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Quantum Electronics and Laser Science Conference

Effects due to the local fields and the phonons in atomic Bose-Einstein condensates: polariton approach

G.J. Uanas, H. J. Carmichael

Published Nov 13, 2002• 0 citations
Publisher

Abstract

Summary form only given. The observation of atomic Bose-Einstein condensates (BECs) in magnetic and optical traps has stimulated theoretical investigation of the optical properties of these systems. Many of the current theories are based on the Heisenberg equations of motion for the radiation field and matter. These equations are nonlinear in the field operators and lead to an infinite hierarchy of equations for the atomic correlation functions. The hierarchy can be decoupled using an approximation. In an alternative development, the Heisenberg equations of motion have been simplified using an adiabatic approximation to eliminate the excited-state field operator. While some previous studies of BECs have employed the polariton approach, in these treatments neither the local field effects nor the polariton-phonon coupling are taken into account. Local field effects play an important role in a dense Bose gas (/spl rho//sup I/3//spl lambda//spl Lt/1) where, due to the resonance dipole-dipole interaction,the atoms respond to the electromagnetic field in a collective manner.In this contribution we examine the effects of both the local field and phonons using the polariton approach. The analysis is based on the quasiparticle concept.

DOI
10.1109/qels.2001.962207

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Summary form only given. The observation of atomic Bose-Einstein condensates (BECs) in magnetic and optical traps has stimulated theoretical investigation of the optical properties of these systems. Many of the current theories are based on the Heisenberg equations of motion for the radiation field and matter. These equations are nonlinear in the field operators and lead to an infinite hierarchy of equations for the atomic correlation functions. The hierarchy can be decoupled using an approximation. In an alternative development, the Heisenberg equations of motion have been simplified using an adiabatic approximation to eliminate the excited-state field operator. While some previous studies of BECs have employed the polariton approach, in these treatments neither the local field effects nor the polariton-phonon coupling are taken into account. Local field effects play an important role in a dense Bose gas (/spl rho//sup I/3//spl lambda//spl Lt/1) where, due to the resonance dipole-dipole interaction,the atoms respond to the electromagnetic field in a collective manner.In this contribution we examine the effects of both the local field and phonons using the polariton approach. The analysis is based on the quasiparticle concept.
The propagation of the electromagnetic field of a laser through a dense Bose gas is examined and nonlinear operator equations for the motion of the center of mass of the atoms are derived. The goal is to present a self-consistent set of coupled Maxwell-Bloch equations for atomic and electromagnetic fields generalized to include the atomic center-of-mass motion. Two effects are considered. The ultracold gas forms a medium for the Maxwell field which modifies its propagation properties. Combined herewith is the influence of the dipole-dipole interaction between atoms which leads to a density-dependent shift of the atomic transition frequency. It is expressed in a position-dependent detuning and is the reason for the nonlinearity. This results in a direct and physically transparent way from the quantum field-theoretical version of the local-field approach to electrodynamics in quantum media. The equations for the matter fields are general. Previously published nonlinear equations are obtained as limiting cases. As an atom-optical application the scattering of a dense beam of a Bose gas is studied in the Raman-Nath regime. The main conclusion is that for increasing density of the gas the dipole-dipole interaction suppresses or enhances the scattering depending on the sign of the detuning.
We have developed the quantum theory of the interaction of ultracold atomic ensemble with the electromagnetic field of vacuum and laser photons. The main attention is paid to the consistent consideration of dynamical dipole-dipole interactions in the case of the second quantized matter. We show that the retardation effects significantly influence the behavior of atomic ensemble in the radiation field. We have derived the general system of equations, which can be used for the investigation of various linear and nonlinear phenomena in atom optics. As an example, we have considered the diffraction of ultracold atomic beam by the standard laser wave. We show that with the increase of the initial density of the intensities of diffractions modes decrease. We also show that the angles of diffraction for different modes depend on the density.
Summary form only given. The dynamics of a medium consisting of a dense collection of two-level atoms interacting via the electromagnetic field has been derived from first principles. In dense media and condensed matter, the microscopic local field that couples with a single atom is related to the macroscopic field and volume propagation by the Lorentz-Lorenz relation written for an isotropic homogeneous medium. The dynamical equations for the medium, coupled self-consistently with the Maxwell inhomogeneous wave equation, are given in the rotating wave and dipole coupling approximations. The microscopic development is used within the framework of full quantization, and the explicit effects of spontaneous relaxation for the host as well as the atoms are treated, together with corresponding fluctuations. Particular effects upon intrinsic adiabatic inversion, self-induced transparency, and lasing without inversion, are presented and discussed. In particular, the equilibrium, stationary, and dynamical effects of the host medium, and medium and field fluctuations upon local field effects are discussed.
Starting from the first principles of nonrelativistic QED we have developed the quantum theory of the interaction of a two-component ultracold atomic ensemble with the electromagnetic field of vacuum and laser photons. The main attention has been paid to the consistent consideration of dynamical dipole-dipole interactions in the radiation field. Taking into account local-field effects we have derived the system of Maxwell-Bloch equations. Optical properties of the two-component Bose gas are investigated. It is shown that the refractive index of the gas is given by the Maxwell-Garnett formula. All equations which are used up to now for the description of the behavior of an ultracold atomic ensemble in a radiation field can be obtained from our general system of equations in the low-density limit. Raman-Nath diffraction of the two-component atomic beam is investigated on the basis of our general system of equations.
The effect of Bose-Einstein condensation, achieved recently for alkaline gases in magnetic traps, should lead to a strong enhancement of non-linear harmonic generation. A nearly resonant light imposed on the gas of two-level atoms excites the intra-atomic transitions and causes generation of various harmonics. Normally, in the thermal state of the gas, a contribution of the inter-atomic interaction to the non-linear harmonic generation is negligible. However, if a Bose-Einstein condensate (BEC) is present, the inter-particle interaction cannot be ignored. Considering second harmonic generation, we show that, in the presence of the BEC, the intensity of the second harmonic is proportional to (aN n)/sup 2/, where N and n are the total number and the effective density of the condensed atoms, respectively, and a stands for the scattering length describing the process of scattering of two excited atoms by each other so that, after the collision, one excited atom enters the condensate. We consider the interaction between light, represented by the electric field E, and the atomic Bose field /spl Psi/ as well as the two body interaction treated within the scattering length approximation.
We investigate the ground state (GS) of a collisionless Bose-Einstein condensate (BEC) trapped in a soft one-dimensional optical lattice (OL), which is formed by two counterpropagating optical beams perturbed by the BEC density profile through the local-field effect (LFE). We show that LFE gives rise to an envelope-deformation potential, a nonlocal potential resulting from the phase deformation, and an effective self-interaction of the condensate. As a result, stable photon-atomic (polaritonic) lattice solitons, including an optical component, in the form of the deformation of the soft OL, in a combination with a localized matter-wave component, are generated in the blue-detuned setting, without any direct interaction between atoms. These self-trapped modes, which realize the system's GS, are essentially different from the gap solitons supported by the interplay of the OL potential and collisional interactions between atoms. A transition to tightly bound modes from loosely bound ones occurs with the increase of the number of atoms in the BEC.