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arXiv:cond-mat/0503041 · Physical Review Letters

Photonic Band Gap via Quantum Coherence in Vortex Lattices of Bose-Einstein Condensates

Özgür Esat Müstecaplıoğlu, Mehmet Özgür Oktel

Published Jun 8, 2005• 6 citations
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Abstract

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.

DOI
10.1103/physrevlett.94.220404

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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.
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.
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.
If the electromagnetic waves are scattered by the periodic structure of media with different refractive indexes, a band gap in the transmitted spectrum can be generated. This is the photonic crystal whose band gap is usually uncontrollable as its structure parameters are fixed after the fabrication. Alternatively, based on the quantum theory in real space for single photons transporting along a one-dimensional waveguide embed by a series of two-level atoms, we propose here a quantum mechanical configuration to implement the photonic crystal with adjustable band gap. It is shown that if the scattering two-level atoms are arranged as a periodic array, the desirable band gap in the photonic transmission spectrum can be formed. This is the atomic-type photonic crystal, in which the center frequency of the gap can be controlled by adjusting the eigenfrequencies of the atoms. The possible physical implementations of our proposal with the voltage-biased superconducting qubits for the centimeter waves and the voltage-biased electrons on liquid helium for the millimeter waves are also discussed.