Instructor: Manas Kulkarni,

TA: Mahaveer Prasad,

Prerequisites: Quantum Mechanics, Statistical Physics

Day/Time: Wednesday and Friday, 4pm - 5:30pm (first class is on January 19th, 2022)

Venue: Online


  1. General formalism and various approaches for Open Quantum Systems
  2. Damped Quantum Harmonic Oscillator and multi-level systems
  3. Exact results for Spin Boson Model (Dephasing) and some generalizations
  4. Integrability of Jaynes-Cummings and quantum Rabi models
  5. Driven-Dissipative Quantum Systems and applications
  6. Hermitian and Non-Hermitian Dicke Model: Chaos and Connections to Random Matrix Theory



Below are some suggested references. I will also be making additional notes.

  1. Howard Carmichael, Statistical Methods in Quantum Optics 1. Master Equations and Fokker-Planck Equations (Springer)
  2. Girish S. Agarwal, Quantum Optics (Cambridge University Press)
  3. Heinz-Peter Breuer and Francesco Petruccione, The theory of open quantum systems (Oxford University Press)
  4. Marlan O. Scully and M. Suhail Zubairy, Quantum optics (Cambridge University Press) 
  5. Fritz Haake, Sven Gnutzmann, Marek Kuś, Quantum signatures of chaos (Springer)
  6. Simulation methods for open quantum many-body systems, Hendrik Weimer, Augustine Kshetrimayum, and Román Orús, Rev. Mod. Phys. 93, 015008  (2021)


Term paper (report + presentation) topics

Below are suggested topics for term paper (report + presentation). The suggested references for each of them is given. Students will need to finalize a topic (latest by February 23rd, 2022), make a report and then give a presentation (at the end of the semester).

1) Circuit-QED with non-trivial lattice geometry and connectivity

-  Line-graph lattices: Euclidean and non-Euclidean flat bands, and implementations in circuit quantum electrodynamics, Kollár, A.J., Fitzpatrick, M., Sarnak, P. and Houck, A.A., 2020. Communications in Mathematical Physics, 376(3), pp.1909-1956.
-  Hyperbolic lattices in circuit quantum electrodynamics, Kollár, A.J., Fitzpatrick, M. and Houck, A.A., 2019. Nature, 571(7763), pp.45-50.
- Probing dynamical phase transitions with a superconducting quantum simulator, Xu, K., Sun, Z.H., Liu, W., Zhang, Y.R., Li, H., Dong, H., Ren, W., Zhang, P., Nori, F., Zheng, D. and Fan, H., 2020. Science advances, 6(25), p.eaba4935.
- Ring-Resonator-Based Coupling Architecture for Enhanced Connectivity in a Superconducting Multiqubit Network, S. Hazra, A. Bhattacharjee, M. Chand, K. V. Salunkhe, S. Gopalakrishnan, M. P. Patankar, and R. Vijay, Physical Review Applied 16, 024018 (2021).

2) Parity-Time Symmetric Systems and exceptional points

- Real Spectra in Non-Hermitian Hamiltonians Having PT Symmetry, Carl M. Bender and Stefan Boettcher, Phys. Rev. Lett. 80, 5243
- Nonlinear waves in PT-symmetric systems, Vladimir V. Konotop, Jianke Yang, and Dmitry A. Zezyulin, Rev. Mod. Phys. 88, 035002 (2016)
- Non-Hermitian physics and PT symmetry, Ramy El-Ganainy, Konstantinos G. Makris, Mercedeh Khajavikhan, Ziad H. Musslimani, Stefan Rotter & Demetrios N. Christodoulides, Nature Physics volume 14, pages11–19 (2018)

3) Opto-mechanical Systems

- Optomechanics and quantum measurement (2015 Les Houches School on Optomechanics), Aashish A. Clerk
- Cavity optomechanics, Markus Aspelmeyer, Tobias J. Kippenberg, and Florian Marquardt, Rev. Mod. Phys. 86, 1391 (2014)
- Cavity optomechanics: nano-and micromechanical resonators interacting with light, Markus Aspelmeyer, Tobias J. Kippenberg, and Florian Marquardt, eds, Springer (2014)

4) Symmetries and spectral properties of Liouvillians

- Universal Signature from Integrability to Chaos in Dissipative Open Quantum Systems, Gernot Akemann, Mario Kieburg, Adam Mielke, and Tomaž Prosen, Phys. Rev.Lett. 123, 254101
- Complex Spacing Ratios: A Signature of Dissipative Quantum Chaos, Lucas Sá, Pedro Ribeiro, and Tomaž Prosen, Phys. Rev. X 10, 021019
- Universality classes of non-Hermitian random matrices, Ryusuke Hamazaki, Kohei Kawabata, Naoto Kura, and Masahito Ueda, Phys. Rev. Research 2, 023286
- Non-Hermitian many-body localization, Hamazaki, R., Kawabata, K. and Ueda, M., 2019. Physical review letters, 123(9), p.090603.


Grading Policy

Homework – 40 %

Term paper (report and presentation) – 30 %

Final Exam – 30 %