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Optics Communications

The master equation for a two-level atom in a laser field with squeezing-like terms

A.‐S. F. Obada, S. Abdel‐Khalek, M. M. A. Ahmed, D. A. M. Abo-Kahla

Published Nov 28, 2008• 14 citations
Publisher
DOI
10.1016/j.optcom.2008.10.073

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If a broadband squeezed vacuum is treated as a reservoir with respect to a two-level atom, the non-zero phase-dependent reservoir correlation functions characterizing the squeezed vacuum introduce `squeezing terms' to the master equation. These terms are responsible, for example, for the well known narrowing of the spectral lines in the resonance fluorescence spectrum of the atom. For a squeezed vacuum reservoir with finite bandwidth it is possible to derive the master equation that is consistent with the Born-Markov approximation by a two-step procedure which consists in dressing the atom first and next coupling it to the finite-bandwidth reservoir. The master equation is valid whenever the bandwidth of the reservoir is much broader than the atomic linewidth but not necessarily broader than the Rabi frequency. This procedure can be applied not only for the squeezed vacuum reservoir but also for the ordinary vacuum with the structure of the mode density that is not flat, e.g., modelled by a Lorentzian function as in a cavity. The master equation for this case, in the operator form, shows some similarities to the master equation for the squeezed vacuum reservoir due to the presence of the `squeezing-like terms'. The similarities and differences of the two master equations are discussed in this paper.
On one hand a two-level atom is utilized as a qubit in quantum information technology and on the other hand the light in quantum optics is usually in the squeezed state. These reasons motivated us to explore the dynamic of a two-level atom which is driven by a field in the squeezed state. To this goal, the atom operators and the Heisenberg-Langevin equation have been employed. The master equation which reveals the dynamic of the atom has been derived using some features of the squeezed state and doing some algebra. Finally, the dynamic of the two-level atom which is driven by squeezed state field has been simulated by the derived master equation. Also, the effect of atom parameters on the dynamic has been investigated.