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arXiv:1001.1818 · Physical Review A

Quantum noise of a Bose-Einstein condensate in an optical cavity, correlations, and entanglement

Gergely Szirmai, D. Nagy, P. Domokos

Published Apr 29, 2010• 56 citations
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Abstract

A Bose-Einstein condensate of ultracold atoms inside the field of a laser-driven optical cavity exhibits dispersive optical bistability. We describe this system by using mean-field approximation and by analyzing the correlation functions of the linearized quantum fluctuations around the mean-field solution. The entanglement and the statistics of the atom-field quadratures are given in the stationary state. It is shown that the mean-field solution, that is, the Bose-Einstein condensate, is robust against entanglement generation for most of the phase diagram.

DOI
10.1103/physreva.81.043639

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A Bose-Einstein condensate of ultracold atoms inside the field of a laser-driven optical cavity exhibits dispersive optical bistability. We describe this system by using mean-field approximation and by analyzing the correlation functions of the linearized quantum fluctuations around the mean-field solution. The entanglement and the statistics of the atom-field quadratures are given in the stationary state. It is shown that the mean-field solution, that is, the Bose-Einstein condensate, is robust against entanglement generation for most of the phase diagram.
A system of low dimensional condensed ultracold atomic gases inside a field of a laser-driven optical cavity exhibits dispersive optical bistability. During such a process the system also shows quantum fluctuations. Condensate fluctuations are highly manifested particularly in low dimensional systems. In this paper we have investigated the theory and manifestation of fluctuations in quantum optical systems in low dimensional Bose-Einstein condensates. We have described the system using the mean-field approximation. In this study we have verified that low dimensional quantum gases exhibit not only highly fascinating properties but also we have indicated that the use of mean field theory to describe quantum gases in low dimensions is highly restricted since the possibility of generating low dimensional bosonic condensates is dominated by the existence of highly sensitive and intrinsic quantum fluctuations.
We theoretically investigate the dispersive interaction of a Bose-Einstein condensate (BEC) trapped inside an optomechanical cavity with a moving end mirror in the presence of the laser phase noise (LPN) as well as the atomic collisions. We assume that the effective frequency of the optical mode is much greater than those of the mechanical and the Bogoliubov modes of the movable mirror and the BEC. In the adiabatic approximation where the damping rate of the cavity is faster than those of the other modes, the system behaves as an effective two-mode model in which the atomic and mechanical modes are coupled to each other through the mediation of the optical field by an effective coupling parameter. We show that in the effective two-mode model, the LPN appears as a classical stochastic pump term which drives the amplitude quadratures of the mechanical and the Bogoliubov modes. It is also shown that a strong stationary mirror-atom entanglement can be established just in the dispersive and Doppler regimes where the two modes come into resonance with each other and the effect of the LPN gets very small.
We consider the model of a weakly driven optical cavity containing two clouds of atomic Bose–Einstein condensates (BECs). Nonclassical photon correlations and correlations between the two atomic BECs are investigated under different cavity conditions including strong atom-field coupling and bad cavity regime. We show that the nonlinear interatom collisional interactions in BEC leads to a significant loss of cavity light coherence. Various types of nonclassical properties are investigated such as sub-Poissonian statistics, antibunching and entanglement. We show that the entanglement can be generated between BECs and the cavity field. The time evolution of entanglement is also numerically studied.
We consider a two-component Bose–Einstein condensate in a one-dimensional optical cavity. Specifically, the condensate atoms are taken to be in two degenerate modes due to their internal hyperfine spin degrees of freedom and they are coupled to the cavity field and an external transverse laser field in a Raman scheme. A parallel laser also excites the cavity mode. When the pump laser is far detuned from its resonance atomic transition frequency, an effective nonlinear optical model of the cavity–condensate system is developed under the discrete mode approximation (DMA), while matter–field coupling has been considered beyond the rotating wave approximation. By analytical and numerical solutions of the nonlinear dynamical equations, we examine the mean cavity field and population difference (magnetization) of the condensate modes. The stationary solutions of both the mean cavity field and normalized magnetization demonstrate bistable behavior under certain conditions for the laser pump intensity and matter–field coupling strength.
We explore the quantum dynamics of photoassociation of Bose-Einstein condensed atoms into molecules using an optical cavity field. Inside of an optical resonator, photoassociation of quantum degenerate atoms involves the interaction of three coupled quantum fields for the atoms, molecules, and the photons. The feedback created by a high-QQQ optical cavity causes the cavity field to become a dynamical quantity whose behavior is linked in a nonlinear manner to the atoms inside and where vacuum fluctuations have a more important role than in free space. We develop and compare several methods for calculating the dynamics of the atom-molecule conversion process with a coherently driven cavity field. We first present an alternate operator representation for the Hamiltonian from which we derive an improved form of mean field theory and an approximate solution of the Heisenberg-Langevin (HL) equations that properly accounts for quantum noise in the cavity field. It is shown that our improved mean field theory corrects several deficiencies in traditional mean field theory based on expectation values of annihilation and creation operators. Also, we show by direct comparison to numerical solutions of the density matrix equations that our approximate quantum solution of HL equations gives an accurate description of weakly or undriven cavities where mean field theories break down.
‎We present a theoretical interacting one-dimensional Bose-Einstein condensate (BEC) inside an optical cavity which is driven through of the fixed end mirrors. Under the Bogoliubov approximation and when the number of photons inside the cavity is not too large, the atomic field operator can be considered as a single-mode quantum field which is coupled to the radiation pressure of the intracavity field. In this way, the system behaves like an optomechanical system with an extra nonlinear term corresponding to the atom-atom interaction.We show that one of the best ways of tracing the effect of atomic interaction is to study the noise power spectrum of the field of the cavity. For this purpose, we study the light intensity spectrum of the cavity as well as the entanglement between the optical cavity and the BEC. We show how the pattern of the power spectrum of the cavity changes due to the nonlinear effect of atomic collisions. Furthermore, it is shown that due to the s-wave scattering frequency of the atom-atom interaction, one can measure the strength of interatomic interaction. Besides, we show how the atomic collisions affect the entanglement between subsystems and cooling behavior of the BEC atoms.