Stratonovich solution of a quantum stochastic differential equation describing light emission and absorption

Abstract

We treat the quantum stochastic differential equation (*) U(t)=A(tU(t) with A(t)=AF(t)-A*F(t) where A is a complex d × d-matrix and F(t) white quantum noise. Its Stratonovich solution yields the quantum analogue of a process with independent stationary increments on the unitary group U(t). Light emission and absorption may be modelled as a two level atom in contact with a heatbath of quantum oscillators and may be described by (*) with d=2 and $A = \left( {\begin{array}{*{20}c}0 & { - i} \\0 & 0 \\\end{array} } \right)$. For a heatbath consisting of finitely many oscillators, F(t) is coloured quantum noise and (*) can easily be solved explicitly. If the heatbath gets infinite in an appropriate sense, F(t) approximates white quantum noise and the solution for the finite heatbath converges to the Stratonovich solution of (*) with white noise F(t).