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arXiv:1311.3848

Dynamics of several two-level atoms in a one-mode cavity

P. Schwendimann, A. Quattropani

Published Nov 15, 2013• 0 citations
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Abstract

The dynamics of few two-level atoms interacting with one cavity mode is described in master equation formalism. Two different configurations are considered: a transient one with all atoms initially in the excited state and a stationary one where a coherent pump acts on either the atoms or the cavity mode. Superradiance, resonant scattering and switching between a low and a high emission state are considered. Cooperation and decoherence as well as the statistics of the emitted radiation field in both cases are discussed.

DOI
10.48550/arxiv.1311.3848

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The dynamics of few two-level atoms interacting with one cavity mode is described in master equation formalism. Two different configurations are considered: a transient one with all atoms initially in the excited state and a stationary one where a coherent pump acts on either the atoms or the cavity mode. Superradiance, resonant scattering and switching between a low and a high emission state are considered. Cooperation and decoherence as well as the statistics of the emitted radiation field in both cases are discussed.
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The interaction is considered between NNN stationary two-level atoms and a radiation field described by a single cavity mode. The state vector for the complete system of atoms plus radiation is expressed as a linear superposition of states constructed from a product of photon states in the nnn representation and products of Pauli spin eigenstates describing all combinations of atoms in the lower and upper energy levels. Equations for the corresponding probability amplitudes are derived by substituting this superposition into the Schr\"odinger equation. The resulting equations are combined into bilinear form and phenomenological damping contributions are added. After the neglect of certain of the bilinear quantities, a master equation is derived which governs the probability Pmn{{P}_{m}}^{n}Pm​n of having mmm atoms in the lower level and nnn photons in the mode. This master equation takes account of multiple single-quantum absorption and emission processes but not of simultaneous multiple processes involving two or more atoms at a time. The equation which governs the expected number of photons 〈n〉〈n〉〈n〉 derived from the master equation bears a close resemblance to a rate equation. The effect of radiation loss from the cavity is incorporated into the master equation. Numerical calculations for a QQQ-spoiled laser show that the statistics of the number of photons in the mode bear a qualitative resemblance to Poisson statistics.
An exact solution for the problem of two two-level atoms interacting with a single-mode detuned quantized radiation field is presented. On resonance, an asymptotic result is derived for large coherent initial fields. It is shown that when the atoms are initially prepared in one of the semiclassical eigenstates, the atom-plus-field wavefunction remains almost factored into an atomic and a field part throughout the interaction. Under certain conditions, the atomic part evolves into a unique pure state at half-revival time. The effects of the cavity detuning on the dynamics of the atomic level occupation probabilities and emission spectra are studied. It is found, for non-symmetrical excitation, that far off-resonance the field acts like a virtual level by means of which the energy is transferred between the atoms. Due to non-zero detuning, nine-peaked spectra are observed and are given a clear explanation from the dressed-state viewpoint. It is established that in the case of symmetrical excitation, the intensity of the emission spectrum is two times larger than that in the case of non-symmetrical excitation.