Spontaneous emission of a two-level system and the influence of the rotating-wave approximation on the final state. I
By using a modified Robertson projection technique an exact equation of motion for the expectation value of the population inversion operatorS z of a single two-level atom in the case of spontaneous emission is derived. Afterwards, by making the Markov approximation, it is shown that the ground state expectation value〈S z 〉 t =− 1/2 fort→∞ will be reached only if the rotating-wave approximation or the Born approximation is made additionally.
Key wordsQuantum statistical mechanics of open systems spontaneous emission two-level atom modified Robertson projection technique Markov approximation rotating-wave approximation
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- 1.M. Sargent III, M. O. Scully, and W. E. Lamb, Jr.,Laser Physics (Addison-Wesley, Reading, Massachusetts, 1974).Google Scholar
- 2.L. Allen and J. H. Eberly,Optical Resonance and Two-Level Atoms (Wiley, New York, 1975).Google Scholar
- 3.G. S. Agarwal,Springer Tracts in Modern Physics No. 70 (Springer, Berlin, 1974).Google Scholar
- 4.P. L. Knight and P. W. Milonni,Phys. Lett. 56A:275 (1976); P. Carrazana and G. Vetri,Nuovo Cimento 55B:191 (1980).Google Scholar
- 5.V. F. Weisskopf and E. P. Wigner,Z. Phys. 63:54 (1930),65:18 (1930).Google Scholar
- 6.B. Robertson,Phys. Rev. 144:151 (1966).Google Scholar
- 7.J. Seke,Phys. Rev. A 21:2156 (1980).Google Scholar
- 8.G. Adam and J. Seke,Phys. Rev. A 23:3118 (1981).Google Scholar
- 9.N. S. Krylov and V. A. Fock,Zh. Eksp. Teor. Fiz. 17:93 (1947).Google Scholar
- 10.L. A. Khalfin,Zh. Eksp. Teor. Fiz. 33:1371 (1957) [Sov. Phys. JETP 6:1053 (1958)];Google Scholar
- 10a.L. Fonda, G. C. Ghirardi, and A. Rimini,Rep. Prog. Phys. 41:587 (1978).Google Scholar