Collapses and revivals of exciton emission in a semiconductor microcavity: detuning and phase-space filling effects

We investigate exciton emission of quantum well embedded in a semiconductor microcavity. The analytical expressions of the light intensity for the cases of excitonic number state and coherent state are presented by using secular approximation. Our results show that the effective exciton-exciton interaction leads to the appearance of collapse and revival of the light intensity. The revival time is twice compared the coherent state case with that of the number state. The dissipation of the exciton-polariton lowers the revival amplitude but does not alter the revival time. The influences of the detuning and the phase-space filling are studied. We find that the effect of the higher-order exciton-photon interaction may be removed by adjusting the detuning.Comment: 7 pages, 3 figure

Exciton-exciton scattering: Composite boson versus elementary boson

This paper introduces a new quantum object, the ``coboson'', for composite particles, like the excitons, which are made of two fermions. Although commonly dealed with as elementary bosons, these composite bosons -- ``cobosons'' in short -- differ from them due to their composite nature which makes the handling of their many-body effects quite different from the existing treatments valid for elementary bosons. Due to this composite nature, it is not possible to correctly describe the interaction between cobosons as a potential $V$. Consequently, the standard Fermi golden rule, written in terms of $V$, cannot be used to obtain the transition rates between exciton states. Through an unconventional expression for this Fermi golden rule, which is here given in terms of the Hamiltonian only, we here give a detailed calculation of the time evolution of two excitons. We compare the results of this exact approach with the ones obtained by using an effective bosonic exciton Hamiltonian. We show that the relation between the inverse lifetime and the sum of transition rates for elementary bosons differs from the one of composite bosons by a factor of 1/2, whatever the mapping from composite bosons to elementary bosons is. The present paper thus constitutes a strong mathematical proof that, in spite of a widely spread belief, we cannot forget the composite nature of these cobosons, even in the extremely low density limit of just two excitons. This paper also shows the (unexpected) cancellation, in the Born approximation, of the two-exciton transition rate for a finite value of the momentum transfer

Phase diagram and critical properties in the Polyakov--Nambu--Jona-Lasinio model

We investigate the phase diagram of the so-called Polyakov--Nambu--Jona-Lasinio model at finite temperature and nonzero chemical potential with three quark flavours. Chiral and deconfinement phase transitions are discussed, and the relevant order-like parameters are analyzed. The results are compared with simple thermodynamic expectations and lattice data. A special attention is payed to the critical end point: as the strength of the flavour-mixing interaction becomes weaker, the critical end point moves to low temperatures and can even disappear.Comment: Talk given at the 9th International Conference on Quark Confinement and the Hadron Spectrum - QCHS IX, Madrid, Spain, 30 August - September 201

Dimensionality dependence of optical nonlinearity and relaxation dynamics in cuprates

Femtosecond pump-probe measurements find pronounced dimensionality dependence of the optical nonlinearity in cuprates. Although the coherent two-photon absorption (TPA) and linear absorption bands nearly overlap in both quasi-one and two-dimensional (1D and 2D) cuprates, the TPA coefficient is one order of magnitude smaller in 2D than in 1D. Furthermore, picosecond recovery of optical transparency is observed in 1D cuprates, while the recovery in 2D involves relaxation channels with a time scales of tens of picoseconds. The experimental results are interpreted within the two-band extended Hubbard model.Comment: 10 pages, 4 figure

Optical spectra of a quantum dot in a microcavity in the nonlinear regime

The optical emission spectrum of a quantum dot in strong coupling with the single mode of a microcavity is obtained in the nonlinear regime. We study how exciton-exciton interactions alter the emission spectrum of the system, bringing the linear Rabi doublet into a multiplet structure that is strongly dependent on the cavity-exciton energy detuning. We emphasise how nonlinearity can be used to evidence the genuine quantum nature of the coupling by producing satellites peaks of the Rabi doublet that originate from the quantized energy levels of the interactions.Comment: Low quality figures. To be published in Phys. Rev. B. 78 (2008

Shiva diagrams for composite-boson many-body effects : How they work

The purpose of this paper is to show how the diagrammatic expansion in fermion exchanges of scalar products of $N$-composite-boson (``coboson'') states can be obtained in a practical way. The hard algebra on which this expansion is based, will be given in an independent publication. Due to the composite nature of the particles, the scalar products of $N$-coboson states do not reduce to a set of Kronecker symbols, as for elementary bosons, but contain subtle exchange terms between two or more cobosons. These terms originate from Pauli exclusion between the fermionic components of the particles. While our many-body theory for composite bosons leads to write these scalar products as complicated sums of products of ``Pauli scatterings'' between \emph{two} cobosons, they in fact correspond to fermion exchanges between any number P of quantum particles, with $2 \leq P\leq N$. These $P$-body exchanges are nicely represented by the so-called ``Shiva diagrams'', which are topologically different from Feynman diagrams, due to the intrinsic many-body nature of Pauli exclusion from which they originate. These Shiva diagrams in fact constitute the novel part of our composite-exciton many-body theory which was up to now missing to get its full diagrammatic representation. Using them, we can now ``see'' through diagrams the physics of any quantity in which enters $N$ interacting excitons -- or more generally $N$ composite bosons --, with fermion exchanges included in an \emph{exact} -- and transparent -- way.Comment: To be published in Eur. Phys. J.

Semiconductor-cavity QED in high-Q regimes: Detuning effect

The non-resonant interaction between the high-density excitons in a quantum well and a single mode cavity field is investigated. An analytical expression for the physical spectrum of the excitons is obtained. The spectral properties of the excitons, which are initially prepared in the number states or the superposed states of the two different number states by the resonant femtosecond pulse pumping experiment, are studied. Numerical study of the physical spectrum is carried out and a discussion of the detuning effect is presented.Comment: 7 pages, 8 figure

Traces of stimulated bosonic exciton-scattering in semiconductor luminescence

We observe signatures of stimulated bosonic scattering of excitons, a precursor of Bose-Einstein-Condensation (BEC), in the photoluminescence of semiconductor quantum wells. The optical decay of a spinless molecule of two excitons (biexciton) into an exciton and a photon with opposite angular momenta is subject to bosonic enhancement in the presence of other excitons. In a spin polarized gas of excitons the bosonic enhancement breaks the symmetry of two equivalent decay channels leading to circularly polarized luminescence of the biexciton with the sign opposite to the excitonic luminescence. Comparison of experiment and many body theory proves stimulated scattering of excitons, but excludes the presence of a fully condensed BEC-like state.Comment: 5 page

Effective Hamiltonian for Excitons with Spin Degrees of Freedom

Starting from the conventional electron-hole Hamiltonian ${\cal H}_{eh}$, we derive an effective Hamiltonian $\tilde{\cal H}_{1s}$ for $1s$ excitons with spin degrees of freedom. The Hamiltonian describes optical processes close to the exciton resonance for the case of weak excitation. We show that straightforward bosonization of ${\cal H}_{eh}$ does not give the correct form of $\tilde{\cal H}_{1s}$, which we obtain by a projection onto the subspace spanned by the $1s$ excitons. The resulting relaxation and renormalization terms generate an interaction between excitons with opposite spin. Moreover, exciton-exciton repulsive interaction is greatly reduced by the renormalization. The agreement of the present theory with the experiment supports the validity of the description of a fermionic system by bosonic fields in two dimensions.Comment: 12 pages, no figures, RevTe