ICTS Course on Open Quantum Systems (Spring 2021)

Instructor: Manas Kulkarni, manas.kulkarni@icts.res.in

TA: Junaid Majeed Bhat, junaid.bhat@icts.res.in

Prerequisites: Quantum Mechanics, Statistical Physics

Syllabus:

  1. Dissipation in Quantum Mechanics: General setup and various approaches

  2. Damped Quantum Harmonic Oscillator, two time averages and quantum regression

  3. Spin Boson Model (Dephasing) and some generalizations

  4. Dissipative two-level and multi-level systems

  5. Cavity-Quantum Electrodynamics (cavity-QED): Exact solutions of the Jaynes-Cummings Model (JCM)

  6. Dispersive limit of the JCM and its generalizations (reduction to Bose-Hubbard systems)

  7. Dissipative process in cavity-QED systems

  8. Driven-Dissipative Quantum Systems and applications (driven JCM)

  9. Dicke Model and phase transitions

Day/Time:

Tuesdays and Fridays from 4pm-5:30pm (first class is on January 15, 2021)

Textbooks:

Below are some suggested books. 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) 


Term paper topics

Below are topics for term paper (report + presentation). Students will need to pick one topic (latest by February 15, 2021) and make a report and then give a presentation (at the end of the semester). The sample suggested literature for each of them are given below. Once students pick one topic, they are encouraged to explore more literature. 

1) Non-Hermitian Random Matrices

- 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


2) Quantum Dot circuit-QED systems

-  Towards hybrid circuit quantum electrodynamics with quantum dots, Viennot, Jérémie J., Matthieu R. Delbecq, Laure E. Bruhat, Matthieu C. Dartiailh, Matthieu M. Desjardins, Matthieu Baillergeau, Audrey Cottet, and Takis Kontos, Comptes Rendus Physique 17, no. 7 (2016): 705-717.
- Semiconductor double quantum dot micromaser, Y.-Y. Liu, J. Stehlik, C. Eichler, M. J. Gullans, J. M. Taylor, J. R. Petta, Science 347, 285
- Photon emission from a cavity-coupled double quantum dot, Y.-Y. Liu, K. D. Petersson, J. Stehlik, J. Taylor, J. R. Petta, Phys. Rev. Lett. 113, 036801

 

3) Optomechanical 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) Self-trapping, localization in Non-Hermitian Systems

- Macroscopic quantum self-trapping and Josephson oscillations of exciton polaritons, Abbarchi, M., Amo, A., Sala, V.G., Solnyshkov, D.D., Flayac, H., Ferrier, L., Sagnes, I., Galopin, E., Lemaître, A., Malpuech, G. and Bloch, J., 2013. Nature Physics, 9(5), pp.275-279.
- Nonequilibrium delocalization-localization transition of photons in circuit quantum electrodynamics, S. Schmidt, D. Gerace, A. A. Houck, G. Blatter, and H. E. Türeci, Phys. Rev. B 82, 100507 (R)
- Observation of a Dissipation-Induced Classical to Quantum Transition, J. Raftery, D. Sadri, S. Schmidt, H. E. Türeci, and A. A. Houck, Phys. Rev. X 4, 031043

 

5) Parity-Time Symmetric Systems

- 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)

 

Grading Policy

Homework – 40 %

Term paper (report and presentation) – 30 %

Final Exam – 30 %