Number Of Polaritons Research Articles

Micropillar resonator in a magnetic field: Zero and finite temperature cases

In this work, we present a theoretical study of a quantum dot–microcavity system which includes a constant magnetic field in the growth direction of the micropillar. First, we study the zero temperature case by means of a self-consistent procedure with a trial function composed of a coherent photon field and a BCS function for the electron–hole pairs. The dependence of the ground state energy on the magnetic field and the number of polaritons is found. We show that the magnetic field can be used as a control parameter for the photon number, and we make explicit the scaling of the total energy with the number of polaritons. Next, we study this problem at finite temperatures and obtain the scaling of the critical temperature with the number of polaritons.

Dominant Effect of Polariton-Polariton Interactions on the Coherence of the Microcavity Optical Parametric Oscillator

The importance of interaction effects in determining the temporal coherence of spectrally and spatially isolated single modes of the microcavity optical parametric oscillator (OPO) is demonstrated. As a function of macroscopic occupancy, the coherence time (tau c) first increases linearly and then exhibits saturation behavior, reaching maximum values of up to 500 ps. Good agreement is found with a model including fluctuations in polariton number and polariton-polariton interactions between the OPO states. tau c is a property of the coupled OPO system, a result confirmed by the finding of equal coherence times for signal and idler, even though the idler is subject to strong additional scattering.

A multiexcitonic quantum dot in an optical microcavity

We theoretically study the coupled modes of a medium-size quantum dot, which may confine a maximum of 10 electron–hole pairs, and a single photonic mode of an optical microcavity. Ground-state and excitation energies, exciton–photon mixing in the wave functions and the emission of light from the microcavity are computed as functions of the pair–photon coupling strength, photon detuning, and polariton number.

Cavity polaritons: Classical behavior of a quantum parametric oscillator

We address theoretically the optical parametric oscillator based on semiconductor cavity exciton polaritons under a pulsed excitation. A ``hyperspin'' formalism is developed which allows, in the case of large number of polaritons, to reduce quantum dynamics of the parametric oscillator wave function to the Liouville equation for the classical probability distribution. Implications for the statistics of polariton ensembles are analyzed.

Theory of dark-state polariton collapses and revivals

We investigate the dynamics of dark-state polaritons in an atomic ensemble with ground-state degeneracy. A signal light pulse may be stored and retrieved from the atomic sample by adiabatic variation of the amplitude of a control field. During the storage process, a magnetic field causes rotation of the atomic hyperfine coherences, leading to collapses and revivals of the dark-state polariton number. These collapses and revivals should be observable in measurements of the retrieved signal field, as a function of storage time and magnetic field orientation.

Dynamics of Polariton Emission in the Linear Regime

The strong coupling between quantum well (QW) excitons and cavity photons leads to the appearance of new quasiparticles, named cavity polaritons [1]. The wave function of these particles is a linear combination of excitonic and photonic wave functions, and the excitonic and photonic content depends crucially on the detuning between bare exciton and cavity photon energies. Polaritons, being composed of bosons, manifest their bosonic nature in optical non-linearities based on quantum state occupancy. Due to their small mass, the photon-like polaritons have a very small density of states and their dispersion exhibits a large curvature. As a consequence, the probability of scattering with phonons is very low resulting in a “relaxation mobility edge” [2]. The experimental manifestation of this effect is a maximum in the emission intensity that is observed not at k = 0, but at larger values corresponding to the so-called bottleneck region. This bottleneck effect can be overridden by increasing the number of polaritons: above a certain excitation density threshold, the energy relaxation occurs via polariton–polariton scattering, stimulated by the final state occupancy [3]. Below this threshold, the

Coherence dynamics in microcavities and polariton lasers

We study theoretically the second-ordercoherence g(2)(0) of light emitted by polariton lasers, i.e., devices based on stimulated relaxation andcondensation of exciton–polaritons in microcavities. We solve kinetic equations for thepolaritons in different approximations and show that (i) the coherence introduced into thepolariton condensate by an external source can be conserved by the system over amacroscopically long time, and (ii) if the total number of polaritons is fixed by theexcitation conditions, the correlations between the populations of the ground and excitedpolariton states can also result in the spontaneous buildup of second-order coherence in thepolariton condensate. Both results are obtained neglecting polariton–polariton interactionsin the condensate.

Quantum gap solitons and soliton pinning in dispersive medium and photonic-band-gap materials: Bethe-ansatz solution.

Quantum electrodynamics of a single two-level atom placed within a frequency dispersive medium whose polariton spectrum has a gap due to photon coupling to a medium excitation (exciton, optical phonon, etc.) is studied. Despite a nonlocal effective polariton-polariton coupling, the system is proven to be integrable and is diagonalized exactly by means of the Bethe-ansatz technique. Its spectrum consists of bound many-polariton complexes (quantum solitons) and exhibits some unusual features due to the existence of the polaritonic gap. Only solitons containing an even number of polaritons propagate within the gap, while a soliton with an odd number of polaritons is pinned to the atom and forms a many-polariton-atom bound state, in which the radiation and the medium polarization are localized in the vicinity of the atom. The model under consideration has a quite general structure and can also be applied to the case of photonic-band-gap materials. \textcopyright{} 1996 The American Physical Society.

Quantum Gap Solitons and Many-Polariton-Atom Bound States in Dispersive Medium and Photonic Band Gap.

A system of polaritons interacting with a two-level atom placed within a frequency dispersive medium is proven to be integrable and diagonalized exactly by the Bethe ansatz method, despite a nonlocal effective polariton-polariton coupling. Its spectrum consists of bound many-polariton complexes (quantum solitons) and exhibits unusual features due to the existence of the polaritonic gap. Only solitons containing an even number of polaritons (``even'' solitons) propagate within the gap, while an ``odd'' soliton is pinned to the atom and forms a many-polariton--atom bound state.

Electron-polariton interactions in submicron semiconductor structures

The present paper is devoted to investigation of the interaction between the directional electron flow and a field of coupled oscillations (polaritons) in electrodynamic systems containing an inhomogeneous semiconductor structure carrying a current. An expression for the matrix element of the electron-polariton interaction Hamiltonian has been obtained. A kinetic equation describing the change of the number of polaritons in the system under investigation specified by the electron injection is found. It is shown that in the interaction of the directional electron flow with polaritons, radiation processes prevail over absorption. Hence under certain definite conditions coupled oscillations of the electrodynamic system with a semiconductor can become unstable. Instability regions as well as the growth rates and the energy losses by electrons for real parameters of the semiconductor and the electrodynamic system are given.

Renormalization of polaritons due to virtual formation of biexcitons at high densities of excitation

AbstractThe change of polariton dispersion is investigated theoretically if a large number of polaritons is present at frequencies near half the biexciton energy. A renormalization process takes place for polaritons via virtual formation of biexcitons and stimulated by the intense polariton distribution. Assuming an energetically sharp distribution as is realised e.g. by dye laser excitation the original polariton dispersion is shown to split into two new branches. These effects should manifest if e.g. an additional but weak probe light is used to testify the optical properties of the laser excited crystal. Furthermore the scattering lines of the two‐photon resonance Raman process via biexcitons are characteristically modified due to both selfrenormalization of the incoming polaritons and renormalization of the scattered polaritons. Explicit results are presented for CuCl where agreement with experimental data recently published is found.

The Master equation in a polariton system

The master equation for the density matrix of polaritons in a dielectric crystal is derived using coherent states as a basis. The Peierls equation for the time rate-of-change of the mean number of polaritons is also derived.