Analytic solutions for degenerate Raman-coupled model
Zhang Zhi-Ming(张智明)† and Yu Ya-Fei(於亚飞)
Laboratory of Photonic Information Technology, School of Information and Photoelectronic Science & Engineering, South China Normal University, Guangzhou 510006, China
Abstract The Raman-coupled interaction between an atom and a single mode of a cavity field is studied. For the cases in which a light field is initially in a coherent state and in a thermal state separately, we have derived the analytic expressions for the time evolutions of atomic population difference $W$, modulus $B$ of the Bloch vector, and entropy $E$. We find that the time evolutions of these quantities are periodic with a period of $\pi $. The maxima of $W$ and $B$ appear at the scaled interaction time points $\tau = k\pi (k = 0,1,2,\ldots)$. At these time points, $E = 0$, which shows that the atom and the field are not entangled. Between these time points, $E \ne 0$, which means that the atom and the field are entangled. When the field is initially in a coherent state, near the maxima, the envelope of $W$ is a Gaussian function with a variance of $1 /{\left( {4\bar {n}} \right)}$ ($\bar {n}$ is the mean number of photons). Under the envelope, $W$ oscillates at a frequency of $\bar {n} / \pi $. When the field is initially in a thermal state, near the maxima, $W$ is a Lorentz function with a width of $1/ \bar {n}$.
Received: 28 June 2007
Revised: 14 August 2007
Accepted manuscript online:
PACS:
42.50.Ar
Fund: Project
supported by the National Natural Science Foundation of
China (Grant Nos 60578055 and 10404007).
Cite this article:
Zhang Zhi-Ming(张智明) and Yu Ya-Fei(於亚飞) Analytic solutions for degenerate Raman-coupled model 2008 Chin. Phys. B 17 1242
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