74 research outputs found
"Commutator formalism" for pairs correlated through Schmidt decomposition as used in Quantum Information
To easily calculate statistical properties of pairs correlated through
Schmidt decomposition, as commonly used in Quantum Information, we propose a
"commutator formalism" for these single-index pairs, somewhat simpler than the
one we developed for double-index Wannier excitons. We use it here to get the
pair number threshold for bosonic behavior of pairs through the requirement
that their number operator mean value must stay close to . While the main
term of this mean value is controlled by the second moment of the Schmidt
distribution, so that to increase this threshold, we must increase the Schmidt
number, higher momenta appearing at higher orders lead to choosing a
distribution as flat as possible
Many-body formalism for thermally excited wave-packets: A way to connect the quantum regime to the classical regime
Free classical particles have well-defined momentum and position, while free
quantum particles have well-defined momentum but a position fully delocalized
over the sample volume. We develop a many-body formalism based on wave-packet
operators that connects these two limits, the thermal energy being distributed
between the state spatial extension and its thermal excitation. The
corresponding `mixed quantum-classical' states, which render the Boltzmann
operator diagonal, are the physically relevant states when the temperature is
finite. The formulation of many-body Hamiltonians in terms of these thermally
excited wave-packets and the resulting effective scatterings is provided.Comment: 7 pages, 2 figures, 2 pages supplementary material. (v2) link to the
coherent states added. Final published version. (v3) 1 Ref. adde
Energy of N Cooper pair by analytically solving Richardson-Gaudin equations
This Letter provides the solution to a yet unsolved basic problem of Solid
State Physics: the ground state energy of an arbitrary number of Cooper pairs
interacting via the Bardeen-Cooper-Schrieffer potential. We here break a 50
year old math problem by analytically solving Richardson-Gaudin equations which
give the exact energy of these pairs via parameters coupled through
non-linear equations. Our result fully supports the standard BCS result
obtained for a pair number equal to half the number of states feeling the
potential. More importantly, it shows that the interaction part of the -pair
energy depends on as only from N=1 to the dense regime, a result
which evidences that Cooper pairs interact via Pauli blocking only
Dressed atom versus exciton polariton: From Rabi oscillations to the Fermi Golden rule
We rederive the dressed atom and the exciton polariton within the {\it same}
framework to make clear that their difference only comes from the number of
electrons available for photoexcitations. Using it, we analytically show how
the time dependence of the photon number transforms from an oscillating
behavior (at the stimulated or vacuum Rabi frequency) to an exponential decay
(identical for atom and semiconductor) when the excited state lifetime
decreases. Although the matter ground state is in both cases coupled by
monochromatic photons {\it not to a continuum but to a discrete state}, this
decay yet follows a kind of Fermi Golden rule. The energy conservation it
contains, is however conceptually different
Scattering amplitudes for dark and bright excitons
Using the composite boson many-body formalism that takes single-exciton
states rather than free carrier states as a basis, we derive the integral
equation fulfilled by the exciton-exciton effective scattering from which the
role of fermion exchanges can be unraveled. For excitons made of
-spin electrons and -spin holes, as in GaAs
heterostructures, one major result is that most spin configurations lead to
brightness-conserving scatterings with equal amplitude , in spite of
the fact that they involve different carrier exchanges. A brightness-changing
channel also exists when two opposite-spin excitons scatter: dark excitons
can end either in the same dark states with an amplitude ,
or in opposite-spin bright states , with a different amplitude
, the number of carrier exchanges being even or odd respectively.
Another major result is that these amplitudes are linked by a striking
relation, , which has decisive consequence for
exciton Bose-Einstein condensation. Indeed, this relation leads to the
conclusion that the exciton condensate can be optically observed through a
bright part only when excitons have a large dipole, that is, when the electrons
and holes are well separated in two adjacent layers.Comment: 8 pages, 4 figure
Composite boson signature in the interference pattern of atomic dimer condensates
We predict the existence of high frequency modes in the interference pattern
of two condensates made of fermionic-atom dimers. These modes, which result
from fermion exchanges between condensates, constitute a striking signature of
the dimer composite nature. From the 2-coboson spatial correlation function,
that we derive analytically, and the Shiva diagrams that visualize many-body
effects specific to composite bosons, we identify the physical origin of these
high frequency modes and determine the conditions to see them experimentally by
using bound fermionic-atom pairs trapped on optical lattice sites. The dimer
granularity which appears in these modes comes from Pauli blocking that
prevents two dimers to be located at the same lattice site.Comment: 10+7 pp, 3 figures. v2: version accepted for publication in New J.
Phy
Way to observe the implausible "trion-polariton"
Using the composite boson (coboson) many-body formalism, we determine under
which conditions "trion-polariton" can exist. Dipolar attraction can bind an
exciton and an electron into a trion having an energy well separated from the
exciton energy. Yet, the existence of long-lived "trion-polariton" is a priori
implausible not only because the photon-trion coupling, which scales as the
inverse of the sample volume, is vanishingly small, but mostly because this
coupling is intrinsically "weak". Here, we show that a moderately dense Fermi
sea renders its observation possible: on the pro side, the Fermi sea overcomes
the weak coupling by pinning the photon to its momentum through Pauli blocking,
it also overcomes the dramatically poor photon-trion coupling by providing a
volume-linear trion subspace to which the photon is coherently coupled. On the
con side, the Fermi sea broadens the photon-trion resonance due to the
fermionic nature of trions and electrons, it also weakens the trion binding by
blocking electronic states relevant for trion formation. As a result, the
proper way to observe this novel polariton is to use doped semiconductor having
long-lived electronic states, highly-bound trion and Fermi energy as large as a
fraction of the trion binding energy.Comment: 6 pages, 3 figure
Correlated Pair Approach to Composite Boson Scattering Lengths
We derive the scattering length of composite bosons (cobosons) within the
framework of the composite boson many-body formalism that uses correlated-pair
states as a basis, instead of free fermion states. The integral equation
constructed from this physically relevant basis makes transparent the role of
fermion exchange in the coboson-coboson effective scattering. Three potentials
used for Cooper pairs, fermionic-atom dimers, and semiconductor excitons are
considered. While the s-wave scattering length for the BCS-like potential is
just equal to its Born value, the other two are substantially smaller. For
fermionic-atom dimers and semiconductor excitons, our results, calculated
within a restricted correlated-pair basis, are in good agreement with those
obtained from procedures numerically more demanding. We also propose model
coboson-coboson scatterings that are separable and thus easily workable, and
that produce scattering lengths which match quantitatively well with the
numerically-obtained values for all fermion mass ratios. These separable model
scatterings can facilitate future works on many-body effects in coboson gases.Comment: 10 pages, 6 figure
- …