Quantum—Classical Correspondence for Two-Level Atoms
After our brief diversion we now return to the theme of Chaps. 3 and 4, namely, the transformation of an operator description for a quantum-optical system into the language of classical statistics. So far we have met methods that accomplish this task for systems described entirely in terms of harmonic oscillator creation and annihilation operators. At least we have seen that a Fokker-Planck equation description is possible for the damped harmonic oscillator, in a variety of versions defined by representations based on different operator orderings. We noted also that there is no guarantee that a system of interacting bosons can be described using a Fokker-Planck equation; although, as attested to by the example of the laser (Chap. 8), there are certainly nontrivial examples that can. The methods used to derive phase-space equations for systems of bosons can be generalized to the treatment of two-level atoms, or more generally, multi-level atomic systems. We now develop the representation for atomic states that is needed for our treatment of the laser.
Unable to display preview. Download preview PDF.
- 6.2H. Haken: Handbuch der Physik, Vol. XXV/2c, ed. by L. Genzel ( Springer-Verlag, Berlin, 1970 ) pp. 64–65Google Scholar
- 6.3W. H. Louisell: Quantum Statistical Properties of Radiation ( Wiley, New York, 1973 ) pp. 375–390Google Scholar
- 6.4C. W. Gardiner: Handbook of Stochastic Methods for Physics, Chemistry and the Natural Sciences (Springer-Verlag, Berlin, 1983) pp. 78, 79, 402Google Scholar
- 6.5A. Einstein: Phys. Z. 18, 121 (1917)Google Scholar
- 6.6M. Sargent III, M. O. Scully, and W. E. Lamb, Jr.: Laser Physics (Addison-Wesley, Reading, Massachusetts, 1974 ) pp. 20–23Google Scholar
- 6.8Min Xiao, H. J. Kimble, and H. J. Carmichael: J. Opt. Soc. Am. B 4, 1546 (1987)Google Scholar
- 6.10G. S. Agarwal: “Quantum Statistical Theories of Spontaneous Emission and their Relation to Other Approaches,” Springer Tracts in Modern Physics, Vol. 70 ( Springer-Verlag, Berlin, 1974 ) pp. 73–83Google Scholar
- 6.11H. J. Carmichael: J. Phys. B 13, 3551 (1980); Phys. Rev. Lett. 43, 1106 (1979)Google Scholar
- 6.17F. Haake and R. J. Glauber: Phys. Rev. A 5, 1457 (1972); Phys. Rev. A 13, 357 (1976)Google Scholar
- 6.22Reference [6.10] pp. 25–38Google Scholar