74 research outputs found
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
Density expansion of the energy of N close-to-boson excitons
Pauli exclusion between the carriers of 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 -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 with
>. An \emph{exact} procedure to get these density dependent terms is given
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
Commutation technique for an exciton photocreated close to a metal
Recently, we have derived the changes in the absorption spectrum of an
exciton when this exciton is photocreated close to a metal. The resolution of
this problem -- which has similarities with Fermi edge singularities -- has
been made possible by the introduction of ``exciton diagrams''. The validity of
this procedure relied on a dreadful calculation based on standard free electron
and free hole diagrams, with the semiconductor-metal interaction included at
second order only, and its intuitive extention to higher orders. Using the
commutation technique we recently introduced to deal with interacting excitons,
we are now able to \emph{prove} that this exciton diagram procedure is indeed
valid at any order in the interaction.
Faraday rotation in photoexcited semiconductors: an excitonic many-body effect
This letter assigns the Faraday rotation in photoexcited semiconductors to
``Pauli interactions'', \emph{i}. \emph{e}., carrier exchanges, between the
real excitons present in the sample and the virtual excitons coupled to the
parts of a linearly polarized light. While \emph{direct Coulomb}
interactions scatter bright excitons into bright excitons, whatever their spins
are, \emph{Pauli} interactions do it for bright excitons \emph{with same spin
only}. This makes these Pauli interactions entirely responsible for the
refractive index difference, which comes from processes in which the virtual
exciton which is created and the one which recombines are formed with different
carriers. To write this difference in terms of photon detuning and exciton
density, we use our new many-body theory for interacting excitons. Its multiarm
``Shiva'' diagrams for -body exchanges make transparent the physics involved
in the various terms. This work also shows the interesting link which exists
between Faraday rotation and the exciton optical Stark effect
The exciton many-body theory extended to arbitrary composite bosons
We have recently constructed a many-body theory for composite excitons, in
which the possible carrier exchanges between excitons can be treated
exactly through a set of dimensionless ``Pauli scatterings'' between two
excitons. Many-body effects with excitons turn out to be rather simple because
excitons are the exact one-electron-hole-pair eigenstates of the semiconductor
Hamiltonian, thus forming a complete orthogonal set for one-pair states. It can
however be of interest to extend this new many-body theory to more complicated
composite bosons, \emph{i. e.}, ``cobosons'', which are not necessarily the
one-pair eigenstates of the system Hamiltonian, nor even orthogonal. The
purpose of this paper is to derive the ``Pauli scatterings'' and the
``interaction scatterings'' of these cobosons formally, \emph{i. e.}, just in
terms of their wave functions and the interaction potentials which exist
between the fermions from which they are constructed. We also explain how to
derive many-body effects in this very general system of composite bosons
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