Monday, 25 September 2023

Quantum mechanics is characterized by some NO-Go principles like uncertainty principle, no-cloning of unknown quantum state, indistinguishability of non-orthogonal states, Impossibility of definite quantum state for subsystem for definite entangled state of the composite system, impossibility of local realistic description of QM etc. Quantum information threory is based on some information processing tasks by exploiting these No-Go theorems in a creative way , which are otherwise impossible in classical world. In these lecture series (three talks), after some discussion on fromalism of QM, basic information processing tasks like dense coding, teleportation, quantum key generation will be introdued along with manipulation of entanglement which is the most important resource in quantum information theory. Basic ideas of quantum nonlocality and quantum computation will also be discussed.

We will discuss the phenomenology of integer and fractional quantum Hall states, paying particular attention to edge modes in abelian quantum Hall states. These modes are one platform for quantum information processing.

The fractional quantum Hall effect (FQHE) forms a paradigm in our understanding of strongly correlated systems. A majority of the FQHE phenomena in the lowest Landau level (LLL) are understood in a unified manner in terms of weakly-interacting composite fermions, which are bound states of electrons and vortices. The most prominent states in the LLL are understood as integer quantum Hall states of composite fermions and the compressible state at 1/2 as a Fermi liquid of composite fermions. For the FQHE in the second LL, such a unified description has been lacking: experimentally observed states are described by different physical mechanisms. In this talk, I will demonstrate that a unified understanding of states in the second LL can be obtained using the ``parton" theory which generalizes the idea of composite fermion. I will elucidate our recent work on the parton construction of wave functions to describe all of the FQH states observed in the second LL. Our work suggests that the parton theory provides a unified description of the quantum Hall effects.

Bulk-boundary correspondence licenses us to probe the bulk topological order by studying the transport properties of the edge modes. However, edge modes in a fractional quantum Hall (FQH) state can undergo edge reconstruction and, on top of that, can be in the coherent regime or exhibit varying degrees of charge and thermal equilibrations, giving rise to a zoo of intriguing models. Distinguishing the different models and equilibration regimes is an outstanding problem, which can not be resolved by finding only conductance plateaus in a quantum point contact (QPC). In this work we show that electrical shot noise at a QPC conductance plateau can serve as such diagnostics. As a prototypical example we consider the ν = 2/3 FQH state, and show that different inequalities between the auto- and cross-correlation electrical shot noise hold for different edge models. In particular, our results offer several possible scenarios for the QPC conductance plateaus e^2/3h (observed previously), e^2/2h (recently observed), and 5e^2/9h (our prediction), as well as how to distinguish among them via shot noise.

Tuesday, 26 September 2023

Quantum mechanics is characterized by some NO-Go principles like uncertainty principle, no-cloning of unknown quantum state, indistinguishability of non-orthogonal states, Impossibility of definite quantum state for subsystem for definite entangled state of the composite system, impossibility of local realistic description of QM etc. Quantum information threory is based on some information processing tasks by exploiting these No-Go theorems in a creative way , which are otherwise impossible in classical world. In these lecture series (three talks), after some discussion on fromalism of QM, basic information processing tasks like dense coding, teleportation, quantum key generation will be introdued along with manipulation of entanglement which is the most important resource in quantum information theory. Basic ideas of quantum nonlocality and quantum computation will also be discussed.

We will discuss the phenomenology of integer and fractional quantum Hall states, paying particular attention to edge modes in abelian quantum Hall states. These modes are one platform for quantum information processing.

Two-dimensional systems can host exotic quasiparticles, called anyons, which obey intermediate quantum statistics characterized by an exchange phase φ varying between 0 and π. As a consequence, contrary to fermions and bosons, anyons keep a robust memory of braiding operations, which consist in moving one anyon around another one. In the fractional quantum Hall regime, obtained by applying a strong magnetic field perpendicular to a two-dimensional electron gas, elementary excitations carry a fractional charge and have been predicted to obey fractional statistics with an exchange phase φ=π/m (where m is an odd integer). I will present how fractional statistics of anyons can be demonstrated in this system by implementing and studying anyon collisions at a beam-splitter. In the low magnetic field regime, where the elementary excitations are electrons obeying fermionic statistics, fermion antibunching shows up as a suppression of the current cross-correlations at the output of the beam-splitter, reflecting the fact that two electrons systematically exit in two different arms of the beam-splitter. In the case of anyons in the fractional quantum Hall regime, specific anyon bunching mechanisms occur, which are directly sensititve to the anyon braiding phase 2φ. They result in the observation of strong negative cross-correlations of the electrical currents at the output of the beam-splitter that can be used to extract the braiding properties of anyons. The presentation will review experimental investigations of the fractional statistics of anyons using the anyon collider geometry.

The state of a quantum system may be steered towards a predesignated target state, employing a sequence of weak blind measurements (where the detector’s readouts are traced out). In this seminar, I will present the steering of a single-qubit system using the interplay of a system Hamiltonian and weak measurements and show that any pure or mixed state can be targeted. I will show that the optimization of such a steering protocol is underlain by the presence of Liouvillian exceptional points. More specifically, for high-purity target states, optimal steering implies purely relaxational dynamics marked by a second-order exceptional point, whereas for low-purity target states, it implies an oscillatory approach to the target state. The dynamical phase transition between these two regimes is characterized by a third-order exceptional point.

Wednesday, 27 September 2023

Quantum mechanics is characterized by some NO-Go principles like uncertainty principle, no-cloning of unknown quantum state, indistinguishability of non-orthogonal states, Impossibility of definite quantum state for subsystem for definite entangled state of the composite system, impossibility of local realistic description of QM etc. Quantum information threory is based on some information processing tasks by exploiting these No-Go theorems in a creative way , which are otherwise impossible in classical world. In these lecture series (three talks), after some discussion on fromalism of QM, basic information processing tasks like dense coding, teleportation, quantum key generation will be introdued along with manipulation of entanglement which is the most important resource in quantum information theory. Basic ideas of quantum nonlocality and quantum computation will also be discussed.

Starting in the mid-1980s with the quantum control and detection of individual atoms/ions, we now have access to a variety of controllable quantum systems. One particular platform which has emerged as a popular choice is superconducting circuits which are macroscopic electrical circuits that can be engineered to show quantum mechanical phenomena like superposition and entanglement. In this series of three lectures, I will introduce the concept of a quantum electrical circuit and how one can use superconducting materials to build them. The flexibility in circuit design allows one to create near ideal custom Hamiltonians which can be used to implement textbook measurements and explore various phenomena in previously unexplored regimes. The same flexibility also enables the possibility of large-scale chips for quantum computing applications. I will discuss some examples to illustrate the versatility of this platform and also highlight the various challenges in building a practical quantum computer.

We will discuss the phenomenology of integer and fractional quantum Hall states, paying particular attention to edge modes in abelian quantum Hall states. These modes are one platform for quantum information processing.

Duality has a long history in physics going back to the electromagnetic symmetry discovered by Dirac in 1931 and and by the duality symmetry of pf the two-dimensional Ising model of Statistical mechanics discovered by Kramers and Wannier in 1941. By now there are many extensions and generalizations of duality isn several areas of physics ranging from condensed matter to quantum field theory and gravity. In the talk I will give brief sketch of this rich history, focusing on recent discoveries. Duality is often a mapping that relates a strongly coupled theory to another weakly coupled one, often with seemingly different nature. I will end my colloquium showing for duality has helped understanding a mysterious symmetry seen in experiments in qunatum Hall fluids.

Thursday, 28 September 2023

Starting in the mid-1980s with the quantum control and detection of individual atoms/ions, we now have access to a variety of controllable quantum systems. One particular platform which has emerged as a popular choice is superconducting circuits which are macroscopic electrical circuits that can be engineered to show quantum mechanical phenomena like superposition and entanglement. In this series of three lectures, I will introduce the concept of a quantum electrical circuit and how one can use superconducting materials to build them. The flexibility in circuit design allows one to create near ideal custom Hamiltonians which can be used to implement textbook measurements and explore various phenomena in previously unexplored regimes. The same flexibility also enables the possibility of large-scale chips for quantum computing applications. I will discuss some examples to illustrate the versatility of this platform and also highlight the various challenges in building a practical quantum computer.

An entangled state is said to be m-uniform if the reduced density matrix of any m qubits is maximally mixed. This is intimately linked to pure quantum error correction codes (QECCs), which allow not only to correct errors, but also to identify their precise nature and location. Here, we show how to create m-uniform states using local gates or interactions and elucidate several QECC applications. We first show that ground states of the D-dimensional cluster Ising model, which are cluster states, are m-uniform with m = 2D. This zero-correlation length cluster state does not have finite size corrections to its m = 2D uniformity, which is exact both for infinite and for large enough but finite lattices. Yet at some finite value of the lattice extension in each of the D dimensions, which we bound, the uniformity is degraded due to finite support operators which wind around the system. We also outline how to achieve larger m values using quasi-D dimensional cluster states. This opens the possibility to use cluster states to benchmark errors on quantum computers. We demonstrate this ability on a superconducting quantum computer, focusing on the 1D cluster state which, we show, allows us to detect and identify 1-qubit errors, distinguishing X, Y and Z errors.

Friday, 29 September 2023

In these three lectures I will cover the theoy of the non-Abelian fractional quantum Hall states. I will cover ideal wave functions and conformal field theory, edge states of non-Abelian fractional quantum Hall states and non-Abelian fractional statistics, edge states and coset constructions, quantum interferometers, effective field theories of non-Abelian states and Fibonacci states.

Starting in the mid-1980s with the quantum control and detection of individual atoms/ions, we now have access to a variety of controllable quantum systems. One particular platform which has emerged as a popular choice is superconducting circuits which are macroscopic electrical circuits that can be engineered to show quantum mechanical phenomena like superposition and entanglement. In this series of three lectures, I will introduce the concept of a quantum electrical circuit and how one can use superconducting materials to build them. The flexibility in circuit design allows one to create near ideal custom Hamiltonians which can be used to implement textbook measurements and explore various phenomena in previously unexplored regimes. The same flexibility also enables the possibility of large-scale chips for quantum computing applications. I will discuss some examples to illustrate the versatility of this platform and also highlight the various challenges in building a practical quantum computer.

Quantum dots have emerged as one of the contenders for a future quantum information processor. Bilayer graphene is now established as a material that allows high quality bi-polar Coulomb blockade measurement, time-dependent transport measurements and first relaxation time measurements. In contrast to the more conventional GaAs and Si-based systems, several exiting and unexpected observations in graphene have been explained by the peculiar graphene bandstructure, which is gate-tunable, the additional valley degree of freedom, and spin-valley coupling. Here we demonstrate shell filling of electronic states in graphene quantum dots and derive the spin and valley Hund rules for the first 24 carriers occupying the quantum dots. Lifetimes of single single spins are measured using the Elzermann read-out. For two carriers occupying a single or double quantum dot we find a complex charge stability diagram with transitions governed by Pauli spin and/or valley blockade. Using these two carrier states we measure spin lifetimes of about 50 ms and valley lifetimes approaching 1s.

In superconducting graphene fabricated using two layers twisted by the magic angle we investigate Josephson junctions as well as a SQUID, where the critical current in the two arms can be independently controlled by gate electrodes.

This work was done in collaboration with Lisa Maria Gächter, Rebekka Garreis, Chuyao Tong, Max Josef Ruckriegel, Benedikt Kratochwil, Folkert Kornelis de Vries, Annika Kurzmann, Wister Wei Huang, Elías Portolés, Shuichi Iwakiri, Giulia Zheng, Peter Rickhaus and Thomas Ihn.

The quantum processors of today are highly susceptible to noise due to unwanted interactions with their environment. Mitigating the effects of such noise poses a significant challenge in our quest for robust and scalable quantum computing devices. Quantum error correction (QEC) provides a framework by which errors affecting quantum states can be systematically addressed and the theory of quantum fault tolerance gives a prescription for constructing noise-resilient quantum circuits with faulty quantum gates. In this talk, we will first give a brief introduction to the theory of quantum error correction and quantum fault tolerance. In the second half, we will discuss our recent works on noise-adapted quantum error correcting codes and their potential role in enabling fault-tolerant quantum computation in today’s era of noisy intermediate-scale quantum (NISQ) devices.

Fractional quantum Hall state at 5/2 filling is intriguing. A typical magnetic field for observing 5/2 state in GaAs systems contributes to sizable Landau level mixing. This mixing can be quantified with a parameter κ as ratio between the Coulomb and cyclotron energy scales. While the theories are developed for zero or small values of κ, the experiments are generally performed for κ∼1. We numerically find [1] that a topological phase transition occurs nearly at κ=0.7. The ground state wave function for the topological phase occurring for κ∼1 is orthogonal to all the well-known wavefunctions, namely, Moore-Read Pfaffian and its particle-hole conjugate anti-Pfaffian, and particle-hole symmetric Pfaffian. Our proposed wave function has very high overlap with this ground state. This wavefunction reproduces state counting of low-lying entanglement spectra with that of the exact ground state. It further describes a Majorana edge mode as manifestation of hidden Z_2 symmetry. The edge modes are consistent with experimentally [2] found 2.5 unit of thermal Hall conductance.

[1] S. Das, S. Das, and S. S. Mandal, Phys. Rev. Lett. 131, 056202 (2023),

[2] M. Banerjee, M. Heiblum, V. Umansky, D. E. Feldman,Y. Oreg, and A. Stern, Nature 559, 205 (2018).

Monday, 02 October 2023

In these three lectures I will cover the theoy of the non-Abelian fractional quantum Hall states. I will cover ideal wave functions and conformal field theory, edge states of non-Abelian fractional quantum Hall states and non-Abelian fractional statistics, edge states and coset constructions, quantum interferometers, effective field theories of non-Abelian states and Fibonacci states.

We'll explore quantum error correction fundamentals, starting with decoherence and key principles of QEC codes. Our discussion will extend to stabilizer and topological codes, as well as more advanced coding schemes. Time permitting, we'll also review the current state of quantum computing across different technologies.

Tuesday, 03 October 2023

In these three lectures I will cover the theoy of the non-Abelian fractional quantum Hall states. I will cover ideal wave functions and conformal field theory, edge states of non-Abelian fractional quantum Hall states and non-Abelian fractional statistics, edge states and coset constructions, quantum interferometers, effective field theories of non-Abelian states and Fibonacci states.

We'll explore quantum error correction fundamentals, starting with decoherence and key principles of QEC codes. Our discussion will extend to stabilizer and topological codes, as well as more advanced coding schemes. Time permitting, we'll also review the current state of quantum computing across different technologies.

We will consider two classes of periodically driven systems in one dimension. In the first case, we consider a spin-1/2 XY model in a transverse field, where the field is driven periodically in time. The periodic driving can generate two kinds of modes, topological modes and non-topological, which are localized at the ends of a finite-sized system. We study the out-of-time-ordered correlators (OTOCs) of spin operators which are local (sigma^z) or non-local (sigma^x) in terms of Jordan-Wigner fermions. The OTOCS are given by infinite-temperature ensembles of a product of four operators, A_l (t) A_0 (0) A_l (t) A_0 (0), where the space labels 0 and l denote one end of the system and an arbitrary point in the system, respectively, and A can denote sigma^z or sigma^x. The OTOCs of non-local operators show pronounced scrambling and unscrambling of quantum information after reflections from the ends of the systems. Further, the OTOCs of both local and non-local operators can detect the presence of end modes which give rise to oscillations as a function of the stroboscopic time.

In the second case, we study a system of fermions where there is an on-site potential which varies periodically in space, and the strength of the potential is varied periodically in time. We find that the system becomes dynamically localized for special values of the driving strength and frequency. The dynamical localization gives rise to an extreme limit of the Su-Schrieffer-Heeger model in which the nearest-neighbor hoppings are zero and non-zero alternately; as a result, there are an extensive number of conserved quantities. Further, if there are density-density interactions between particles on nearest-neighbor sites, the system effectively turns into the transverse field Ising model. We study the half-chain entanglement entropy versus the Floquet quasienergy and find that the large number of conserved quantities can give rise to a highly fragmented structure of the entanglement versus quasienergy plot. A study of the time evolution of the Loschmidt echo and some two-point correlation functions show long-time oscillations indicating that the system has anomalous thermalization behavior. We also examine what happens if dynamical localization and resonances are present simultaneously, and find that there are kinetic constraints which lead to Hilbert space fragmentation.

1. Samudra Sur and DS, arXiv:2210.15302.

2. Sreemayee Aditya and DS, arXiv:2305.06056.

Projective measurements in random quantum circuits lead to a rich breadth of entanglement phases and extend the realm of non-unitary quantum dynamics. Here we explore the connection between measurement-only quantum circuits in one spatial dimension and the statistical mechanics of loop models in two dimensions. We introduce a fundamental symmetry of loop models: the orientability of world lines. We discuss how orientability enters in the measurement framework, acting as a separatrix for the universal long-wavelength behavior in a circuit. When it is broken, the circuit falls into the universality class of closely packed loops with crossings (CPLC) and features a Goldstone phase with a peculiar, universally enhanced growth of the entanglement entropy. In turn, when orientability is preserved, the long-wavelength behavior of the circuit mimics that of (coupled) two-dimensional Potts models. A rich circuit dynamics is observed, ranging from CPLC to the -state Potts model (percolation), the -state Potts model (Ising) and coupled Potts models (BKT) universality class.

Wednesday, 04 October 2023

We'll explore quantum error correction fundamentals, starting with decoherence and key principles of QEC codes. Our discussion will extend to stabilizer and topological codes, as well as more advanced coding schemes. Time permitting, we'll also review the current state of quantum computing across different technologies.

Advancing the frontiers of science often requires the creation of new probes to uncover the underlying microscopic mechanisms giving rise to exotic macroscopic phenomena, such as high-temperature superconductivity. Can quantum entangled probes uncover the inherent entanglement of the target matter? We have recently developed an entangled neutron beam where individual neutrons can be entangled in spin, trajectory, and energy. To demonstrate entanglement in these beams we crafted neutron interferometric measurements of contextuality inequalities whose violation provided an indication of the breakdown of Einstein's local realism. In turn, the tunable entanglement (spin-echo) length of the neutron beam from nanometers to microns and energy differences from peV to neV opens a pathway to a future era of entangled neutron scattering in matter. What kind of information can be extracted with this novel entangled probe? A recent general quantum many-body entangled-probe scattering theory provides a framework to respond to this question. Interestingly, by carefully tuning the probe's entanglement and inherent coherence properties, one can directly access the intrinsic entanglement of the target material. This theoretical framework supports the view that our entangled beam can be used as a multipurpose scientific tool. We are currently pursuing several new ideas and developing spin-textured entangled beams with orbital angular momentum for future experiments in candidate quantum spin liquids, unconventional superconductors, and chiral quantum materials.

We present new facets in the domain of photonic quantum information processing (QIP). A major part of the talk focuses on our recent works in higher dimensional QIP.

We provide a novel scheme for direct determination of different entanglement monotones used to quantify entanglement in arbitrary system dimensions using only one pair of complementary observables, as opposed to the standard d^2 measurements needed in d dimensions. In our scheme, we analytically relate statistical measures of correlations i.e. Pearson Correlation Coefficient, Mutual Predictability and Mutual Information with the standard measures of entanglement i.e. Negativity and Entanglement of Formation for arbitrary dimensional states. In [1], we theoretically formulate, experimentally implement and explore implications of the scheme for actually determining values of the entanglement measures for the first time making use of the standard statistical correlators, essentially for two-qudit pure states. The extension to mixed states is thoroughly studied in [2], showing that the efficacy of this scheme is restricted to not only distillable entangled states, but extends to bound entangled states as well.

Next we discuss our novel approach to higher dimensional quantum state estimation, using interference as a tool [3]. Here we present an interferometric method, in which any qubit state, whether mixed or pure, can be inferred from the visibility, phase shift, and average intensity of an interference pattern using a single-shot measurement—hence, we call it Quantum State Interferography [3]. This provides us with a “black box” approach to quantum state estimation, wherein, between the incidence and extraction of state information, we are not changing any conditions within the setup, thus giving us a true single shot estimation of the quantum state. An extension of the scheme to pure states involving d−1 interferograms for d-dimensional systems (qudits) is also presented. The scaling gain is even more dramatic in the qudit scenario for our method, where, in contrast, standard QST, scales roughly as d2.

In the final part, we briefly present the first loophole-free experiment wherein both the LGI and the WLGI inequalities have been decisively violated using single photons[4], thus providing a comprehensive refutation of the classical realist worldview along with measurements ensured to be non-invasive. This provides a powerful platform for harnessing this most general unambiguous signature of nonclassicality of single photon states towards various information theoretic applications wherein the single photon is a ubiquitous workhorse.

[1] Direct determination of entanglement monotones for arbitrary dimensional bipartite states using statistical correlators and one set of complementary measurements, D. Ghosh, T.Jennewein, U.Sinha, Quantum Science and Technology, 7 045037, 2022.

[2] Relating an entanglement measure with statistical correlators for two-qudit mixed states using only a pair of complementary observables, S. Sadana, S. Kanjilal, D.Home, U.Sinha, arXiv: 2201.06188, 2022.

[3] Quantum State Interferography, S.Sahoo, S. Chakraborti, A.K.Pati, U.Sinha, Phys. Rev. Lett. 125 123601, 2020.

[4] Loophole free interferometric test of macrorealism using heralded single photons, K.Joarder, D.Saha, D.Home, U.Sinha, PRX Quantum, 3, 010307, 2022.

Our theoretical investigation explores a feasible route to engineer the two-dimensional (2D) Kitaev model of first-order topological superconductivity (TSC) introducing a magnetic spin texture. The main outcome of 2D Kitaev’s model is that a px + py type superconductor can exhibit a gapless topological superconducting phase in bulk hosting non-dispersive Majorana flat edge mode (MFEM) at the boundary. Our proposed general minimal model Hamiltonian is suitable to describe magnet/superconductor heterostructure. It reveals robust MFEM within the emergent gap of Shiba bands, spatially localised at the edges of a 2D magnetic domain of spin-spiral. We finally verify this concept from real material perspectives by considering Mn (Cr) monolayer grown on an s-wave superconducting substrate, Nb(110) under strain (Nb(001)). In both the 2D cases, the antiferromagnetic spin-spiral solutions exhibit robust MFEM at certain domain edges. This approach, particularly when the MFEM appears in the TSC phase for such heterostructure materials, offers significant prospect to extend the realm of TSC in 2D. Very recently, we expand this theoretical framework for engineering a 2D second-order topological superconductor (SOTSC) by utilising a heterostructure: incorporating non-collinear magnetic textures between an s-wave superconductor and a 2D quantum spin Hall insulator. It stabilises the higher order topological superconducting phase, resulting in Majorana corner modes (MCMs) at the four corners of a 2D domain. Such first and second order Majorana modes are believed to be the building blocks for the fault-tolerant topological quantum computation.

From the perspective of many-body physics, the transmon qubit architectures currently developed for quantum computing are systems of coupled nonlinear quantum resonators. A significant amount of intentional frequency detuning (disorder) is required to protect individual qubit states against the destabilizing effects of nonlinear resonator coupling. In this talk, we will discuss the stability of this variant of a many-body localized phase for system parameters relevant to current quantum processors. An essential element in of our diagnostic toolbox are classical simulations, which can be run, e.g., for upcoming IBM designs comprising hundreds of qubits. The overall conclusion of this study is that it will take considerable engineering efforts to protect transmon quantum computers from the destructive influence of chaotic fluctuations.

An analytical approach to studying free fermions subject to random measurements of local site occupation numbers is developed, based on the Keldysh sigma model and replica trick. On the Gaussian level, this theory predicts a logarithmic behavior for the entanglement entropy of one-dimensional systems. However, the one-loop renormalization group analysis demonstrates that this logarithmic growth saturates at a finite value even for rare measurements, through "weak-localization" quantum corrections similar to those in 2D disordered systems. This yields the area-law phase in the thermodynamic limit and implies the absence of a measurement-induced entanglement phase transition for monitored 1D free fermions. For 2D free fermions, this approach predicts the entanglement transition from the area-law to the critical phase. No volume-law phase is realized for fermions in arbitrary dimensions in the absence of interactions.

Bilayer graphene exhibits a rich phase diagram in the quantum Hall (QH) regime, arising from a multitude of internal degrees of freedom, including spin, valley, and orbital indices. The variety of fractional QH states between filling factors 1 and 2 suggests, among other things, a quantum phase transition between valley-polarized and unpolarized states at a perpendicular electric-field D*. We find that the behavior of D* with filling factor changes markedly as the magnetic field B is reduced. We present a theoretical model for lattice-scale interactions, which explains these observations; contrary to earlier studies, it involves finite-ranged terms comprising both repulsive and attractive components. Within this model, we analyze the nature of the phase at filling factor 2, and predict that valley-coherence may emerge at high B fields. This suggests that the system may support bond-ordered phases which may be amenable to experimental verification.

Thursday, 05 October 2023

Cavity electromechanical systems are extensively used for sensing and controlling the vibrations of a mechanical mode down to their quantum limit. In this talk, I will discuss results from an electromechanical device consisting of a transmon qubit and mechanical resonator. We find that in strength of the light-matter interaction in such a device could be engineered to see strong backaction on a mechanical resonator by using less than one photon.

I will show how the analysis of electron waiting times and the correlation between them help in understanding topological Andreev bound states in an Andreev interferometer where a superconducting loop with a controllable phase difference is connected to a quantum spin Hall edge. The edge state helicity enables the transfer of electrons and holes into separate leads controlled by the phase difference of the loop. In this setup, the topological phase transition with emerging topological bound states occurs at $\phi=\pi$ and electron waiting times are sensitive to it. However, the waiting times for the Andreev-reflected holes remain insensitive. These two different waiting times show opposite behaviors when we consider the correlation between them. Some of the cross-distributions also show unique features indicating the appearance of topological Andreev bound states.

Two dimensional moire systems have recently emerged as a platform in which the interplay between topology and strong correlations of electrons play out in non-trivial ways. Among these systems, twisted double bilayer graphene (TDBG) is of particular interest as its topological properties may be tuned via both twist angle and applied perpendicular electric field. In this system, energy gaps are observed at half filling of particular bands, which can be associated with correlated spin polarized states. In this work, we investigate the fate of these states as the system is doped away from this filling. We demonstrate that, for a broad range of fractional fillings, the resulting ground state is partially valley polarized, and supports multiple broken symmetries, including a textured spin order indicative of skyrmions, with a novel stripe ordering that spontaneously breaks $C_3$ symmetry.

Two-dimensional systems at low temperatures and high magnetic field can host exotic particles “anyons” with elementary excitations, very different from bosonic and fermionic excitations. They carry fractional charge and have fractional statistics. The fractional charge of these anyons has been studied successfully using low-frequency shot noise measurement. However, no universal method for sensing them unambiguously exists. Here we exploited the Josephson relation of these anyonic states to determine the fractional charge of excited quasiparticles. The microwave photons emitted by voltage biased anyonic system obey the Josephson relation, like Josephson junction but with the charge q = e* rather than e. This provides direct evidence of fractional charge in fractional quantum Hall effect. I will conclude the talk with recent advancement in experiments on fractional statistics in mesoscopic anyonic collider, see talk by Gwendal Fevé.

Topologically protected quantum Hall edge states carry quantum information over long distances, since they are orthogonal eigenstates of the Quantum Hall Insulator. As a consequence quantum Hall edge states possess large relaxation length and coherence length at low temperatures. Quantum interference of electrons in the edge states is regarded as flying qubit rotation operation. Based on the quantum interference, few architectures for quantum information processing are proposed. In this talk, I will review various approaches and our results on controlled coupling of the spin-resolved edge states, quantum interference in spin-resolved edge states, finding robust fractional quantum Hall edge modes etc. and elaborate future perspectives of quantum information processing.

Friday, 06 October 2023

Recent years have seen the discovery of and a surge of interest in a phenomenon dubbed “chiral state conversion”. Under cyclic adiabatic non-Hermitian evolution, all system states get converted to one eigenstate of the Hamiltonian. When the evolution path encircles an exceptional point of the Hamiltonian, the conversion is chiral: depending on the path orientation, the final state is different.

At the same time, a number of (theoretical and experimental) examples have emerged, demonstrating that the conversion may be chiral without encircling an exceptional point or non-chiral despite encircling one.

I will present a newly-developed general theory of this phenomenon, which explains the mechanism behind the phenomenon, as well as all the unusual examples.