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 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 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 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.
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.
This thesis covers a theoretical analysis of non-interacting and interacting quasi\nparticles, called polaritons. Polaritons are composites, based on photonic and atomic\nexcitations in a tunable and controlled manner. Dark-state polaritons, as a subclass\nof polaritons, are very curious objects, as they can act as a quantum memory of\nphotons within an ensemble of alkali-metal atoms in -type conguration which\nadmit electromagnetically induced transparency (EIT). This thesis focus on the\nformation of dark-state polaritons in degenerate two-level systems, where two light\nelds, a quantum probe and a classical driving eld, couple the same transition\nbetween the ground state and excited state manifold. An algorithm is going to\nbe derived in order to determine the dispersion relation and inherent composition\nof the dark-state polaritons in the degenerate two-level system. The algorithm is\nbased on a microscopic equation of motion technique and provides an extension of\nthe non-degenerate case. Depending on the polarization of the light elds, it will be\nshown that either one or two dark-state polaritons can exist. Further, the calculated\ndark-state polaritons can be used in order to perform a frequency conversion and\neven a conversion of linear light polarization.\nIn the second part of the thesis, interacting polaritons in arrays of coupled QED\ncavities will be discussed. In rst place, the standard Jaynes-Cummings model is\ndiscussed in order to provide a better insight to polaritons in QED cavities. Then,\na modied Jaynes-Cummings model is introduced and derived in order to study\ndark-polaritons and their interaction. It will be shown that dark-polaritons directly\ndepend on the common single photon detuning of the two coupling elds, quantum\nprobe and classical driving eld. The interaction between dark-polaritons will be\ndiscussed where the emergence of dark-polariton bound pairs will be shown. By\ntuning the Stark-shift due to the classical control eld, the number and the composition\nof dark-polariton bound pairs can be controlled. It will be demonstrated\nthat there exists a dark-polariton bound pair which diers from the aforementioned\nones, because it represents a ground state of the system. Using that kind of a darkpolariton\nbound pair, storage and retrieval of a single photon can be performed,\neven though that the photons are in a two-photon bound state.\nIn the last part of the thesis, disorder between QED cavities will be introduced\nin a controlled manner through staggered inter-cavity photon hopping strengths J1\nand J2. Further, the appearance of a dark-polariton bound pair of a completely\ndierent type will be presented.
We consider the fundamental problem of high-temperature phase transitions in the system of high-density two-level atoms off-resonantly interacting with a pump field in the presence of optical collisions (OCs) and placed in the cavity. OCs are considered in the framework of thermalization of atomic dressed-state (DS) population. For the case of a strong atom-field coupling condition, we analyze the problem of a thermodynamically equilibrium superradiant phase transition for the order parameter representing a real amplitude of cavity mode and taking place as a result of the atomic DSs thermalization process. Such a transition is also connected with condensed (coherent) properties of low branch DS polaritons occurring in the cavity. For describing nonequilibrium phase transitions we derive Maxwell-Bloch--like equations which account for cavity decay rate, collisional decay rate, and spontaneous emission. Various aspects of transitions to laser field formation by using atomic DS levels for both positive and negative detuning of a pump field from atomic transition frequency are studied in detail. It is revealed that for positive atom-light detuning DS lasing can be obtained in the presence of quasiequilibrium DS population that corresponds to a true two-level atomic system with the inversion in a nonresonant limit.