Energy relaxation of excitonlike polaritons in semiconductor microcavities: Effect on the parametric scattering of polaritons

Polariton emission in GaAs-based microcavities has been studied under variable conditions, which made it possible to excite (a) polaritons from the upper polariton branch and hot free polaritons and electrons, (b) polaritons from the lower polariton branch (LPB) and localized excitons, and (c) the mixed system. Variation of the excitation conditions leads to substantial differences in the energy distributions of polaritons and in the temperature dependences of polariton emission. It is established that the energy relaxation of resonantly excited LPB polaritons via polariton and localized exciton states at liquid helium temperatures is ineffective. Instead, the relaxation bottleneck effect is suppressed with increasing temperature by means of exciton delocalization (due to thermal excitation by phonons). The most effective mechanism of relaxation to the LPB bottom is via scattering of delocalized excitons on hot free carriers. It is found that the slow energy relaxation of polaritons excited below the free exciton energy can be significantly accelerated at low temperatures by means of additional weak generation of hot excitons and, especially, hot electrons. This acceleration of the energy relaxation of polaritons by means of additional overbarrier photoexcitation sharply decreases the barrier for stimulated parametric scattering of polaritons excited at an LPB inflection point. Therefore, additional illumination can be used to control the polariton-polariton scattering.     

The plasmon–exciton interaction in layered nanostructures with two-dimensional J-aggregates

The transformation of the electronic excitation energy in a plane-layered nanostructure with two-dimensional J-aggregates of a cyanine dye has been studied theoretically. The dependences of the plasmon–exciton interaction energy on the system parameters have been determined. In the case of small values of the Rabi frequency, the rates of nonradiative energy transfer from surface plasmon–polaritons of the metal substrate to molecular excitons of J-aggregates have been calculated in terms of the perturbation theory. The dispersion laws for hybrid plasmon–exciton states have been determined, and it has been shown that the Rabi splitting can range up to 100 meV.     

Dynamics of microcavity polaritons in the Markovian limit

A master equation for the reduced density matrix of the microcavity polaritons coupled with the reservoir of high energy excitons is derived. It is allowed both the polaritons and the excitons to be self-interacting systems. Long time asymptotic properties of the polariton population is studied in the whole range of the reservoir temperatures and the corresponding decoherence effects are reported.     

Internal Structure of Vortices in a Two-Component Exciton-Polariton Condensate

Vortex solutions of coupled Gross–Pitaevskii equations for a two-component Bose–Einstein condensate of exciton polaritons have been described theoretically with the inclusion of the dependence of the Rabi splitting energy on the density of the exciton component. It has been shown that the inclusion of blueshift leads to a considerable decrease in the densities of both components of the condensate. The spatial profiles of excitons and photons in the polariton system, as well as the energy of vortex excitation formation, have been calculated taking into account nonlinear corrections.     

Optical control of excitons in a pair of quantum dots coupled by the dipole-dipole interaction

We demonstrate coherent nonlinear-optical control of excitons in a pair of quantum dots (QDs) coupled via dipolar interaction. The single-exciton population in the first QD is controlled by resonant picosecond excitation, giving rise to Rabi oscillations. As a result, the exciton transition in the second QD is spectrally shifted and concomitant Rabi oscillations are observed. We identify coupling between permanent excitonic dipole moments as the dominant interaction mechanism, whereas quasiresonant (F?rster) energy transfer is weak. Such control schemes based on dipolar interaction are a prerequisite for realizing scalable quantum logic gates.     

Polariton condensation with localized excitons and propagating photons

We estimate the condensation temperature for microcavity polaritons, allowing for their internal structure. We consider polaritons formed from localized excitons in a planar microcavity, using a generalized Dicke model. At low densities, we find a condensation temperature T(c) proportional, rho, as expected for a gas of structureless polaritons. However, as T(c) becomes of the order of the Rabi splitting, the structure of the polaritons becomes relevant, and the condensation temperature is that of a BCS-like mean-field theory. We also calculate the excitation spectrum, which is related to observable quantities such as the luminescence and absorption spectra.     

Rabi oscillations of excitons in single quantum dots

Transient nonlinear optical spectroscopy, performed on excitons confined to single GaAs quantum dots, shows oscillations that are analogous to Rabi oscillations in two-level atomic systems. This demonstration corresponds to a one-qubit rotation in a single quantum dot which is important for proposals using quantum dot excitons for quantum computing. The dipole moment inferred from the data is consistent with that directly obtained from linear absorption studies. The measurement extends the artificial atom model of quantum dot excitonic transitions into the strong-field limit, and makes possible full coherent optical control of the quantum state of single excitons using optical pi pulses.     

Polarization instability in a polariton system in semiconductor microcavities

The kinetics of a field on a quantum well in the active region of a planar microcavity with strong exciton-photon coupling has been investigated under the conditions of resonance pulse excitation by a small degree of circular polarization. It has been shown that the system of polaritons at the early stage of the development of instability induced by polariton-polariton interaction tends to transit to a circularly polarized state, but does not reach 100% circular polarization and returns to a polarized state whose polarization is close to the pump polarization. It has been shown that the observed effects are caused by the excitation of an unpolarized reservoir of excitons in quantum wells, which leads to fast relaxation of the difference between the effective resonance frequencies of excitons with different circular polarizations.     

Strong coupling between Tamm plasmon and QW exciton

We report on the strong coupling between a Tamm plasmon mode and excitons from inorganic quantum wells. The sample is formed by an AlAs/GaAlAs Bragg reflector containing InGaAs QWs in its high refractive index layers, on top of which a thin silver film is deposited. Angle resolved reflectometry experiments at low temperature (77 K) show a clear anticrossing in the dispersion relations, evidencing the strong coupling regime. The Rabi splitting amounts to 11.5 meV. Emission from low and high energy Tamm plasmon/exciton polaritons is also demonstrated. Experimental data are in very good agreement with transfer matrix simulations.     

Exciton warming in III–V semiconductors and microcavities

We present a time resolved experiment in which we dynamically tailor the occupation and temperature of a photogenerated exciton distribution in QWs by excitation with two delayed picosecond pulses. The modification of the excitonic distribution results in ultrafast changes in the PL dynamics. Our experimental results are well accounted by a quasiequilibrium thermodynamical model, which includes the occupation and momentum distribution of the excitons. We use this model and the two-pulse experimental technique to study the polariton dynamics in InGaAs-based microcavities in the strong coupling regime. In particular, we demonstrate that resonantly injected upper polaritons mainly relax to the lower polariton branch via scattering to large momentum polariton states, producing the warming of the polariton reservoir.     

Bose-einstein condensation of exciton polaritons in high-<Emphasis Type="Italic">Q</Emphasis> planar microcavities with GaAs quantum wells

Condensation of exciton polaritons in planar microcavities with GaAs/AlAs quantum wells in the active area has been studied. It has been found that an increase in the lifetime of polaritons up to ∼10–15 ps when the Q factor of a microcavity exceeds 7000 makes it possible to detect Bose-Einstein condensation of polaritons with a dominant (>90%) photon component. Condensation occurs under thermodynamically nonequilibrium conditions in lateral traps with diameters ∼10 μm formed due to long-range fluctuations of the polariton potential. The violet shift of the polariton emission line at the condensation threshold significantly exceeds the energy of the repulsive interaction between polaritons in the condensate. It has been shown that the shift is mainly due to a decrease in the oscillator strength of bright excitons in lateral traps, caused by the localization of photoexcited long-living dark excitons.     

Interplay of Rabi oscillations and quantum interference in semiconductor quantum dots

We investigated the manifestation of Rabi oscillation in the coherent dynamics of excitons in self-assembled semiconductor quantum dots. The Rabi oscillation phenomenon was directly observed as a function of the input pulse area. Furthermore, by performing wave packet interferometry in the nonlinear excitation regime, we discover a new type of quantum interference phenomenon, resulting from the interplay between Rabi oscillation and quantum interference.     

Intensities of resonant brillouin scatterings from multicomponent exciton-polaritons

To reduce the arbitrariness in the current analysis of resonant Brillouin scattering (RBS) from multicomponent polaritons, the intensities of scattering peaks are theoretically studied. The interaction among the multicomponent excitons may contain linear and quadratic terms in translational wave vector, electron-hole exchange interaction, and any other terms that retain translational symmetry. As the scattering mechanisms due to TA and LA phonons, we consider various deformation and piezoelectric potentials. In certain cases, this theory leads to a “selection rule”, which can solve the controversy between the two different dispersion curves for CuBr obtained from RBS and two photon resonant Raman scattering, in favor of the latter. The theory also provides a basis to discuss the problem of additional boundary conditions for multicomponent polaritons in terms of the relative intensities of scattering peaks.     

Parametric control of a superconducting flux qubit

Parametric control of a superconducting flux qubit has been achieved by using two-frequency microwave pulses. We have observed Rabi oscillations stemming from parametric transitions between the qubit states when the sum of the two microwave frequencies or the difference between them matches the qubit Larmor frequency. We have also observed multiphoton Rabi oscillations corresponding to one- to four-photon resonances by applying single-frequency microwave pulses. The parametric control demonstrated in this work widens the frequency range of microwaves for controlling the qubit and offers a high quality testing ground for exploring nonlinear quantum phenomena of macroscopically distinct states.     

Photon-field-shape effects on Rabi splitting energies in CuCl microcavities

We have investigated the photon-field-shape effects on Rabi splitting energies in CuCl microcavities with HfO₂/SiO₂ distributed Bragg reflectors (DBRs). The CuCl active layer was prepared by vacuum deposition, while HfO₂ and SiO₂ layers were prepared by rf magnetron sputtering. The photon-field shape was tuned to a node-type or an antinode-type by changing the order of the refractive indices in the DBR. In order to control of the Rabi splitting energies, the active-layer thickness was changed from λ/12 to 9λ/20. In angle-resolved reflectance spectra at 10 K, three cavity polaritons resulting from the strong coupling between the Z₃ and Z_1,2 excitons and cavity photon were clearly detected. We estimated the energies of the exciton-photon interaction, the so-called vacuum Rabi splitting energies, from the analysis of the cavity polariton dispersions using a phenomenological Hamiltonian for the strong exciton-photon coupling. The active-layer-thickness dependence of the Rabi splitting energies are explained by a semi-quantitative analysis taking account of the overlap between the exciton and photon-field wave functions. We have demonstrated that the photon-field shape drastically affects the active-layer-thickness dependence of the Rabi splitting energies.     

Cavity plasmon polaritons in monolayer graphene

Plasmon polaritons in a new system, a monolayer doped graphene embedded in optical microcavity, are studied here. The dispersion law for lower and upper cavity plasmon polaritons is obtained. Peculiarities of Rabi splitting for the system are analyzed; particularly, role of Dirac-like spinor (envelope) wave functions in graphene and corresponding angle factors are considered. Typical Rabi frequencies for maximal (acceptable for Dirac-like electron spectra) Fermi energy and frequencies of polaritons near polariton gap are estimated. The plasmon polaritons in considered system can be used for high-speed information transfer in the THz region.     

From superradiant Rayleigh scattering to Bragg scattering

We present the results of an experiment on light scattering from an elongated Bose-Einstein condensate interacting with far off resonant laser light. Due to superradiant Rayleigh scattering a coherent superposition of two atomic wavepackets with different momenta forms in the presence of a single laser beam. Varying the intensity of a weak counterpropagating laser beam we observe the transition from the pure superradiant regime to the Bragg scattering regime, where Rabi oscillations in a two-level system are observed. The process is limited by the decoherence between the two atomic wavepackets.     

Excitonic Rabi oscillations in a quantum dot: local field impact

The influence of local fields on the excitonic Rabi oscillations in an isolated, arbitrary shaped quantum dot (QD) has been theoretically investigated. QD interaction with both a classical electromagnetic field and quantum light has been considered. In the classical light, time harmonic and ultrashort pulse excitations are analyzed. The general formalism has been formulated for quantum light and applied to the case of a Fock qubit. Noticeable modification of the Rabi oscillation dynamics induced by the local fields is predicted to be observable in QDs exposed to both classical and quantum light. In particular, the bifurcation and anharmonism in the Rabi oscillations have been revealed under time harmonic excitation and a dependence of the Rabi oscillation period on the QD depolarization has been obtained.     

Driving-dependent damping of Rabi oscillations in two-level semiconductor systems

We propose a mechanism to explain the nature of the damping of Rabi oscillations with an increasing driving-pulse area in localized semiconductor systems and have suggested a general approach which describes a coherently driven two-level system interacting with a dephasing reservoir. Present calculations show that the non-Markovian character of the reservoir leads to the dependence of the dephasing rate on the driving-field intensity, as observed experimentally. Moreover, we have shown that the damping of Rabi oscillations might occur as a result of different dephasing mechanisms for both stationary and nonstationary effects due to coupling to the environment. Present calculated results are found in quite good agreement with available experimental measurements.     

On the type of a phase transition in the system of exciton polaritons in an optical microcavity

The type of a phase transition in the quasi-equilibrium system of exciton polaritons in a two-dimensional optical microcavity has been analyzed. It has been shown that, although the system contains two types of bosons undergoing mutual transformations into each other, only one phase transition to the superfluid state with the quasilong-range order occurs in the two-dimensional system. This phase transition is a Kosterlitz-Thouless phase transition. A new physical implementation—excitons in a photon crystal—has been proposed for the Bose condensation of exciton polaritons. The superfluid properties of the ordered phase are discussed, and the superfluid density and Kosterlitz-Thouless transition temperature have been calculated in the low-density approximation.