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Communications in Theoretical Physics

Dynamics of Bose-Einstein Condensed and Excited Atoms in a Quantized Cavity

Yi Xue-Xi, Sun Changpu

Published Oct 30, 1997• 1 citation
Publisher

Abstract

The dynamics of the Bose–Einstein condensed and excited atoms in a cavity interacting with quantized electromagnetic field of single mode is studied for both the cases with and without dissipation. It is shown that the frequencies of oscillation between the condensed atomic state and an excited state are related to the number of Bose–Einstein condensed atom in a certain form. This relation may be used for the reliable detection of the appearance of the Bose–Einstein condensate.

DOI
10.1088/0253-6102/28/3/359

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The dynamics of the Bose–Einstein condensed and excited atoms in a cavity interacting with quantized electromagnetic field of single mode is studied for both the cases with and without dissipation. It is shown that the frequencies of oscillation between the condensed atomic state and an excited state are related to the number of Bose–Einstein condensed atom in a certain form. This relation may be used for the reliable detection of the appearance of the Bose–Einstein condensate.
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Abstract In this paper we consider a system consisting of a number of two-level atoms in a Bose–Einstein condensate (BEC) and a single-mode quantized field, which interact with each other in the presence of two different damping sources, i.e. cavity and atomic reservoirs. The reservoirs which we consider here are thermal and squeezed vacuum ones corresponding to field and atom modes. Strictly speaking, by considering both types of reservoirs for each of the atom and field modes, we investigate the quantum dynamics of the interacting bosons in the system. Then, via solving the quantum Langevin equations for such a dissipative BEC system, we obtain analytical expressions for the time dependence of atomic population inversion, mean atom as well as photon number and quadrature squeezing in the field and atom modes. Our investigations demonstrate that for modeling the real physical systems, considering the dissipation effects is essential. Also, numerical calculations which are presented show that the atomic population inversion, the mean number of atoms in the BEC and the photons in the cavity possess damped oscillatory behavior due to the presence of reservoirs. In addition, non-classical squeezing effects in the field quadrature can be observed especially when squeezed vacuum reservoirs are taken into account. As an outstanding property of this model, we may refer to the fact that one can extract the atom–field coupling constant from the frequency of oscillations in the mentioned quantities such as atomic population inversion.
We study the dynamics of weakly interacting Bose-Einstein condensates consisting of alkali atoms with two or more internal eigenstates. Three separate problems are examined in this thesis, which look at the behavior of the condensates in the presence of electromagnetic fields, which couple the internal states of the atoms. First, we examine the ground state and quasiparticle excitations for a condensate with a spatially uniform and time independent field, which couples two of the internal states. In particular, we address the nature of the instabilities that have been predicted in these systems. Second, we look at the time evolution of small condensates with a time dependent field, which couples two states. It is shown that the atomic population in the two components, as a function of time, is very different for a condensate with a precisely defined number of atoms and one that exhibits spontaneous symmetry breaking. Finally, we propose two methods for mapping information about the quantum state of the condensate to a mode of an electromagnetic cavity. The first method, which is irreversible, is only able to transfer the population statistics of the condensate to the cavity field. The second method involves the adiabatic transfer of the quantum state of the condensate to the cavity field.
We study the zero-temperature dynamics of Bose-Einstein condensates in driven high-quality optical cavities in the limit of large atom-field detuning in a one-dimensional model. We calculate the stationary ground state and the spectrum of coupled atom and field mode excitations for standing-wave cavities as well as for traveling-wave cavities. Finite cavity response times lead to damping or controlled amplification of these excitations. Analytic solutions in the Lamb-Dicke expansion are in good agreement with numerical results for the full problem and show that oscillation frequencies and the corresponding damping rates are qualitatively different for the two cases.
The spectrum shape of atomic radiation in the case of ideal Bose–Einstein condensate (BEC) excited by quantized light is derived through the Wigner–Weisskopf approximation. Besides the split and gap in the excitation spectrum, a doublet structure appears in the emission spectrum with different widths for the non-resonant case and the same widths for the resonant case. The survival probability is found to decrease exponentially for the non-resonant case and with oscillation for the resonant case. A suppressed radiation also appears in the non-resonant case. All these results can be used to detect the existence of BE condensation.