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arXiv:1205.3063 · Physical Review A

Bose-Einstein condensation for trapped atomic polaritons in a biconical waveguide cavity

Igor Yu. Chestnov, A. P. Alodjants, Sergei M Arakelyan, Jan Klaers, Frank Vewinger, Martin Weitz

Published May 31, 2012• 11 citations
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Abstract

We study the problem of high-temperature Bose-Einstein condensation (BEC) of atom-light polaritons in a waveguide cavity appearing due to the interaction of two-level atoms with (nonresonant) quantized optical radiation in the strong-coupling regime and in the presence of optical collisions (OCs) with buffer-gas particles. Specifically, we propose a special biconical waveguide cavity (BWC), permitting localization and trapping of low-branch (LB) polaritons imposed by the variation of the waveguide radius in longitudinal direction. We have shown that the critical temperature of BEC occurring in the system can be high enough---a few hundred kelvins; it is connected with the photonlike character of LB polaritons and strongly depends on waveguide-cavity parameters. In the case of a linear trapping potential we obtain an Airy-shaped polariton condensate wave function which, when disturbed out of equilibrium, exhibits small-amplitude oscillations with the characteristic period in the picosecond domain.

DOI
10.1103/physreva.85.053648

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We study the problem of high-temperature Bose-Einstein condensation (BEC) of atom-light polaritons in a waveguide cavity appearing due to the interaction of two-level atoms with (nonresonant) quantized optical radiation in the strong-coupling regime and in the presence of optical collisions (OCs) with buffer-gas particles. Specifically, we propose a special biconical waveguide cavity (BWC), permitting localization and trapping of low-branch (LB) polaritons imposed by the variation of the waveguide radius in longitudinal direction. We have shown that the critical temperature of BEC occurring in the system can be high enough---a few hundred kelvins; it is connected with the photonlike character of LB polaritons and strongly depends on waveguide-cavity parameters. In the case of a linear trapping potential we obtain an Airy-shaped polariton condensate wave function which, when disturbed out of equilibrium, exhibits small-amplitude oscillations with the characteristic period in the picosecond domain.
We propose a method for obtaining a Bose-Einstein condensate of an ideal one-dimensional gas of atom-light polaritons of the lower branch in a trap at high temperatures (on the order of room temperature or higher). The system under consideration is an atomic ensemble that interacts with a single-mode quantum electromagnetic field in the presence of optical collisions with a high-pressure buffer gas. The possibility of using biconical waveguides for revealing the predicted phenomenon is discussed. The dynamics of the polariton condensate in the trap is investigated on the basis of the variational approach.
The problem of photonic phase transition for the system of a two-level atomic ensemble interacting with a quantized single-mode electromagnetic field in the presence of optical collisions (OCs) is considered. We have shown that for large and negative atom-field detuning a photonic field exhibits high-temperature second-order phase transition to superradiant state under thermalization condition for coupled atom-light states. Such a transition can be connected with superfluid (coherent) properties of photonlike low branch (LB) polaritons. We discuss the application of metallic cylindrical waveguide for observing predicted effects.
We present a theoretical description of Bogolyubov-type excitations of exciton-polariton Bose-Einstein condensates (BECs) in semiconductor microcavities. For a typical two-dimensional (2D) BEC we focus on two limiting cases, the weak- and strong-coupling regimes, where a perturbation theory and the Thomas-Fermi approximation, respectively, are valid. We calculate integrated scattering intensity spectra for probing the collective excitations of the condensate in both considered limits. Moreover, in relation to recent experiments on optical modulation allowing localization of condensates in a trap with well-controlled shape and dimensions, we study the quasi-one-dimensional (1D) motion of the BEC in microwires and report the corresponding Bogolyubov excitation spectrum. We show that in the 1D case the characteristic polariton-polariton interaction constant is expressed as ${g}_{1}=3\ensuremath{\lambda}\mathcal{N}/(2{L}_{y})$ ($\ensuremath{\lambda}$ is the 2D polariton-polariton interaction parameter in the cavity, N\mathcal{N}N the number of the particles, and Ly{L}_{y}Ly​ the wire cavity width). We reveal some interesting features for 2D and 1D Bogolyubov spectra for both repulsive $(\ensuremath{\lambda}>0)$ and attractive $(\ensuremath{\lambda}<0)$ interactions.
A quantum model of Bose-Einstein condensation based on processes involving polaritons excited in an intracavity absorbing cell with resonance atoms, which is manifested in the spectral characteristics of the system, is considered. It is shown that the spectral 'condensation' appears which is directly related to the degeneracy of a weakly interacting gas of polaritons resulting in quasi-condensation at room temperature. The possibility of obtaining polariton condensation as a new phase state by using the confinement of polaritons in an atomic optical harmonic trap is discussed.
Bose-Einstein condensation has in the last two decades been observed in cold atomic gases and in solid-state physics quasiparticles, exciton-polaritons and magnons, respectively. The perhaps most widely known example of a bosonic gas, photons in blackbody radiation, however exhibits no Bose-Einstein condensation, because the particle number is not conserved and at low temperatures the photons disappear in the system’s walls instead of massively occupying the cavity ground mode. This is not the case in a small optical cavity, with a low-frequency cutoff imprinting a spectrum of photon energies restricted to values well above the thermal energy. The here reported experiments are based on a microscopic optical cavity filled with dye solution at room temperature. Recent experiments of our group observing Bose-Einstein condensation of photons in such a setup are described. Moreover, we discuss some possible applications of photon condensates to realize quantum manybody states in periodic photonic lattices and photonic Josephson devices.
The experimental realization of Bose-Einstein condensation (BEC) with atoms and quasiparticles has triggered wide exploration of macroscopic quantum effects.Microcavity polaritons are of particular interest because quantum phenomena such as BEC and superfluidity can be observed at elevated temperatures.However, polariton lifetimes are typically too short to permit thermal equilibration.This has led to debate about whether polariton condensation is intrinsically a nonequilibrium effect.Here we report the first unambiguous observation of BEC of optically trapped polaritons in thermal equilibrium in a high-Q microcavity, evidenced by equilibrium Bose-Einstein distributions over broad ranges of polariton densities and bath temperatures.With thermal equilibrium established, we verify that polariton condensation is a phase transition with a well-defined density-temperature phase diagram.The measured phase boundary agrees well with the predictions of basic quantum gas theory.