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Laser Physics

Vortex lattice of a Bose-Einstein condensate as a photonic band gap material

Mehmet Emre Taşgın, Özgür Esat Müstecaplıoğlu, Mehmet Özgür Oktel

Published Apr 1, 2009• 0 citations
Publisher

Abstract

Photonic crystal behavior of a rotating Bose-Einstein condensate with a triangular vortex lattice is reviewed and a scheme for getting much wider band gaps is proposed. It is shown that photonic band gaps can be widened an order of magnitude more by using a Raman scheme of index enhancement, in comparison to previously considered upper level microwave scheme.

DOI
10.1134/s1054660x09040197

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Photonic crystal behavior of a rotating Bose-Einstein condensate with a triangular vortex lattice is reviewed and a scheme for getting much wider band gaps is proposed. It is shown that photonic band gaps can be widened an order of magnitude more by using a Raman scheme of index enhancement, in comparison to previously considered upper level microwave scheme.
We investigate the optical response of an atomic Bose-Einstein condensate with a vortex lattice. We find that it is possible for the vortex lattice to act as a photonic crystal and create photonic band gaps, by enhancing the refractive index of the condensate via a quantum coherent scheme. If high enough index contrast between the vortex core and the atomic sample is achieved, a photonic band gap arises depending on the healing length and the lattice spacing. A wide range of experimentally accessible parameters are examined and band gaps in the visible region of the electromagnetic spectrum are found. We also show how directional band gaps can be used to directly measure the rotation frequency of the condensate.
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.
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 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.
Quantum manipulation of polaritonic band gaps of two coherently coupled BosendashndashndashEinstein condensates confined in an optical lattice