Joint syllabus
«Quantum Optics Through the Exersises»
Alexander A. Pukhov
Professor of the DPPE of MIPT
pukhov@mail.ru
Constantin R. Simovsky
Professor of the Aalto University, Finland
konstantin.simovski@aalto.fi
Degree program: 010900 «Applied Physics and Mathematics»
Specialization: 010999 «Electrophysics»
Chair of Electrodynamics of Complex Objects and Nanophotonics
4st academic year of the Master’s degree
1st and 2nd semester
Head of chair,
Academician of RAS
A.N.Lagarkov
The first semester
Lecture 1. What is the Quantum Optics? (2 hours)
What is the Quantum Optics? Values, estimations and limits of validility. The
electromagnetic field quantization in media with spectral peculiarities. The conception of the
photon and vacuum fluctations. Fock states of the field, the occupation numbers representation.
The creation and annihilation operator of the photons.
Lecture 2. Coherent (Glauber) states. (2 hours)
Coherent (Glauber) states as eigenstates of the annihilation operator. Quantum squeezing,
squeezed states of light. Uncertainty relations and squeezing operator. Squeezing coherent states
and the squeezing of fluctuations. Noise Reduction.
Lecture 3. Berry phase. (2 hours)
Dynamical and geometrical phase of the oscillator. Berry phase. The interference in
phase space. Coherent (Glauber) states in the theory of laser, superfluidity and magnetism.
Lecture 4. The Hanbury Brown-Twiss effect. (2 hours)
The Sagnac effect. The laser gyroscope. The Hanbury Brown-Twiss effect. The secondorder correlation functions.
Lecture 5. The statistics of the photons. (2 hours)
The statistics of the photons. The Plank light. The Poisson and sub-Poisson light. Photon
anti-bunching is a true manifestation of the quantum nature of light. Pure and entangled states of
the oscillator. The entropy of quantum ensemble. The entropy and the fluctations of
electromagnetical field.
Lecture 6. The Maxwell-Bloch equations. (2 hours)
The interaction of the atomic electron with electromagnetical field. The two-level atom
model. The semiclassical theory, the Maxwell-Bloch equations. The rotating wave
approximation. Constants of motion.
Lecture 7. The Jaynes-Cummings model. (2 hours)
The interaction of the atomic electron with electromagnetic field in the occupation
number representation. The interaction of two-level atom with single mode field. The Rabi
oscillatons. The Jaynes-Cummings model. The «dressed» states of the field. The dynamics,
preparation and collapses of the field states.
Lecture 8. The Weisskopf-Wigner approximation. (2 hours)
The classical radiation damping. The natural linewidth. The decay law of the exited state
of two-level system. The Weisskopf-Wigner approximation. The Lorentzian natural line-shape.
The resolvent method. The Lamb shift. The control of The Lamb shift in the resonator.
Lecture 9. The self-induced transparancy. (2 hours)
The Hanle effect. The laser generation without inversion. The coherent trapping, dark
states. The self-induced transparancy. The propagation of the pulse in the two-level-atom
medium. The area theorem. The dispersion of saturated media and the self-focusing.
Lecture 10. The Dicke superradiance. (2 hours)
The Dicke superradiance. The coherent states and the Dicke states of two-level-atom
medium. The spin and the photonic echo.
Lecture 11. The resonance fluorescence. (2 hours)
The light-matter interaction. The perturbation theory. The Feynmann diagrams. The
emission and the absorbtion of the photons. The resonance fluorescence. The light scattering.
The Raman scattering. The resonance Raman scattering.
Lecture 12. The non-equilibrium phase transition in the laser. (2 hours)
The non-equilibrium phase transition in the laser. The laser light as the Bose-Einstein
condensate.
The second semester
Lecture 1. The quantum theory of relaxation. (2 hours)
The quantum theory of relaxation. Open quantum systems. The Heisenberg-Langevin
equations. The density matrix method and the Fokker-Plank equation. The interaction of the
open quantum system with the bosonic reservoir.
Lecture 2. The semiclassical laser theory. (2 hours)
The semiclassical Lamb laser theory. The generation threshold. The laser rate equations.
The photon yield and laser light intensity.
Lecture 3. The quantum theory of the laser. (2 hours)
The quantum theory of the laser. The photon statistic of laser light. The phase transition
of the laser over the generation threshold. The laser line-width. The quantum mechanics and
statistical physics of the laser.
Lecture 4. The atomic optics. (2 hours)
The atomic optics. The mechanical action of light. The gradient force, the quantum limit
of atomic recoil. The Paul trapp. The laser cooling.
Lecture 5. The quantum electrodynamics “in cavity”. (2 hours)
The quantum electrodynamics “in cavity”. The spontaneous emission in the resonator.
The single-atom maser. The Pursell factor.
Lecture 6. The optical Bloch equations. (2 hours)
The magnetic and optical resonance. The optical Bloch equations. The Bloch vector. The
optical nutation and free precession. The laser mode competition and synchronization. «Spectral
hole burning ». The Lamb dip and the Bennet dip.
Lecture 7. The non-linear optics. (2 hours)
The non-linear optics of condenced matter. Second harmonic generation. Frequency
mixing processes. Optical Kerr effect. The multi-photon processes. The scattering of light by
light.
Lecture 8. The phase of quantized field. (2 hours)
The commutation rules for photon numbers and field amplitudes. The phase of quantized
field. The measurement of the phase. The quantum phase operator problem. «Trigonometric»
phase operator. Оператор фазы Пегга-Барнетта.
Lecture 9. The quantum mechanics of the photon. (2 hours)
The quantum mechanical properties of the photon. The angular momentum. The parity.
The polarization and partial polarization.
Lecture 10. The optics of quantum dots. (2 hours)
The optics of quantum dots. The optical properties of Bose-Einstein condensation in
traps. The enhancement and suppression of spontaneous emission. The Casimir effect and its
possible experimental realizations.
Lecture 11. The noise-induced transitions. (2 hours)
The Langevin equation and the Fokker-Plank equation. The non-Markovian processes.
Power-law noise. The colored noise. The noise-induced transitions.
Lecture 12. What else? The scope of quantum optics and the perspectives. (2 hours)
What else? The scope of quantum optics and the modern perspectives.
References
Basic references
1. W. Heitler, The quantum theory of radiation, 3rd ed., (Oxford University Press,
London, 1954) (reprinted by Dover, New York, 1984).
2. E. A. Power, Introductory quantum electrodynamics, (Longman, London, 1964).
J. R. Klauder and E. C. G. Sudarshan, Fundamentals of quantum optics, (W. A.
Benjamin, New York, 1968).
3. H. M. Nussenzveig, Introduction to quantum optics, (Gordon and Breach, London,
1973).
4. E. B. Davies, Quantum theory of open systems, (Academic Press, London, 1976).
5. W. H. Louisell, Quantum Statistical Properties of Radiation, (John Wiley & Sons, New
York, 1973).
6. R. Graham and F. Haake, Quantum Statistics in Optics and Solid-State Physics,
Springer Tracts in Modern Physics 66, (Springer, Berlin, 1973).
7. G. S. Agarwal, Quantum statistical theories of spontaneous emission and their relation
to other approaches, Springer tracts in modern physics 70, (Springer, Berlin, 1974).
8. M. Sargent III, M. O. Scully, and W. E. Lamb, Jr., Laser physics, (Addison-Wesley,
London, 1974).
9. L. Allen and J. H. Eberly, Optical resonance and two-level atoms, (Dover, New York,
1987).
10. H. Haken, Light Vol. 1: Waves, photons, atoms, (North-Holland, Amsterdam, 1981).
11. H. Haken, Light Vol. 2: Laser light dynamics, (North-Holland, Amsterdam, 1985).
12. H. Haken, Laser theory, (Springer, Berlin, 1984).
13. H.-A. Bachor and T. C. Ralph, A guide to experiments in quantum optics, 2nd ed.,
(Wiley-VCH Verlag, Weinheim, 2004)
14. S. M. Barnett and P. M. Radmore, Methods in theoretical quantum optics, (Clarendon
Press, Oxford, 1997).
15. V. B. Braginsky and F. Ya. Khalili, Quantum measurement, (Cambridge University
Press, Cambridge, 1992).
16. H.-P. Breuer and F. Petruccione, The Theory of Open Quantum Systems, (Oxford
University Press, Oxford, 2002).
17. H. Carmichael, An open systems approach to quantum optics, (Springer, Berlin,
1993).
18. H. J. Carmichael, Statistical methods in quantum optics 1: Master equations and
Fokker-Planck equations, (Springer, Berlin, 1999).
19. H. J. Carmichael, Statistical Methods in Quantum Optics 2: Non-Classical Fields ,
(Springer, Berlin, 2008).
20. C. Cohen-Tannoudji, J. Dupont-Roc, and G. Grynberg, Photons and atoms
Introduction to quantum electrodynamics, (John Wiley & Sons, New York, 1989).
21. C. Cohen-Tannoudji, J. Dupont-Roc, and G. Grynberg, Atom-photon interactions
Basic processes and applications, (John Wiley & Sons, New York, 1992).
22. P. D. Drummond and Z. Ficek, Eds., Quantum squeezing, (Springer, Berlin, 2004).
23. Z. Ficek and S. Swain, Quantum Interference and Coherence: Theory and
Experiments, (Springer, Berlin, 2005).
24. M. Fox, Quantum Optics: An Introduction, (Oxford University Press, Oxford, 2006).
25. C. W. Gardiner and P. Zoller, Quantum noise A handbook of Markovian and nonMarkovian quantum stochastic methods with applications to quantum optics, 3rd ed., (Springer,
Berlin, 2004).
26. J. C. Garrison and R. Y. Chiao, Quantum Optics, (Oxford University Press, Oxford,
2008).
27. C. C. Gerry and P. L. Knight, Introductory Quantum Optics, (Cambridge University
Press, Cambridge, 2005).
28. E. Hanamura, Y. Kawabe, and A. Yamanaka, Quantum Nonlinear Optics , (Springer,
Berlin, 2007).
29. S. Haroche and J.-M. Raimond, Exploring the Quantum: Atoms, Cavities, and
Photons, (Oxford University Press, Oxford, 2006).
30. H. A. Haus, Electromagnetic Noise and Quantum Optical Measurements, (Springer,
Berlin, 2000).
31. A. B. Klimov and S. M. Chumakov, A Group-Theoretical Approach to Quantum
Optics: Models of Atom-Field Interactions , (Wiley-VCH Verlag, Weinheim, 2009).
32. D. N. Klyshko, Photons and Non-Linear Optics, (Gordon and Breach, New York,
1988).
33. P. Lambropoulos and D. Petrosyan, Fundamentals of Quantum Optics and Quantum
Information, (Springer, Berlin, 2007).
34. U. Leonhardt, Measuring the quantum state of light, (Cambridge University Press,
Cambridge, 1997).
35. U. Leonhardt, Essential Quantum Optics: From Quantum Measurements to Black
Holes, (Cambridge University Press, Cambridge, 2010).
36.| R. Loudon, The quantum theory of light, 3rd ed., (Oxford University Press, Oxford,
2000).
37. L. Mandel and E. Wolf, Optical coherence and quantum optics, (Cambridge
University Press, Cambridge, 1995).
38. P. Meystre and M. Sargent III, Elements of quantum optics, 4th ed., (Springer, Berlin,
2007).
Additional reading
39. P. W. Milonni, The Quantum Vacuum: An Introduction to Quantum
Electrodynamics, (Academic Press, San Diego, 1994).
40. M. Namiki, S. Pascazio, and H. Nakazato, Coherence and Quantum Measurements,
(World Scientific, Singapore, 1997).
41. M. Orszag, Quantum Optics: Including Noise Reduction, Trapped Ions, Quantum
Trajectories, and Decoherence, 2nd ed., (Springer, Berlin, 2008).
42. H. Paul, Introduction to Quantum optics: From Light Quanta to Quantum
Teleportation, (Cambridge University Press, Cambridge, 2004).
43. J.-S. Peng and G.-X. Li, Introduction to modern quantum optics, (World Scientific,
Singapore, 1998).
44. J. Perina, Quantum statistics of linear and nonlinear optical phenomena, 2nd ed.,
(Kluwer, Dordrecht, 1991).
45. J. Perina, Z. Hradil, and B. Jurco, Quantum optics and fundamentals of physics,
(Kluwer, Dordrecht, 1994).
46. V. Perinova, A. Luks, and J. Perina, Phase in optics, (World Scientific, Singapore,
1998).
47. E. R. Pike and S. Sarkar, The quantum theory of radiation, (Clarendon Press, Oxford,
1995).
48. A. K. Prykarpatsky, U. Taneri, and N. N. Bogoliubov, Quantum Field Theory With
Application to Quantum Nonlinear Optics, (World Scientific, Singapore, 2002).
49. R. R. Puri, Mathematical Methods of Quantum Optics, (Springer, 2001).
50. W. P. Schleich, Quantum optics in phase space, (Wiley-VCH, Weinheim, 2001).
51. M. Schubert and B. Wilhelmi, Nonlinear Optics and Quantum Electronics, (John
Wiley & Sons, 1986).
52. M. O. Scully and M. S. Zubairy, Quantum Optics, (Cambridge University Press,
Cambridge, 1997).
53. M. Suda, Quantum Interferometry in Phase Space: Theory and Applications ,
(Springer, Berlin, 2006).
54. V. Vedral, Modern Foundations Of Quantum Optics, (Imperial COllege Press,
London, 2005).
55. W. Vogel and D. G. Welsch, Quantum Optics, 3rd ed., (Wiley-VCH, Weinberg,
2006).
56. D. F. Walls and G. J. Milburn, Quantum Optics, 2nd ed., (Springer, Berlin, 2008).
57. M. Weissbluth, Photon-atom interactions, (Academic Press, Boston, 1989).
58. Y. Yamamoto and A. Imamoglu, Mesoscopic quantum optics, (John Wiley & Sons,
New York, 1999).