Josephson dynamics for coupled polariton modes under the atom–field interaction in the cavity

We consider a new approach to the problem of Bose–Einstein condensation (BEC) of polaritons for atom–field interaction under the strong coupling regime in the cavity. We investigate the dynamics of two macroscopically populated polariton modes corresponding to the upper and lower branch energy states coupled via Kerr-like nonlinearity of atomic medium. We found out the dispersion relations for new type of collective excitations in the system under consideration. Various temporal regimes like linear (nonlinear) Josephson transition and/or Rabi oscillations, macroscopic quantum self-trapping (MQST) dynamics for population imbalance of polariton modes are predicted. We also examine the switching properties for time-averaged population imbalance depending on initial conditions, effective nonlinear parameter of atomic medium and kinetic energy of low-branch polaritons. PACS 03.75.Lm; 71.36.+c; 42.50.Fx     

Polariton excitations in a non-ideal array of microcavities with quantum dots

The polariton spectrum of a one-dimensional non-ideal array of coupled microcavities containing quantum dots has been studied. The specific features of the dispersion of electromagnetic excitations, which are induced in this system both by a variation in the distance between the adjacent microcavities and by a variation in the composition of the quantum dots, have been investigated using the numerical simulation within the framework of the virtual crystal approximation. The density of states of the quasiparticles under consideration has been determined.     

Zur Quantentheorie der stimulierten RAMAN-Streuung in Molekülkristallen. II. Spezielle Fälle eines stationären RAMAN-Oszillators

Two kinds of stationary RAMAN oscillators are investigated theoretically for molecular crystals. The calculations are done firstly for the generation of one first order anti-STOKES mode and secondly for the generation of one second order STOKES mode. By using a quantum theoretical model described in an earlier paper for treatment of molecular crystals RAMAN scattering is assumed to be polariton scattering. Within this framework coupled nonlinear equations for the polariton operators of the excited modes are derived, stationary occupation numbers for the different modes and threshold conditions are calculated. The influence of phase fluctuations of the pump wave on the line widths of the RAMAN modes are investigated.     

Zur Quantentheorie der stimulierten RAMAN-Streuung in Molekülkristallen. I. Einige Bemerkungen zur Theorie nach K. GROB

Stimulated RAMAN scattering in molecular crystals is quantum theoretically described as stimulated polariton scattering. The quantum theoretical treatment of molecular crystals is given within the framework of a second quantization described in an earlier work. In the HEISENBERG picture the equations of motion for the operators of the polaritons are derived and specialized for RAMAN scattering. By supposing quasi-stationary behaviour the operators of the polaritons that are mixtures of phonons and photons are eliminated. The resulting equations are shown to have the same structure but a generalized physical meaning as those derived by GROB on other way.     

Surface phonon–polaritons in rectangular quantum wires of polar ternary mixed crystals

In this paper, the dispersion relations of surface phonon–polaritons in freestanding rectangular quantum wire systems of polar ternary mixed crystals are derived. The numerical calculations for Al_xGa_1−xAs and Zn_xCd_1−xSe quantum wire systems are performed. The results reveal that the frequencies of surface phonon–polariton modes are sensitive to the geometric structures of the quantum wires, the wave-vectors in z-direction, and the compositions of the ternary mixed crystal materials. The effects of the “two-mode” and “one-mode” behaviors of the ternary mixed crystals on the surface phonon–polariton modes are also discussed.     

Quantum degeneracy of microcavity polaritons

We investigate experimentally one of the main features of a quantum fluid constituted by exciton polaritons in a semiconductor microcavity, that is, quantum degeneracy of a macroscopic fraction of the particles. We show that resonant pumping allows us to create a macroscopic population of polaritons in one quantum state. Furthermore, we demonstrate that parametric polariton scattering results in the transfer of a macroscopic population of polariton from one single quantum state into another one. Finally, we briefly outline a simple method which provides direct evidence of the first-order spatial coherence of the transferred population.     

Superradiance of polaritons in finite one-dimensional crystals of increasing length: Passage from a dimer to an infinite crystal

Solutions of the dispersion equations for polariton states in finite one-dimensional crystals of arbitrary length are obtained. The appearance and evolution of the radiative and nonradiative polariton branches are traced as the length varies from two monomers to limiting values, above which the spectrum no longer undergoes significant changes. The dependences of the frequencies and radiative widths on the polariton wave vector are found for various orientations of the dipole moment of the quantum transition. The evolution of superradiance as the length of the crystal increases is traced. Some previously unknown significant features of the polariton spectrum are noted particularly the damping of the branch traditionally termed nonradiative as a consequence of emission from the end faces. Fiz. Tverd. Tela (St. Petersburg) 40, 2136–2140 (November 1998)     

Exciton-polariton solitary waves

Effects of the exciton and polariton dispersions and the nonlinear exciton and photon interactions on the properties of polariton solitons in molecular crystals are investigated. Higher-order terms and phase-modulation (chirp) are taken into account. Bright- and dark-soliton solutions of the resulting modified nonlinear Schr?dinger (NLS) equation are presented. Nonlinearity- and dispersion-induced critical points on the polariton dispersion curve are obtained, separating regions with different solutions. Received 2 October 2001 / Received in final form 23 May 2002 Published online 2 October 2002 RID="a" ID="a"e-mail: Stoychev@issp.bas.bg     

Quantum Theory of Surface Polaritons in Semi-Infinite Dielectric Systems

The interaction system of a semi-infinite diatomic dielectric and the electromagnetic field propagating parallelly to the surface is studied. The long-wave optical phonon modes of the semi-infinite dielectric are calculated including the electronic polarizability by a quantum-mechanical theory. Retardation effects are neglected. A quantum field theory method of surface polaritons is developed to calculate the operator describing the interaction between a photon and the phonon polarization fields of the semi-infinite crystal, with explicit inclusion of surface effects. The dispersion relations of the surface phonon-polaritons are derived and discussed. The results are in good agreement with those obtained by the conventional, macroscopic dielectric theory of surface polaritons and experimental ATR (attenuated total reflection) spectra. The dispersion cuwes of polariton leaking modes caused by the interaction between bulk TO mode with surface effect and photons are presented in a graphical form. The k_||-dependence of the electric field strength in each polariton branch is calculated and presented also in a graphical form. We also research the spatial dependence of the field strength in each polariton branch. It is found that these properties are influenced and modulated by the surface phonons because of the interaction between photons and the surface phonon modes of the semi-infinite dielectric system. Hence the divergent nature (diffraction effect) of light propagating along the fib& and waveguides is restrained. We present a method how to use the boundary conditions in the quantum theory, which will be discussed in detail.     

Direct observation of whispering gallery mode polaritons and their dispersion in a ZnO tapered microcavity

We report direct observation of the strong exciton-photon coupling in a ZnO tapered whispering gallery (WG) microcavity at room temperature. By scanning excitations along the tapered arm of the ZnO tetrapod using a micro-photoluminescence spectrometer with different polarizations, we observed a transition from the pure WG optical modes in the weak interaction regime to the excitonic polariton in the strong coupling regime. The experimental observations are well described by using the plane wave model including the excitonic polariton dispersion relation. This provides a direct mapping of the polariton dispersion, and thus a comprehensive picture for coupling of different excitons with differently polarized WG modes.     

Resonance tunneling of polaritons in 1D chain with a single defect

We consider propagation of coupled waves (polaritons) formed by a scalar electromagnetic wave and excitations of a finite one-dimensional chain of dipoles. It is shown that a microscopic defect (an impurity dipole) embedded in the chain causes resonance tunneling of the electromagnetic wave with a macroscopic wavelength through the forbidden band between two polariton branches. We demonstrate that the resonance tunneling occurs due to local polariton states caused by the defect.     

Theorie der nichtstationären Anregung von Exziton-Polaritonen durch Zweiphotonenabsorption

Theory of nonstationary Exciton-Polariton Generation by Two-photon Absorption A theory of nonstationary two-photon absorption for nonlinear non-centrosymmetric crystals is presented. The time-dependent radiation flux density of the generated polariton beam is calculated under the condition of an ultrashort laser pulse duration T_L ? ΓT^?1 (ΓT is the exciton line width) and a stationary incoherent test field. The “mechanical” response of the excitons and different group velocities of the polariton and the laser and test fields are taken into account. the spatial dispersion of the exciton motion being neglected. With a rectangular laser pulse shape the analytically nonstationary solutions are discussed for identical and for different group velocities of laser and test fields. Using the conservation laws for energy and quasimomentum we illustrate, by considering the polariton dispersion branches, the various possible cases of two-photon absorption in uniaxial piezocrystals.     

Effects of exciton-photon interaction and spatial dispersion in xenon crystals

New data on luminescence from xenon crystals are discussed in terms of the polariton theory, and the treatment of a fine spectrum structure is proposed based on the polariton scattering with participation of some acoustic phonons.The effect of spatial dispersion on transmission and reflection spectra of solid Xe is considered. Verification of the basic parameters of polariton spectrum in xenon is made by comparing calculated and experimental data.     

Dispersion relation of LT mixed mode polaritons

Simple equations are presented for polariton dispersion relations in anisotropic medium for an arbitrary direction of wave vector, where LT (longitudinal-transverse) mixed modes occur in general. The use of the polarizability tensor defined for pure external (not for the total) field is essentially important to obtain the simple result. The relation between all the tensor components of the polarizability and dielectric function is also explicitly given. The result can be used for any elementary excitations relevant to dielectric function. In the case of multi-component excitons of LT mixed mode character, the dispersion equation is rewritten in a matrix form, which is useful to obtain the allowed values of polariton wave vector for a given frequency.     

Picosecond spectroscopy of polaritons in anthracene crystals II. Luminescence

The low-temperature luminescence spectrum of anthracene crystals is investigated by applying simultaneous time and frequency resolution. The complicated kinetics of the emission in the polariton bottleneck region reflects directly the evolution and relaxation of the polariton distribution in the crystal. Three distinct relaxation stages are distinguished: (1) the ultrafast decay of initial vibronic excitations, mediated by optical phonons and resulting in a broad distribution of polaritons near the band bottom; (2) the formation of a narrow distribution of polaritons with a characteristic time of 30 ps, which is caused by scattering on acoustic phonons; (3) relaxation through the bottleneck region on a subnanosecond time scale. It is suggested that the polaritons immediately below the resonance frequency are responsible for the observed excitonic energy transfer in anthracene crystals.     

Amplitude-mode dynamics of polariton condensates

We study the stability of collective amplitude excitations in nonequilibrium polariton condensates. These excitations correspond to renormalized upper polaritons and to the collective amplitude modes of atomic gases and superconductors. They would be present following a quantum quench or could be created directly by resonant excitation. We show that uniform amplitude excitations are unstable to the production of excitations at finite wave vectors, leading to the formation of density-modulated phases. The physical processes causing the instabilities can be understood by analogy to optical parametric oscillators and the atomic Bose supernova.     

New collective modes in multiferroic TbMnO3: The electromagnons

Using a phenomenological Landau theory as well as equations of motion, we look for new excitations in the multiferroic TbMnO₃. Coupling these excitations to an electromagnetic field, we derived the magneto–polariton dispersion relation. Further, the frequency as well as temperature dependent dielectric susceptibility, and hence the refractive index, are obtained in this formulation. The imaginary part of the latter is computed and compared with the existing experimental data.     

Size effects on polaritons in thin crystals with perfect interference spectra

Size effects on polaritons in thin plane parallel CdS and CdSe crystals are discussed. For samples not thinner than 0.1 μm the measurements of transmittance and reflectance show the size quantization of the mechanical exciton dispersion and a shift of the resonance frequency of the exciton to the high-energy side with decreasing thickness. However no evidence for the alteration of the oscillator strength or other parameters has been obtained. This conclusion is in conflict with the recently published data taken on CdS samples. The stability of the polariton dispersion in our case is supported by the theoretical study of reflectance ignoring the effects of the finiteness of the exciton radius.     

Four-wave polariton scattering of light in LiNbO3

Four-wave Stokes k-spectra for light scattering on polaritons in lithium niobate crystals with an Mg impurity are studied experimentally. The mechanisms for direct, cascade, coherent, and incoherent four-wave mixing of light are discussed in the course of interpreting the angular dependences of the scattered light intensity. It is shown that the dispersion of the real part of the polariton wave vector and the refractive index of the crystals at the polariton frequencies can be measured with an order of magnitude greater accuracy than by spontaneous three-wave polariton light scattering. A significant discrepancy is found between determinations of the polariton absorption coefficient from the angular spectra of three-wave scattering and four-wave scattering in terms of the model employed here. Zh. éksp. Teor. Fiz. 112, 441–452 (August 1997)     

Raman scattering by phonon polaritons in ZnS

The experimental difficulties in recording the phonon-polariton spectra of ZnS crystals are discussed. The measured polariton dispersion in cubic ZnS is presented and is found to be in good agreement with the calculated one.