Introduction to Quantum Optics 

Doctoral Programme in Physics and Materials Science. University of Luxembourg.
November 16th - December 7th 2023, Campus Limpertsberg.

Content

1. Quantization of the electromagnetic field. Quantum states of light.

2. Atom-light interactions.

3. Quantum optical master equation.

4. Beam splitters and interferometers.

Main references:

• C. C. Gerry and P. L. Knight, Introductory Quantum Optics, Cambridge university press.

• H. P. Breuer and F. Petruccione. The theory of open quantum systems. Oxford University Press, USA.

• D. F. Walls and G. J. Milburn. Quantum Optics. Berlin, Heidelberg: Springer Berlin Heidelberg. 

Final presentation

Presentation of a scientific paper (20 - 30 min) or a chapter of book about a topic not covered in the course (30 min).
Below a list of suggested papers/chapters.

Suggested papers or book chapters for the final presentation

Below each reference some keywords in square brackets.

Book chapters:

• Quantum coherence functions.
  C. C. Gerry and P. L. Knight, Introductory Quantum Optics, Cambridge university press. (chap 5)
  [photon bunching and antibunching, g2]

• Nonclassical light.
  C. C. Gerry and P. L. Knight, Introductory Quantum Optics, Cambridge university press. (chap 7)
  [squeezing, squeezed states, Schrödinger cat states]

• Input-Output Formulation of Optical Cavities.
  D. F. Walls and G. J. Milburn. Quantum Optics. Berlin, Heidelberg: Springer Berlin Heidelberg. (chap 7)

Papers:

1. Quantum electrodynamics near a photonic band gap: Photon bound states and dressed atoms.
   S. John and J. Wang. Phys. Rev. Lett. 64, 2418 (1990)

2. Spontaneous emission near the edge of a photonic band gap.
   S. John and T. Quang. Phys. Rev. A 50, 1764 (1994)

3. Nonperturbative decay of an atomic system in a cavity.
   B. M. Garraway. Phys. Rev. A 55, 2290 (1997)

4. Strongly Interacting Photons in a Nonlinear Cavity.
   A. Imamoglu, H. Schmidt, G. Woods, and M. Deutsch. Phys. Rev. Lett. 79, 1467 (1997)
   [photon blockade]

5. Cavity quantum electrodynamics for superconducting electrical circuits: An architecture for quantum computation.
   Alexandre Blais, Ren-Shou Huang, Andreas Wallraff, S. M. Girvin, and R. J. Schoelkopf. Phys. Rev. A 69, 062320 (2004)
   [circuit QED]

6. Laser Cooling of a Nanomechanical Resonator Mode to its Quantum Ground State.
   I. Wilson-Rae, P. Zoller, and A. Imamoglu. Phys. Rev. Lett. 92, 075507 (2004)

7. Dynamics in a coupled-cavity array.
   C. D. Ogden, E. K. Irish, and M. S. Kim. Phys. Rev. A 78, 063805 (2008)

8. Theory of single-photon transport in a single-mode waveguide. I. Coupling to a cavity containing a two-level atom.
   Jung-Tsung Shen and Shanhui Fan. Phys. Rev. A 79, 023837 (2009)
   [atoms coupled to the electromagnetic field in 1D, waveguide QED]

9. Quantum optics in the phase space - A tutorial on Gaussian states.
   S. Olivares. Eur. Phys. J. Special Topics 203, 3-24 (2012)

10. Photon localization versus population trapping in a coupled-cavity array.
    F. Lombardo, F. Ciccarello, and G. M. Palma. Phys. Rev. A 89, 053826 (2014)

11. Direct sampling of electric-field vacuum fluctuations.
    C. Riek et al. Science 350 , 420-423 (2015)

12. Dynamical polaron Ansatz: A theoretical tool for the ultrastrong-coupling regime of circuit QED.
    G. Díaz-Camacho, A. Bermudez, and J. J. García-Ripoll. Phys. Rev. A 93, 043843 (2016)

13. Atom-field dressed states in slow-light waveguide QED.
    G. Calajó, F. Ciccarello, D. E. Chang, and P. Rabl. Phys. Rev. A 93, 033833 (2016)

14. Bound States in Boson Impurity Models.
    Tao Shi, Ying-Hai Wu, A. González-Tudela, and J. I. Cirac. Phys. Rev. X 6, 021027 (2016)

15. Collision models in quantum optics.
    F. Ciccarello. Quantum Measurements and Quantum Metrology 4 (1), 53-63 (2017)

16. Atom-light interactions in quasi-one-dimensional nanostructures: A Green's-function perspective.
    A. Asenjo-Garcia, J. D. Hood, D. E. Chang, and H. J. Kimble. Phys. Rev. A 95, 033818 (2017)

17. Quantum Emitters in Two-Dimensional Structured Reservoirs in the Nonperturbative Regime.
    A. González-Tudela and J. I. Cirac. Phys. Rev. Lett. 119, 143602 (2017)

18. Colloquium: Quantum matter built from nanoscopic lattices of atoms and photons.
    D. E. Chang, J. S. Douglas, A. González-Tudela, C.-L. Hung, and H. J. Kimble. Rev. Mod. Phys. 90, 031002 (2018)

19. Quantum Optical Realization of Arbitrary Linear Transformations Allowing for Loss and Gain.
    N. Tischler, C. Rockstuhl, and K. Słowik. Phys. Rev. X 8, 021017 (2018)

20. Introduction to the Dicke model: from equilibrium to nonequilibrium, and vice versa.
    P. Kirton, M. M. Roses, J.Keeling, and E.G. Dalla Torre. Advanced Quantum Technologies, 2(1-2), 1970013 (2019)
    [superrandiant phase transition]

21. Non-exponential decay of a giant artificial atom.
    G. Andersson, B. Suri, L. Guo, T. Aref, and P. Delsing. Nat. Phys. 15, 1123–1127 (2019)

22. Quantum Optics with Giant Atoms—the First Five Years.
    A. F. Kockum. International Symposium on Mathematics, Quantum Theory, and Cryptography. Mathematics for Industry, vol 33. Springer, Singapore (2021)
    [beyond the dipole approximation]

23. Universality of Dicke superradiance in arrays of quantum emitters.
    S. J. Masson and A. Asenjo-Garcia. Nat Commun 13, 2285 (2022)

24. Dicke Superradiance Requires Interactions beyond Nearest Neighbors.
    W. K. Mok, A. Asenjo-Garcia, T. C. Sum, and L. C. Kwek. Phys. Rev. Lett. 130, 213605 (2023)

25. Schrödinger cat states of a 16-microgram mechanical oscillator.
    M. Bild et al. Science 380 , 274-278 (2023)
    [generation of cat states]

26. A cavity quantum electrodynamics implementation of the Sachdev-Ye-Kitaev model.
    P. Uhrich, S. Bandyopadhyay, N. Sauerwein, J. Sonner, J. P. Brantut, P. Hauke. arXiv:2303.11343 (2023)

27. An atom-doped photon engine: Extracting mechanical work from a quantum system via radiation pressure.
    A. Tejero, D.Manzano, and P. I. Hurtado. arXiv:2311.15712 (2023)