Short note on the excitonic Mott phase

An exciton gas on a lattice is analysed in terms of a convergent hopping expansion. For a given chemical potential, our calculation provides a sufficient condition for the hopping rate to obtain an exponential decay of the exciton correlation function. This result indicates the existence of a Mott phase in which strong fluctuations destroy the long range correlations in the exciton gas at any temperature, either by thermal or by quantum fluctuations.     

Γ-X mixing of the free and bound exciton in GaAs1-xPx

Photoluminescence in GaAs_1-xP_x near crossover at liquid He temperature gives evidence of a Γ-x interaction of the bound and free exciton. The interaction in the FE case is made possible by the breaking down of the translational symmetry of the Hamiltonian due to fluctuations in the random-alloy potential. The matrix elements of such interaction are found equal to 0.5 and 3.5 meV for the free and donor-bound exciton respectively.     

The influence of exciton motion on spin-resonance absorption

We use a stochastic model for the exciton motion which comprises both the coherent and the incoherent motion. The incoherent part is taken care of by a stochastic process which allows the local excitation energy and the transition matrix element to fluctuate by means of a Markovian process. The interaction between the spins and their surroundings is described by the usual spin-Hamiltonian which is, however, simplified to a spin 1/2 particle (instead of the triplet state). In the present paper we solve exactly the two limiting cases of completely coherent and incoherent motion (for two molecules). In the incoherent case the influence of the exchange interaction integral is taken into account by perturbation theory. We find expressions which are immediately comparable with ESR-experimental data. This comparison and additional information derived from optical absorption measurements allow us to determine all free parameters of our model uniquely. In particular, the fluctuations of the exchange interaction integral (with strength γ₁) play an important role. From these parameters we may furthermore calculate the correlation time of the proton spin resonance in agreement with experimental data. The results show clearly that at room temperature in anthracene crystals the exciton undergoes a hopping process.     

Origin of the Landau-Lifshitz hydrodynamic fluctuations in nonequilibrium systems and a new method for reducing the Boltzmann equation

The Landau-Lifshitz fluctuating fluxes in fluctuating hydrodynamics are derived from the deterministic Boltzmann equation with the aid of a reduction method developed by Fujisaka and Mori. Thus it is shown that the hydrodynamic fluctuations innonequilibrium systems are generated by the reduction of variables from the-space distribution function to its five momentum moments, i.e., the hydrodynamic variables. This differs from the Bixon-Zwanzig and Fox-Uhlenbeck theories, in which the Landau-Lifshitz fluctuating fluxes are derived from the molecular fluctuating force in thestochastic Boltzmann-Langevin equation, which is, however, negligible in nonequilibrium systems. Thus the present method improves the Chapman-Enskog reduction method so as to include the hydrodynamic fluctuations generated by the reduction of variables.Supported in part by the Scientific Research Fund of the Ministry of Education.     

Time-resolved photoluminescence study of GaInAs/AlGaInAs superlattices

We present results of time-resolved photoluminescence experiments performed at 77 K on a GaInAs/AlGaInAs superlattice grown by molecular beam epitaxy and lattice matched to an InP substrate. The superlattice is the intrinsic part of a p–i–n diode. Photoluminescence spectra, reconstructed at various delay times between 5 ps and 100 ps after the laser pulse, show lines associated to the 1s and 2s heavy-hole exciton states and to the free carrier recombination. This result provides a direct determination of the binding energy of the heavy-hole exciton which is shown to be equal to 15 meV. Such a large value of the Rydberg is due to the fluctuations of composition which cause the heavy-hole exciton to be localized within a single well. The spectra also exhibit a shoulder which corresponds to the electron-to-light-hole transition. The 2s heavy-hole-exciton transition is coupled to the latter by an LO phonon. Finally a transition 21 meV below the 1s heavy-hole-exciton energy is related to Be residual impurities.     

Exciton condensation in coupled quantum wells

Bound electron-hole pairs—excitons—are Bose particles with small mass. Exciton Bose-Einstein condensation is expected to occur at a few degrees Kelvin—a temperature many orders of magnitude higher than for atoms. Experimentally, an exciton temperature well below 1 K is achieved in coupled quantum well (CQW) semiconductor nanostructures. In this contribution, we review briefly experiments that signal exciton condensation in CQWs: a strong enhancement of the indirect exciton mobility consistent with the onset of exciton superfluidity, a strong enhancement of the radiative decay rate of the indirect excitons consistent with exciton condensate superradiance, strong fluctuations of the indirect exciton emission consistent with critical fluctuations near the phase transition, and a strong enhancement of the exciton scattering rate with increasing concentration of the indirect excitons revealing bosonic stimulation of exciton scattering. Novel experiments with exciton condensation in potential traps, pattern formation in exciton system and macroscopically ordered exciton state will also be reviewed briefly.     

Equal-time second-order moments of a harmonic oscillator with stochastic frequency and driving force

Using a simple matrix method, we have obtained exact second-order equilibrium moments for a linearly damped harmonic oscillator with a fluctuating frequency (t) and driven by a fluctuating forcef(t). We have assumed each of the fluctuating quantities to be delta-correlated. We demonstrate that the final answers are identical whetherf(t) and (t) are statistically independent or delta-correlated. We have also established the region of parameter space in which the oscillator is energetically stable. The results are shown to be completely determined by the coefficients of the first and second cumulants of the fluctuations.Supported in part by the Office of Naval Research, NSF Grant # CHE 78-21460, and by a grant from Charles and Renée Taubman.     

Brownian motion with active fluctuations

We study the effect of different types of fluctuation on the motion of self-propelled particles in two spatial dimensions. We distinguish between passive and active fluctuations. Passive fluctuations (e.g., thermal fluctuations) are independent of the orientation of the particle. In contrast, active ones point parallel or perpendicular to the time dependent orientation of the particle. We derive analytical expressions for the speed and velocity probability density for a generic model of active Brownian particles, which yields an increased probability of low speeds in the presence of active fluctuations in comparison to the case of purely passive fluctuations. As a consequence, we predict sharply peaked Cartesian velocity probability densities at the origin. Finally, we show that such a behavior may also occur in non-Gaussian active fluctuations and discuss briefly correlations of the fluctuating stochastic forces.     

Influence of the coupled coherent and incoherent motion of triplet excitons on the ESR line shape in molecular crystals in the quasi-incoherent case

The exciton motion is described by the Hamiltonian of the Haken-Strobl-model, which contains a coherent and a fluctuating part, and which allows to represent the coupled coherent and incoherent motion of Frenkel excitons. The Hamiltonian of the spin motion contains the usual Zeeman term and fine structure terms of the various inequivalent molecules in the unit cell of the crystal. Starting from this Hamiltonian an exact infinite set of equations of motion for the correlation functions, describing the ESR line shape, is given. With the assumption that phase relations of the exciton motion decay rapidly, the number of this set of equations may be reduced considerably being now determined by the number of molecules within the unit cell and the dimension of the spin space under consideration. In this reduced set of equations the motion of the triplet excitons is described by an effective hopping rateΓ ₁ between the inequivalent molecules within the unit cell, containing also a contribution of the coherent interaction.     

Exciton-polariton absorption in periodic and disordered quantum-well chains

The exciton-polariton transfer and absorption in regular and disordered structures with a finite number of quantum wells are studied theoretically. The transfer matrix method is invoked in the exciton resonance region to calculate the reflectivity, transmissivity, and absorptivity spectra, as well as the integrated absorptivity as a function of the γ/Γ₀ ratio of the parameters of nonradiative and radiative damping of quasi-two-dimensional excitons. It is shown that the integrated absorptivity as a function of γ (temperature) follows a universal pattern, more specifically, it increases monotonically from zero at γ = 0 to saturate at γ/Γ₀ ? 1. Because the exciton-polariton absorption being single mode, the integrated absorptivity in Bragg quantum-well structures is substantially lower than that in short-period structures, in which absorption involves the whole spectral multitude of modes. The intrawell disorder associated with fluctuations in the frequencies of exciton excitation in quantum wells enhances the integrated absorptivity to the level typical of light absorption with no resonance among excitons of different quantum wells. The interwell disorder originating from fluctuations in quantum-well separation likewise leads to an increase in the integrated absorptivity.     

Quantum theory of light propagation in a fluctuating laser-active medium

The basic equations are derived which describe the propagation of an electromagnetic field in a fluctuating laser-active medium. The well-known methods of Langevinequations and master-equation for a few discrete modes are generalized to meet also the case of a radiation field with continuous spectrum. The medium is described by two-level atoms which are embedded in a merely passive solid matrix and homogeneously distributed over space. They have an inversion which is kept constant by an externally applied pump. The atomic line may be homogeneously or inhomogeneously broadened. We obtain a complete set of partial differential equations for the field operators with damping terms and fluctuating forces homogeneously distributed over the material. The telegraph equation with a fluctuating force occurs as a special case. After the exact elimination of the atomic variables we obtain a nonlinear field equation for the radiation field alone. By means of a pseudo-Hamiltonian and by a simple one-dimensional example we show that in a certain sense there exists a close formal analogy between the present theory and the theory of an interacting Bose gas. The characteristic differences between the two theories are also discussed. We find, that there occurs a phase transition of the radiation field because above a certain threshold of the pump the photons condense into a single mode and establish an “offdiagonal-long-range order”. The amplitude fluctuations and the phase fluctuations, which restore the broken phase symmetry, are calculated in detail. A new condition for the occurrence of undamped spiking (pulse formation) for a continuum of modes is derived.     

Resonant Rayleigh scattering from excitons in CdxZn1−xTe:ZnTe quantum wells: measurement of homogeneous linewidths

The technique of resonant Rayleigh scattering is used to determine the homogeneous linewidth across the inhomogeneously broadened exciton resonance in a Cd_0.25Zn_0.75Te/ZnTe multiple quantum well structure. An order of magnitude increase of the Rayleigh scattering signal over background is observed on tuning a narrow-band laser through the exciton resonance at low temperatures. Spectral and temporal measurements show the effect to be a true scattering process rather than luminescence. The interface and alloy fluctuations in the quantum well give rise to spatial fluctuations in the dielectric response of the system while the large exciton resonance causes strong enhancement of scattering. The homogeneous linewidth was calculated across the exciton resonance. The technique is compared with the dephasing and hole-burning techniques more commonly used in homogeneous linewidth measurements.     

Glassy dynamics and coarsening

In this paper I present a short review of the present theoretical understanding of the dynamics, global and fluctuating, in the glassy out of equilibrium regime. The first part of the talks dealt with a summary of the results of mean-field models and served to introduce the conjecture that time-reparametrization invariance controls the fluctuating dynamics. Finally, I briefly discussed very recent results on the domain size fluctuations in coarsening problems and how these and similar studies of the dynamics of elastic lines could help us in understanding the evolution of more complex glassy systems.     

Quantum optical effects in semiconductor microcavities

Investigations of quantum effects in semiconductor quantum-well microcavities interacting with laser light in the strong-coupling regime are presented. Modifications of quantum fluctuations of the outgoing light are expected due to the non-linearity originating from coherent exciton–exciton scattering. In the strong-coupling regime, this scattering translates into a four-wave mixing interaction between the mixed exciton–photon states, the polaritons. Squeezing and giant amplification of the polariton field and of the outgoing light field fluctuations are predicted. However, polariton–phonon scattering is shown to yield excess noise in the output field, which may destroy the non-classical effects. Experiments demonstrate evidence for giant amplification due to coherent four-wave mixing of polaritons. Noise reduction below the thermal noise level was also observed. To cite this article: E. Giacobino et al., C. R. Physique 3 (2002) 41–52     

Stochastic Spacetime and Brownian Motion of Test Particles

The operational meaning of spacetime fluctuations is discussed. Classical spacetime geometry can be viewed as encoding the relations between the motions of test particles in the geometry. By analogy, quantum fluctuations of spacetime geometry can be interpreted in terms of the fluctuations of these motions. Thus, one can give meaning to spacetime fluctuations in terms of observables which describe the Brownian motion of test particles. We will first discuss some electromagnetic analogies, where quantum fluctuations of the electromagnetic field induce Brownian motion of test particles. We next discuss several explicit examples of Brownian motion caused by a fluctuating gravitational field. These examples include lightcone fluctuations, variations in the flight times of photons through the fluctuating geometry, and fluctuations in the expansion parameter given by a Langevin version of the Raychaudhuri equation. The fluctuations in this parameter lead to variations in the luminosity of sources. Other phenomena that can be linked to spacetime fluctuations are spectral line broadening and angular blurring of distant sources.     

Theory of slightly fluctuating ratchets

We consider a Brownian particle moving in a slightly fluctuating potential. Using the perturbation theory on small potential fluctuations, we derive a general analytical expression for the average particle velocity valid for both flashing and rocking ratchets with arbitrary, stochastic or deterministic, time dependence of potential energy fluctuations. The result is determined by the Green’s function for diffusion in the time-independent part of the potential and by the features of correlations in the fluctuating part of the potential. The generality of the result allows describing complex ratchet systems with competing characteristic times; these systems are exemplified by the model of a Brownian photomotor with relaxation processes of finite duration.     

One-body dynamics modified by collective fluctuations

We show how the fluctuating part of the residual coupling between collective and intrinsic motion of a dissipative heavy-ion collision induces correlations in either subspace. They lead in general to a transport equation for the collective motion, and to a new term in the equation for the one-body density which describes collisions with the collective fluctuations. The resulting redistribution of the single-particle occupation numbers ρ_α and the evolution of the fluctuations are coupled with each other due to the dependence of the transition rates in the master equation on the fluctuations, and of the transport coefficients on ρ_α. Considering the special case of a long contact phase, we find the fluctuations to be most effective, with respect to a randomization of ρ_α, within a certain critical region where they pass from stable to unstable behaviour. Estimates are made for the corresponding relaxation times employing a schematic model.     

Dynamics of dilute spin systems in random fluctuating magnetic fields

The problem of stochastic evolution of dilute spins in a randomly fluctuating environment is considered within the frameworks of the Schrödinger equation with Gaussian fluctuating magnetic fields. The evolution equations for the averaged correlators are derived and it is shown that the density matrix of a spin system coupled with the thermoequilibrium fluctuations of fields tends asymptotically with time to the thermodynamic density matrix. The general results are illustrated by examples of coupling with magnons, phonons, and relaxation in paramagnetics. The evolution of spins in artificial high-frequency stochastic fields (Simonius' effect) is also considered. The high-temperature limit and the limit of classical spins are considered separately and the applicability of the Bloch equations is discussed. Then the results are generalized to the single-ion anisotropy and movable spins. Finally, it is shown how the results can be generalized to multi-spin systems.     

On the response of a gravitational radiation detector to magnetic field fluctuations

An attempt was made to measure the sensitivity of the Maryland gravitational radiation detector to fluctuating magnetic fields with frequencies of 0.1 to 30 Hertz. No response was found for fields along the cylinder axis and normal to it. For some of the tests, the weakest intensity to which any part of the cylinder was exposed exceeded 100 times the intensity of fluctuations of the earth's magnetic field at these frequencies.