Spontaneous emission and scattering in a two-atom system: Conservation of probability and energy

Physical Review A - Atomic, Molecular, and Optical Physics

Volumn 76, Issue 4, 2007, Pages

  Berman, P R ^a  

^a UNIVERSITY OF MICHIGAN   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

ATOMS; ENERGY ABSORPTION; PROBABILITY; RADIATION; SCATTERING;

EXPLICIT CALCULATION; RESCATTERING; SOURCE ATOM; WEISSKOPF WIGNER APPROXIMATION;

SPONTANEOUS EMISSION;

EID: 35248885760     PISSN: 10502947     EISSN: 10941622     Source Type: Journal    
DOI: 10.1103/PhysRevA.76.043816     Document Type: Article

References (22)

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20. In considering the field emitted by an atomic dipole, one can justify extension of the frequency integral to minus infinity by including non-energy-conserving terms in the calculation. The resulting integrals are perfectly convergent and lead to expressions for the average field that take the same form as the classical results. Thus, no Weisskopf-Wigner approximation is needed to obtain expressions for the field in terms of the dipole operator and its derivatives-see, for example, P. R. Berman, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.69.022101 69, 022101 (2004), and references therein.
21. If the atom is excited "instantaneously," one can question the use of the adiabatic hypothesis. To avoid such problems, one can assume that the source atom is excited to its initial state by an optical pulse whose duration is much longer than |Δ| -1. The pulse duration is also assumed to be much shorter than γ-1, enabling one to neglect any radiation during the excitation pulse. The only property of b 2,0 (0) (t) used in this paper is that it is real and this property is in no way restrictive.
22. In both Eqs. 44 45 one encounters terms of the form t′ 0t d t″ δ (t′ - t″) b2,0 (t″) = t′ [b2,0 (t′) Θ (t- t′) Θ (t′)] =Θ (t- t′) Θ (t′) t′ b2,0 (t′) - b2,0 (t) δ (t- t′) Θ (t′) + b2,0 (0) Θ (t- t′) δ (t′). It can be shown, however, that if one simply sets t′ 0t d t″ δ (t′ - t″) b2,0 (t″) = t′ b2,0 (t′) in Eqs. 44 45 as I have done, the final results are the same that are obtained using the complete expression for the time derivatives of the integrals.