The exciton many-body theory extended to any kind of composite bosons

We have recently constructed a many-body theory for composite excitons, in which the possible carrier exchanges between N excitons can be treated exactly through a set of dimensionless “Pauli scatterings” between two excitons. Many-body effects with free excitons turn out to be rather simple because these excitons are the exact one-pair eigenstates of the semiconductor Hamiltonian, in the absence of localized traps. They consequently form a complete orthogonal basis for one-pair states. As essentially all quantum particles known as bosons are composite bosons, it is highly desirable to extend this free exciton many-body theory to other kinds of “cobosons” — a contraction for composite bosons — the physically relevant ones being possibly not the exact one-pair eigenstates of the system Hamiltonian. The purpose of this paper is to derive the “Pauli scatterings” and the “interaction scatterings” of these cobosons in terms of their wave functions and the interactions which exist between the fermions from which they are constructed. It is also explained how to calculate many-body effects in such a very general composite boson system.     

The Girardeau's fermion-boson procedure in the light of the composite-boson many-body theory

We reconsider the procedure developed for atoms a few decades ago by Girardeau, in the light of the composite-boson many-body theory we recently proposed. The Girardeau's procedure makes use of a so called “unitary Fock-Tani operator” which in an exact way transforms one composite bound atom into one bosonic “ideal” atom. When used to transform the Hamiltonian of interacting atoms, this operator generates an extremely complex set of effective scatterings between ideal bosonic atoms and free fermions which makes the transformed Hamiltonian impossible to write explicitly, in this way forcing to some truncation. The scatterings restricted to the ideal-atom subspace are shown to read rather simply in terms of the two elementary scatterings of the composite-boson many-body theory, namely, the energy-like direct interaction scatterings — which describe fermion interactions without fermion exchange — and the dimensionless Pauli scatterings — which describe fermion exchanges without fermion interaction. We here show that, due to a fundamental difference in the scalar products of elementary and composite bosons, the Hamiltonian expectation value for N ground state atoms obtained by staying in the ideal-atom subspace and working with boson operators only, differ from the exact ones even for N = 2 and a mapping to the ideal-atom subspace performed, as advocated, from the fully antisymmetrical atomic state, i.e., the state which obeys the so-called “subsidiary condition”. This shows that, within this Girardeau's procedure too, we cannot completely forget the underlying fermionic components of the particles if we want to correctly describe their interactions.     

Electron-hole diagrams versus exciton diagrams: the simplest problem on interacting excitons

We study the interaction of an exciton with a distant metal, which is the simplest problem on interacting excitons: The semiconductor and metal electrons being “different” species, we do not have to worry about the tricky consequences of Pauli exclusion between identical carriers, which appear in any other problem on interacting excitons. We show how the exciton absorption, in the presence of semiconductor-metal interaction, can be derived in a very simple and transparent way from an exciton diagram procedure, provided that we use the appropriate exciton-metal interaction vertex, which contains the scattering from an exciton state to another exciton state under a Coulomb excitation. We also show that the resolution of this problem using standard electron-hole diagrams is dreadfully complicated at the lowest order in the semiconductor-metal interaction already, preventing a full calculation of the exciton-metal coupling from this usual technique. Received 26 February 2001     

Commutation technique for interacting close-to-boson excitons

The correct treatment of the close-to-boson character of excitons is known to be a major problem. In a previous work, we have proposed a “commutation technique” to include this close-to-boson character in their interactions. We here extend this technique to excitons with spin degrees of freedom as they are of crucial importance for many physical effects. Although the exciton total angular momentum may appear rather appealing at first, we show that the electron and hole angular momenta are much more appropriate when dealing with scattering processes. As an application of this commutation technique to a specific problem, we reconsider a previous calculation of the exciton-exciton scattering rate and show that the proposed quantity is intrinsically incorrect for fundamental reasons linked to the fermionic nature of the excitons. Received 25 October 2001 Published online 25 June 2002     

Ab initio study of the Fe intra- and inter-layer magnetic order in Fe/Ir(001) superlattices

We reconsider the semiconductor trions from scratch. We first determine the very many “reasonable” ways to write the trions in first quantization. We then select the forms which are easy to relate to physical pictures. In a second part, we derive the corresponding creation operators in second quantization. We pay particular attention to the expression of the X^- trion in terms of exciton and free-electron, as it is the one adapted to future works on many-body effects with trions. Received 27 May 2002 / Received in final form 18 December 2002 Published online 20 June 2003 RID="a" ID="a"e-mail: combescot@gps.jussieu.fr     

Density expansion of the energy of N close-to-boson excitons

Pauli exclusion between the carriers of N excitons induces novel many-body effects, quite different from the ones generated by Coulomb interaction. Using our commutation technique for interacting close-to-boson particles, we here calculate the Hamiltonian expectation value in the N-ground-state-exciton state. Coulomb interaction enters this quantity at first order only by construction; nevertheless, due to Pauli exclusion, subtle many-body effects take place, which give rise to terms in (Na _x ³/)ⁿ with n ≥ 2. An exact procedure to get these density dependent terms is given. Received 11 February 2002 / Received in final form 30 May 2002 Published online 6 March 2003 RID="a" ID="a"e-mail: combescot@gps.jussieu.fr     

Polaron effects on excitons in parabolic quantum wells: fractional-dimension variational approach

Polaron effects on excitons in parabolic quantum wells are studied theoretically by using a variational approach with the so-called fractional dimension model. The numerical results for the exciton binding energies and longitudinal-optical phonon contributions in GaAs/Al_0.3Ga_0.7As parabolic quantum well structures are obtained as functions of the well width. It is shown that the exciton binding energies are obviously reduced by the electron (hole)-phonon interaction and the polaron effects are un-negligible. The results demonstrate that the fractional-dimension variational theory is effectual in the investigations of excitonic polaron problems in parabolic quantum wells.     

The q-deformed Bose gas: integrability and thermodynamics

We investigate the exact solution of the q-deformed one-dimensional Bose gas to derive all integrals of motion and their corresponding eigenvalues. As an application, the thermodynamics is given and compared to an effective field theory at low temperatures.     

Quantum corrections to the energy density of a homogeneous Bose gas

Quantum corrections to the properties of a homogeneous interacting Bose gas at zero temperature can be calculated as a low-density expansion in powers of , where is the number density and a is the S-wave scattering length. We calculate the ground state energy density to second order in . The coefficient of the correction has a logarithmic term that was calculated in 1959. We present the first calculation of the constant under the logarithm. The constant depends not only on a, but also on an extra parameter that describes the low energy scattering of the bosons. In the case of alkali atoms, we argue that the second order quantum correction is dominated by the logarithmic term, where the argument of the logarithm is ,and is the length scale set by the van der Waals potential. Received 2 February 1999     

Exact and approximate results of non-extensive quantum statistics

We develop an analytical technique to derive explicit forms of thermodynamical quantities within the asymptotic approach to non-extensive quantum distribution functions. Using it, we find an expression for the number of particles in a boson system which we compare with other approximate scheme (i.e. factorization approach), and with the recently obtained exact result. To do this, we investigate the predictions on Bose-Einstein condensation and the blackbody radiation. We find that both approximation techniques give results similar to (up to ) the exact ones, making them a useful tool for computations. Because of the simplicity of the factorization approach formulae, it appears that this is the easiest way to handle with physical systems which might exhibit slight deviations from extensivity. Received 19 August 1999 and Received in final form 1 November 1999     

Anomalous dephasing of bosonic excitons interacting with phonons in the vicinity of the Bose-Einstein condensation

The dephasing and relaxation kinetics of bosonic excitons interacting with a thermal bath of acoustic phonons is studied after coherent pulse excitation. The kinetics of the induced excitonic polarization is calculated within Markovian equations both for subcritical and supercritical excitation with respect to a Bose-Einstein condensation (BEC). For excited densities n below the critical density , an exponential polarization decay is obtained, which is characterized by a dephasing rate . This dephasing rate due to phonon scattering shows a pronounced exciton-density dependence in the vicinity of the phase transition. It is well described by the power law that can be understood by linearization of the equations around the equilibrium solution. Above the critical density we get a non-exponential relaxation to the final condensate value p⁰ with that holds for all densities. Furthermore we include the full self-consistent Hartree-Fock-Bogoliubov (HFB) terms due to the exciton-exciton interaction and the kinetics of the anomalous functions . The collision terms are analyzed and an approximation is used which is consistent with the existence of BEC. The inclusion of the coherent exciton-exciton interaction does not change the dephasing laws. The anomalous function F_k exhibits a clear threshold behaviour at the critical density. Received 13 December 1999     

Bose-Einstein condensation in interacting gases

We study the occurrence of a Bose-Einstein transition in a dilute gas with repulsive interactions, starting from temperatures above the transition temperature. The formalism, based on the use of Ursell operators, allows us to evaluate the one-particle density operator with more flexibility than in mean-field theories, since it does not necessarily coincide with that of an ideal gas with adjustable parameters (chemical potential, etc.). In a first step, a simple approximation is used (Ursell-Dyson approximation), which allow us to recover results which are similar to those of the usual mean-field theories. In a second step, a more precise treatment of the correlations and velocity dependence of the populations in the system is elaborated. This introduces new physical effects, such as a change of the velocity profile just above the transition: the proportion of atoms with low velocities is higher than in an ideal gas. A consequence of this distortion is an increase of the critical temperature (at constant density) of the Bose gas, in agreement with those of recent path integral Monte-Carlo calculations for hard spheres. Received 13 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     

Phase dynamics of Bose-Einstein condensates: Losses versus revivals

In the absence of losses the phase of a Bose-Einstein condensate undergoes collapses and revivals in time due to elastic atomic interactions. As experiments necessarily involve inelastic collisions, we develop a model to describe the phase dynamics of the condensates in presence of collisional losses. We find that a few inelastic processes are sufficient to damp the revivals of the phase. For this reason the observability of phase revivals for present experimental conditions is limited to condensates with a few hundreds of atoms. Received: 23 February 1998 / Revised: 21 July 1998 / Accepted: 23 July 1998     

Binary mixtures of Bose-Einstein condensates: Phase dynamics and spatial dynamics

We investigate the relative phase coherence properties and the occurrence of demixing instabilities for two mutually interacting and time evolving Bose-Einstein condensates in traps. Our treatment naturally includes the additional decoherence effect due to fluctuations in the total number of particles. Analytical results are presented for the breathe-together solution, an extension of previously known scaling solution to the case of a binary mixture of condensates. When the three coupling constants describing the elastic interactions among the atoms in the two states are close to each other, a dramatic increase of the phase coherence time is predicted. Numerical results are presented for the parameters of the recent JILA experiments. Received 23 April 1999 and Received in final form 21 September 1999     

Fully quantum mechanical moment of inertia of a mesoscopic ideal Bose gas

The superfluid fraction of an atomic cloud is defined using the cloud's response to a rotation of the external potential, i.e. the moment of inertia. A fully quantum mechanical calculation of this moment is based on the dispersion of L_z instead of quasi-classical averages. In this paper we derive analytical results for the moment of inertia of a small number of non-interacting Bosons using the canonical ensemble. The required symmetrized averages are obtained via a representation of the partition function by permutation cycles. Our results are useful to discriminate purely quantum statistical effects from interaction effects in studies of superfluidity and phase transitions in finite samples. Received 30 June 2000     

Structural dependence of exciton in carbon nanotubes

The binding energies and sizes of excitons, and energy splitting of the bright-dark excitons in single-walled carbon nanotubes have been calculated using the nonorthogonal tight-binding model, supplemented by the long-range Coulomb interaction. It is found that the binding energies and the sizes of excitons not only depend on tube's diameter d, but also its chirality. However, the splitting of the bright-dark excitons mostly depends on 1/d². Our obtained results show that the curvature effect is very important for the exciton excitations in the SWNTs, especially in the smaller diameter ones.     

Perturbation expansion, Bogoliubov inequality and integral representations in nonextensive Tsallis statistics

By using integral representations the perturbation expansion and the Bogoliubov inequality in nonextensive Tsallis statistics are investigated in a unified way. This procedure extends the analysis performed recently by Lenzi et al. [Phys. Rev. Lett. 80, 218 (1998)] to the quantum (discrete spectra) case, for q<1. An example is presented in order to illustrate the method. Received 19 November 1998     

Lateral carrier tunnelling in stacked In(Ga)As/GaAs quantum rings

Exciton recombination dynamics in vertical stacks of InGaAs quantum rings have been studied by means of continuous wave and time resolved photoluminescence under low excitation density conditions. We have paid special attention to the effect of the carrier coupling on the exciton radiative lifetime: weak (14 nm spacer sample), intermediate (4.5 nm spacer sample), where the size filtering effects (towards small rings) compensate partially that arising from carrier coupling (towards lower energies), and strong electron and hole coupling (1.5 nm spacer sample) between layers. Experimental decay times in the latter two cases have been compared to the times simulated with a multi-quantum well based model, which accounts for the observed change of carrier coupling regime. The most important effect is observed when the hole wave function overlap along the growth direction becomes important (1.5 nm spacer sample). This situation makes important the lateral tunneling of excitons between rings, given their large lateral size, which is characterized by times around 5 ns at the emission peak energy (rings with the most probable size of the distribution).     

Coupled atomic-molecular condensates in a double-well potential: decaying molecular oscillations

We present a four-mode model that describes coherent photo-association (PA) in a double-well Bose-Einstein condensate, focusing on the average molecular populations in certain parameters. Our numerical results predict an interesting strong-damping effect of molecular oscillations by controlling the particle tunnellings and PA light strength, which may provide a promising way for creating a stable molecular condensate via coherent PA in a magnetic double-well potential.