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

Analytical approach to semiconductor Bloch equations

Although semiconductor Bloch equations have been widely used for decades to address ultrafast optical phenomena in semiconductors, they have a few important drawbacks: (i) Coulomb terms between free electron-hole pairs require Hartree-Fock treatment which, in its usual form, preserves excitonic poles but loses biexcitonic resonances. (ii) Solving the resulting coupled differential equations imposes heavy numerics which completely hide the physics. This can be completely avoided if, instead of free electron-hole pairs, we use correlated pairs, i.e., excitons. Their interactions are easy to handle through the recently constructed composite-exciton many-body theory, which allows us to \emph{analytically} obtain the time evolution of the polarization induced by a laser pulse. This polarization comes from Coulomb interactions between virtual excitons, but also from Coulomb-free fermion exchanges, which are dominant at large detuning

Collective mode of homogeneous superfluid Fermi gases in the BEC-BCS crossover

We perform a detailed study of the collective mode across the whole BEC-BCS crossover in fermionic gases at zero temperature, covering the whole range of energy beyond the linear regime. This is done on the basis of the dynamical BCS model. We recover first the results of the linear regime in a simple form. Then specific attention is payed to the non linear part of the dispersion relation and its interplay with the continuum of single fermionic excitations. In particular we consider in detail the merging of collective mode into the continuum of single fermionic excitations. This occurs not only on the BCS side of the crossover, but also slightly beyond unitarity on the BEC side. Another remarkable feature is the very linear behaviour of the dispersion relation in the vicinity of unitarity almost up to merging with the continuum. Finally, while on the BEC side the mode is quite analogous to the Bogoliubov mode, a difference appear at high wavevectors. On the basis of our results we determine the Landau critical velocity in the BEC-BCS crossover which is found to be largest close to unitarity. Our investigation has revealed interesting qualitative features which would deserve experimental exploration as well as further theoretical studies by more sophisticated means.Comment: 21 page

Atomic lattice excitons: from condensates to crystals

We discuss atomic lattice excitons (ALEs), bound particle-hole pairs formed by fermionic atoms in two bands of an optical lattice. Such a system provides a clean setup to study fundamental properties of excitons, ranging from condensation to exciton crystals (which appear for a large effective mass ratio between particles and holes). Using both mean-field treatments and 1D numerical computation, we discuss the properities of ALEs under varying conditions, and discuss in particular their preparation and measurement.Comment: 19 pages, 15 figures, changed formatting for journal submission, corrected minor errors in reference list and tex

Effective scatterings between electrons, excitons and trions

The final goal of this paper is to derive the effective scattering ruling the time evolution of two semiconductor trions using the many-body formalism for composite fermions we have just proposed. However, to understand the importance of the particle composite nature, their bosonic/fermionic character and their overall charge, we also report on scatterings between free electrons, excitons and trions. This leads us to identify the form factors associated to direct processes involving excitons and trions. For transitions between ground states, these form factors reduce to zero and one respectively, in the small momentum transfer limit. Copyright EDP Sciences, SIF, Springer-Verlag Berlin Heidelberg 2011