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arXiv:1108.2322 · International Journal of Geometric Methods in Modern Physics

AN APPROXIMATE SOLUTION OF THE JAYNES–CUMMINGS MODEL WITH DISSIPATION II: ANOTHER APPROACH

Kazuyuki Fujii, Tatsuo Suzuki

Published Apr 24, 2012• 10 citations
arXivHTMLPDF

Abstract

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.

DOI
10.1142/s0219887812500363

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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.
Completely solving the dissipative dynamics of nonlinear Jaynes–Cumming model is a very difficult task. In our recent work (Phys. Lett. A284 (2001) 156), we just obtained analytical results of the field dissipative dynamics of the nonlinear JCM. In the present paper, employing the perturbative expansion of master equation, we obtain the density operator of the system (field +atom). The coherence losses of the system and of the atom are investigated when two-photon process is involved. We also study the effect of different atomic initial states and the influence of the field amplitude on the atomic coherence loss.
Completely solving the dissipative dynamics of nonlinear Jaynes-Cumming model is a very difficult task. In our recent work(Phys.Lett.A284(2001)156),we just obtained analytical results of the field dissipative dynamics of the nonlinear JCM.In the present paper,employing the perturbative expansion of master equation,we obtain the density operator of the system(field+atom).The coherence losses of the system and of the atom are investigated when two-photon process is involved.We also study the effect of different atomic initial states and the influence of the field amplitude on the atomic coherence loss.