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Slow and Fast Light (SL)

Stationary light and Bose-Einstein Condensation of Slow-Light Polaritons

Michael Fleischhauer, Johannes Otterbach, Razmik G. Unanyan

Published Jan 1, 2008• 0 citations
Publisher

Abstract

The generation of stationary distributions of light with three-dimensional confinement is discussed and a novel scheme for Bose-Einstein condensation of the associated quasi-particles, dark-state polaritons (DSP), is proposed. DSPs are created in the Raman interaction of laser fields with atoms and are the basis of ultra-slow, stopped, and stationary light. Stationary DSPs have a quadratic dispersion profile with very small and variable effective mass and have a long intrinsic lifetime. Due to the small mass the corresponding condensation temperature can be many orders of magnitude higher than that of atoms. After introducing stationary dark-state polaritons their incoherent generation and thermalization is discussed and conditions for condensation analyzed. Finally potential methods for an experimental observation of the condensation will be put forward.

DOI
10.1364/sl.2008.sma2

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The generation of stationary distributions of light with three-dimensional confinement is discussed and a novel scheme for Bose-Einstein condensation of the associated quasi-particles, dark-state polaritons (DSP), is proposed. DSPs are created in the Raman interaction of laser fields with atoms and are the basis of ultra-slow, stopped, and stationary light. Stationary DSPs have a quadratic dispersion profile with very small and variable effective mass and have a long intrinsic lifetime. Due to the small mass the corresponding condensation temperature can be many orders of magnitude higher than that of atoms. After introducing stationary dark-state polaritons their incoherent generation and thermalization is discussed and conditions for condensation analyzed. Finally potential methods for an experimental observation of the condensation will be put forward.
We propose and analyze a mechanism for Bose-Einstein condensation of stationary dark-state polaritons. Dark-state polaritons (DSPs) are formed in the interaction of light with laser-driven 3-level Lambda-type atoms and are the basis of phenomena such as electromagnetically induced transparency, ultraslow, and stored light. They have long intrinsic lifetimes and in a stationary setup, a 3D quadratic dispersion profile with variable effective mass. Since DSPs are bosons, they can undergo a Bose-Einstein condensation at a critical temperature which can be many orders of magnitude larger than that of atoms. We show that thermalization of polaritons can occur via elastic collisions mediated by a resonantly enhanced optical Kerr nonlinearity on a time scale short compared to the decay time. Finally, condensation can be observed by turning stationary into propagating polaritons and monitoring the emitted light.
We put forth and discuss in detail a scheme to achieve Bose-Einstein condensation of stationary-light dark-state polaritons with dipolar interaction. To this end we introduce a diamondlike coupling scheme in a vapor of Rydberg atoms under the frozen gas approximation. To determine the system's dynamics we employ normal modes and identify the dark-state polariton corresponding to one of the modes. We show that in contrast to atomic dipolar ultracold vapors, the dark-state polariton Bose-Einstein condensates proposed here can be stable for a negative dipolar interaction constant.
Dark-state polaritons (DSPs) based on the effect of electromagnetically induced transparency are bosonic quasiparticles, representing the superpositions of photons and atomic ground-state coherences. It has been proposed that stationary DSPs are governed by the equation of motion closely similar to the Schrödinger equation and can be employed to achieve Bose-Einstein condensation (BEC) with transition temperature orders of magnitude higher than that of the atomic BEC. The stationary-DSP BEC is a three-dimensional system and has a far longer lifetime than the exciton-polariton BEC. In this Letter, we experimentally demonstrated the stationary DSP dressed by the Rydberg-state dipole-dipole interaction (DDI). The DDI-induced phase shift of the stationary DSP was systematically studied. Notably, the experimental data are consistent with the theoretical predictions. The phase shift can be viewed as a consequence of elastic collisions. In terms of thermalization to achieve BEC, the μm^{2}-size interaction cross section of the DDI can produce a sufficient elastic collision rate for the stationary DSPs. This Letter makes a substantial advancement toward the realization of the stationary-DSP BEC.
The generation of a trapping potential for dark-state polaritons in a two-dimensional electromagnetically induced transparency system is theoretically studied. We show that such a trap can arise from a spatially inhomogeneous effective mass of the dark-state polariton. Because this mass inhomogeneity can be engineered by tuning the parameters of the control fields, the motion, spatial profile, and coherent behavior of bound dark-state polaritons can be tailored accordingly. Our results enable spatial controls of optical information and provide a possible route toward realizing Bose-Einstein condensation of dark-state polaritons in a trapping potential.
We theoretically analyze the quasiparticle properties of stationary light polariton (SLP) modes in atoms via perturbative approaches of effective atom-light interaction Hamiltonian. First, we explicitly show the five SLP eigenmodes of the Hilbert space of the SLP system. Then, the quasiparticle properties, such as group velocities and effective masses of SLPs, are investigated under various parametric conditions, which include the emergence of negative effective mass and effective mass singularity. Finally, we derive the intrinsic lifetimes of each SLP mode, which features a complementary relation among the lifetimes of SLP modes. Our results offer quantitative analysis of the quasiparticle properties in Hilbert space spanned by the SLP modes, and it is expected to contribute to SLP-based atom-light interaction applications, such as photonic quantum gates, optical simulation of many-body physics, and exotic dispersion engineering.
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.