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Journal of Optics B Quantum and Semiclassical Optics

Quantum manipulation of polaritonic band gaps of two coherently coupled Bose$ndash$Einstein condensates confined in an optical lattice

Aranya B. Bhattacherjee

Published Jun 19, 2002• 5 citations
Publisher

Abstract

A scheme is proposed to study and manipulate band gaps of an entangled coherent system composed of superposition of two atomic Bose–Einstein condensates (BECs) (corresponding to different internal sub-levels and different quantum statistics) and light fields moving in two different optical potentials. The band gaps are found to be a consequence of the periodic dielectric behaviour of the ground state BECs.

DOI
10.1088/1464-4266/4/5/304

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Quantum manipulation of polaritonic band gaps of two coherently coupled BosendashndashndashEinstein condensates confined in an optical lattice
A scheme is proposed to study and manipulate band gaps of an entangled coherent system composed of superposition of two atomic Bose–Einstein condensates (BECs) (corresponding to different internal sub-levels and different quantum statistics) and light fields moving in two different optical potentials. The band gaps are found to be a consequence of the periodic dielectric behaviour of the ground state BECs.
Summary form only given. Recent research is rapidly moving toward all-optical confinement of Bose-Einstein condensate (BEC) in optical traps. The optical trap provides an effective tool to manipulate the dynamics of BEC for practical purposes. In particular it opens the possibilities to study BEC in an optical lattice. In this work, we focus on studying the properties of propagation of a weak probe light through a BEC confined in an optical lattice. The key point in the topic is that the ground state of the lattice BEC acts as a periodic dielectric medium for the probe light propagating through it. We show that photonic, or rather polaritonic band gaps are created for probe light due to the spatial periodicity of the ground state of the lattice BEC. However being different from the ordinary periodic dielectric, the lattice BEC can experience elementary excitations which lead to a perturbative distortion of the periodicity of the lattice BEC. Such non-periodic perturbations are similar to lattice defects in solid state physics. Here they will produce defect states inside the photonic band gaps. By analyzing the elementary excitations of the lattice BEC, we study the frequency spectrum of photonic band gaps and defect states induced by such excitations in the lattice BEC. These photonic defect states may technically have the potential to be employed to acquire knowledge about the quantum degeneracy in an optical lattice.
We study the interaction of a Bose-Einstein condensate in an optical lattice with an additional largely detuned light field propagating through it. If the condensate is in its ground state it acts as a periodic dielectric, and gives rise to photonic band gaps at optical frequencies. The band structure of the combined system of condensed lattice atoms and photons is studied by using the concept of polaritons. If elementary excitations of the condensate are present, they will produce defect states inside the photonic band gaps. The frequency of localized defect states is calculated using the Koster-Slater model.
An extended Bose-Einstein condensate (BEC) in an optical lattice provides a kind of periodic dielectric and causes band gaps to occur in the spectrum of light propagating through it. We examine the question whether these band gaps can modify the spontaneous emission rate of atoms excited from the BEC, and whether they can lead to a self-stabilization of the BEC against spontaneous emission. We find that self-stabilization is not possible for BECs with a density in the order of 10 14 cm −3. However, the corresponding non-Markovian behavior produces significant effects in the decay of excited atoms even for a homogeneous BEC interacting with a weak laser beam. These effects are caused by the occurrence of an avoided crossing in the photon (or rather polariton) spectrum. We also predict a new channel for spontaneous decay which arises from an interference between periodically excited atoms and periodic photon modes. This new channel should also occur in ordinary periodic dielectrics. 1
We overview our recent theoretical studies on nonlinear atom optics of the Bose-Einstein condensates (BECs) loaded into optical lattices. In particular, we describe the band-gap spectrum and nonlinear localization of BECs in one- and two-dimensional optical lattices. We discuss the structure and stability properties of spatially localized states (matter-wave solitons) in 1D lattices, as well as trivial and vortex-like bound states of 2D gap solitons. To highlight similarities between the behavior of coherent light and matter waves in periodic potentials, we draw useful parallels with the physics of coherent light waves in nonlinear photonic crystals and optically-induced photonic lattices.
We analyze the existence and stability of spatially extended (Bloch-type) and localized states of a Bose-Einstein condensate loaded into an optical lattice. In the framework of the Gross-Pitaevskii equation with a periodic potential, we study the band-gap structure of the matter-wave spectrum in both the linear and nonlinear regimes. We demonstrate the existence of families of spatially localized matter-wave gap solitons, and analyze their stability in different band gaps, for both repulsive and attractive atomic interactions.