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arXiv:1005.1772 · Journal of Physics B Atomic Molecular and Optical Physics

Strongly localized polaritons in an array of trapped two-level atoms interacting with a light field

A P Alodjants, I O Barinov, Sergei M Arakelyan

Published Apr 12, 2010• 30 citations
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Abstract

We propose a new type of spatially periodic structure, i.e. polaritonic crystal (PolC), to observe a "slow"/"stopped" light phenomenon due to coupled atom-field states (polaritons) in a lattice. Under the tightbinding approximation, such a system realizes an array of weakly coupled trapped two-component atomic ensembles interacting with optical field in a tunnel-coupled one dimensional cavity array. We have shown that the phase transition to the superfluid Bardeen-Cooper-Schrieffer state, a so-called (BCS)-type state of low branch polaritons, occurs under the strong coupling condition. Such a transition results in the appearance of a macroscopic polarization of the atomic medium at non-zero frequency. The principal result is that the group velocity of polaritons depends essentially on the order parameter of the system, i.e. on the average photon number in the cavity array.

DOI
10.1088/0953-4075/43/9/095502

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We propose a new type of spatially periodic structure, i.e. polaritonic crystal (PolC), to observe a "slow"/"stopped" light phenomenon due to coupled atom-field states (polaritons) in a lattice. Under the tightbinding approximation, such a system realizes an array of weakly coupled trapped two-component atomic ensembles interacting with optical field in a tunnel-coupled one dimensional cavity array. We have shown that the phase transition to the superfluid Bardeen-Cooper-Schrieffer state, a so-called (BCS)-type state of low branch polaritons, occurs under the strong coupling condition. Such a transition results in the appearance of a macroscopic polarization of the atomic medium at non-zero frequency. The principal result is that the group velocity of polaritons depends essentially on the order parameter of the system, i.e. on the average photon number in the cavity array.
A new developed for storing quantum information on atomic polaritons being at thermal equilibrium is developed for the first time. We propose a new type of spatially periodic structure - polaritonic crystal (PolC) formed by trapped two-level atoms interacting with quantum electromagnetic field in one-dimensional array of tunnelcoupled microcavities, which allows polaritons to be fully localized. The quantum degeneracy and phase transition to superfluid (Bardeen-Cooper-Schrieffer-type) state for low branch polaritons is discussed. The principal result is that the group velocity of polaritons depends essentially on the order parameter of the system, i.e. on the average photon number in the cavity array. An algorithm for the spatially distributed writing, storing, and retrieving of quantum optical information using polariton wave packet propagated in the cavity array is examined. To take into account decoherence processes in polaritonic system the quantum Brownian particle model is discussed as well.
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Coherent properties of a two-dimensional spatially periodic structure, polaritonic crystal (PolC) formed by trapped two-level atoms in an optical cavity array interacting with a light field, are analyzed. By considering the wave function overlapping for both photonic and atomic states, a cubic-quintic complex nonlinear Schr\"odinger equation is derived for the dynamics of coupled atom-light states, wave function of low-branch polaritons, associated with PolC in the continuous limit. A variational approach predicts that a stable ground-state wave function of PolC exists but is accompanied by an oscillating width. For a negative scattering length, the wave function collapses in the presence of a small quintic nonlinearity appearing due to a three-body polariton interaction. By studying the nonequilibrium (dissipative) dynamics of polaritons with adiabatic approximation, we have shown that the collapse of PolC wave function can be prevented even in the presence of small decaying of a number of polariton particles.
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We suggest the model of lattice low branch (LB) polaritons based on the array of weakly coupled microsize cavities, each containing a small but macroscopic number of two-level systems (qubits). We reveal various dynamical regimes, such as diffusive, self-trapped, breathing and solitonic for polariton wave packet propagation under tight-binding approximation. We focus our attention on the bright polariton soliton formation in a high quality cavity array emerging due to two-body polariton-polariton scattering processes that take place at each cavity under the qubit-light interaction. A physical algorithm for the spatially distributed storage of optical information where various dynamical LB polariton soliton states are used is proposed. This algorithm can be realized with the help of manipulating group velocity of a polariton soliton in the cavity array and obtained by smooth variation of qubit-light detuning.
We examine the problem of polariton soliton formation in the array of weakly coupled optical cavities, each containing an ensemble of ultracold non-interacting two-level atoms. An effective complex Ginzburg-Landau equation (GLE) is derived in the continuum limit taking into account the effects of cavity field dissipation and atomic polarization dephasing. Bright solitons are found to be supported under perturbations only in the upper (optical) branch of polaritons, for which the corresponding group velocity is controlled by tuning the atom-light detuning. With the help of perturbation theory for solitons, we also demonstrate that the group velocity of these polariton solitons is suppressed by the diffusion process.