is carried out on a single photon. I will say a few words about possible practical applications of this "weak value amplification" scheme, and their limitations.

Time permitting, I will also describe other future and past work related to quantum metrology and ultracold atoms – in particular, we have implemented a quantum-information-inspired protocol to beat “Rayleigh’s curse” for resolving closely-separated spots in classical imaging; and we have preliminary evidence of a narrow Fabry-Perot resonance for atoms.



T. S. Mahesh

Exploring Quantum Physics using Spin Ensembles

Nuclear spin ensembles controlled via nuclear magnetic resonance (NMR) techniques have long been used to study various aspects of quantum physics. The nuclear spins with weak magnetic moments are reclusive enough to retain quantum coherences for long durations – seconds to minutes – sufficient for implementing intricate unitary operators. Highly sophisticated modern spectrometers also allow precise control over spin dynamics via digitally modulated radio waves. Accordingly, NMR has been regarded as a convenient testbed for emulating quantum phenomena. After a brief introduction, I will describe some of our recent experiments, particularly – (i) simulating ‘quantum pigeon hole effect’ and (ii) discriminating between von Neuman and Lüders measuring devices.



Suvrat Raju

The Information Paradox and State-Dependence

Over the past few years, our understanding of the information paradox has improved greatly. In flat space, it appears to be now clear that the paradox can be satisfactorily resolved through black-hole complementarity. This is the idea that local operators in the interior of the black hole can be represented as very complicated polynomials of local operators in the exterior, and it can be realized explicitly in some simple examples. However, I will describe how a consideration of the information paradox in anti-de Sitter space leads to some new questions, including whether local operators in quantum gravity may be "state dependent".



Herbert Spohn

Landau-lifshitz Equations of Radiative Damping

In a $\bar{h} = 0$ world radiative friction is very small but the effective equations for the motion of charges are still unsettled. Based on a model for a charge coupled to the Maxwell field I will explain why the equations written down around 1950 by Landau and Lifshitz are the appropriate effective equations.