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arXiv:1207.7293 · Physical Review A

Solitons in cavity-QED arrays containing interacting qubits

I-H. Chen, Y. Y. Lin, Y.-C. Lai, Evgeny S. Sedov, A. P. Alodjants, Sergei M Arakelyan, Ray‐Kuang Lee

Published Aug 17, 2012• 22 citations
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Abstract

We reveal the existence of polariton soliton solutions in the array of weakly coupled optical cavities, each containing an ensemble of interacting qubits. An effective, complex Ginzburg-Landau equation is derived in the continuum limit, taking into account the effects of cavity field dissipation and qubit dephasing. We have shown that an enhancement of the induced nonlinearity can be achieved by two orders of magnitude with negative interaction strength, which implies a large negative qubit-field detuning as well. 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 interacting strength. 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.

DOI
10.1103/physreva.86.023829

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We reveal the existence of polariton soliton solutions in the array of weakly coupled optical cavities, each containing an ensemble of interacting qubits. An effective, complex Ginzburg-Landau equation is derived in the continuum limit, taking into account the effects of cavity field dissipation and qubit dephasing. We have shown that an enhancement of the induced nonlinearity can be achieved by two orders of magnitude with negative interaction strength, which implies a large negative qubit-field detuning as well. 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 interacting strength. 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.
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.
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.
Considering two-level media in the array of weakly coupled nanocavities, we reveal a variety of dynamical regimes, such as diffusion, self-trapping, soliton, and breathers for the wave packets in the presence of photon tunneling processes between the next-nearest cavities. We focus our attention on the low-branch bright polariton soliton formation, due to the two-body polariton-polariton scattering processes. When detuning frequency is manipulated adiabatically, the low-branch lattice polariton localized states, i.e., solitons and breathers evolving between photonlike and matterlike states, are shown to act as carriers for spatially distributed storage and retrieval of optical information.
In view of current research effort on semiconducting photonic-crystal defect microcavities, we consider the dynamics of an array of coupled optical cavities, each containing an ensemble of qubits. By concentrating on the strong coupling regime, we analytically prove that the nonlinearity inherent in the dynamics of each ensemble coupled to the respective cavity field allows the formation of solitons. We further show how the use of the Holstein–Primakoff transformation and the large-detuning limit with the cavity allows one to recover the Bose–Hubbard model.
We show experimentally optical bistability and the existence of bright and dark resonator solitons in the strong coupling regime between quantum-well excitons and the optical field in a semiconductor microcavity. The strong coupling results in a quasi-particle exciton-polariton, which gives access to positive and negative reactive and dissipative optical nonlinearities, as opposed to the usual room temperature semiconductor nonlinearities possessing essentially only one sign. The existence range and the properties of solitons can be varied widely by the detuning between polariton states and light frequency.
The coherent and nonlinear properties of a polaritonic crystal (PolC), formed by trapped two-level atoms in an optical cavity array and interacting with an optical field, are analyzed. The nonlinear Schrödinger equation is considered for the dynamics of coupled atom-light states and low-branch polaritons associated with PolCs in the continuous medium limit. The existence of a stable ground-state PolC wave function is predicted using the variational approach. For negative scattering lengths, the wave function collapses in the presence of small quintic nonlinearity.