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arXiv:1103.0329 · International Journal of Geometric Methods in Modern Physics

AN APPROXIMATE SOLUTION OF THE JAYNES–CUMMINGS MODEL WITH DISSIPATION

Kazuyuki Fujii, Tatsuo Suzuki

Published Dec 1, 2011• 13 citations
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Abstract

In this paper we treat the Jaynes–Cummings model with dissipation and give an approximate solution to the master equation for the density operator under the general setting by making use of the Zassenhaus expansion.
DOI
10.1142/s0219887811005944

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Modern Physics Letters B•Aug 30, 1996•0 citations
In the preceding paper (arXiv: 1103.0329 [quant-ph]) we treated the Jaynes–Cummings model with dissipation and gave an approximate solution to the master equation for the density operator under the general setting by making use of the Zassenhaus expansion. However, to obtain a compact form of the approximate solution (which is in general complicated infinite series) is very hard when an initial condition is given. To overcome this difficulty we develop another approach and obtain a compact approximate solution when some initial condition is given.
We present a simple exactly solvable extension of of the Jaynes-Cummings model by adding dissipation. This is done such that the total number of excitations is conserved. The Liouville operator in the resulting master equation can be reduced to blocks of 4×44\times 44×4 matrices.
In the present paper a new technique for treating relaxation processes, based on the author’s self-consistent projection-operator method, is developed. This new technique, which yields (instead of a master equation for a reduced density operator) equations of motion for probability amplitudes for a reduced set of states of the total system, opens a new way for treating relaxation processes. The applicability of the new method is demonstrated in the case of a damped harmonic oscillator and in that of the Jaynes-Cummings model with cavity losses.