Scattering rates and lifetime of exact and boson excitons

Although excitons are not exact bosons, they are commonly treated as such provided that their composite nature is included in effective scatterings dressed by exchange. We here \emph{prove} that, \emph{whatever these scatterings are}, they cannot give both the scattering rates $T_{ij}^{-1}$ and the exciton lifetime $\tau_0$, correctly: A striking factor 1/2 exists between $\tau_0^{-1}$ and the sum of $T_{ij}^{-1}$'s, which originates from the composite nature of excitons, irretrievably lost when they are bosonized. This result, which appears as very disturbing at first, casts major doubts on bosonization for problems dealing with \emph{interacting} excitons

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

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 n_c, an exponential polarization decay is obtained, which is characterized by a dephasing rate G=1/T_2. 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 G (n-n_c)^2 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 p^0 with |p(t)|-|p^0| ~1/t 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 F_k= . The collision terms are analyzed and an approximation is used which is consistent with the existence of BEC. The inclusion of the coherent x-x interaction does not change the dephasing laws. The anomalous function F_k exhibits a clear threshold behaviour at the critical density.Comment: European Physical Journal B (in print

Many-body effects between unbosonized excitons

We here give a brief survey of our new many-body theory for composite excitons, as well as some of the results we have already obtained using it. In view of them, we conclude that, in order to fully trust the results one finds, interacting excitons should not be bosonized: Indeed, all effective bosonic Hamiltonians (even the hermitian ones !) can miss terms as large as the ones they generate; they can even miss the dominant term, as in problems dealing with optical nonlinearities

How composite bosons really interact

The aim of this paper is to clarify the conceptual difference which exists between the interactions of composite bosons and the interactions of elementary bosons. A special focus is made on the physical processes which are missed when composite bosons are replaced by elementary bosons. Although what is here said directly applies to excitons, it is also valid for bosons in other fields than semiconductor physics. We in particular explain how the two basic scatterings -- Coulomb and Pauli -- of our many-body theory for composite excitons can be extended to a pair of fermions which is not an Hamiltonian eigenstate -- as for example a pair of trapped electrons, of current interest in quantum information.Comment: 39 pages, 12 figure