arXiv subjects

Monique Combescot

Publications and source records attributed to Monique Combescot.

At least 37 records · Page 2Linked to original sources

arXiv2016

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.

cond-mat.str-el↗

arXiv2016

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 $(\pm1/2)$-spin electrons and $(\pm3/2)$-spin holes, as in GaAs heterostructures, one major result is that most spin configurations lead to brightness-conserving scatterings with equal amplitude $Δ$, 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 $(2,-2)$ can end either in the same dark states with an amplitude $Δ_e$, or in opposite-spin bright states $(1,-1)$, with a different amplitude $Δ_o$, the number of carrier exchanges being even or odd respectively. Another major result is that these amplitudes are linked by a striking relation, $Δ_e+Δ_o=Δ$, 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.

cond-mat.quant-gas↗

arXiv2016

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.

cond-mat.quant-gas↗

arXiv2016

Effect of Pauli blocking on coherent states of composite bosons

The quantum nature of elementary bosons can be completely erased by using coherent states known as Glauber states. Here, we consider composite bosons (cobosons) made of two fermions and look for the possibility to erase the bosonic quantum nature of the field and the fermionic quantum nature of its constituents, when the distribution of the coboson Schmidt decomposition is either flat like Frenkel excitons, or localized like Wannier excitons. We show that for Frenkel-like cobosons, complete erasure of the field quantum nature is possible up to a density which corresponds to a sizable fraction of the number of fermion-pair states making the coboson at hand. At higher density, the Pauli exclusion principle between fermionic constituents shows up dramatically. It induces: (i) the decrease of number-operator eigenvalues down to 1 and the increase of the number-state second-order correlation function up to 2; (ii) the disappearance of the usual sharp peak in the coherent-state distribution and the increase of the coherent-state second-order correlation function up to 2. It also is possible to construct number states and coherent states for Wannier-like cobosons, but their forms are far more complex. Finally, we show that Pauli blocking makes the coboson coherent states qualitatively different from the Anderson's ansatz.

cond-mat.quant-gas↗

arXiv2016

Mysterious dimensionality effect: the cancellation of the $N$-coboson correlation energy under a BCS-like potential

We use Richardson-Gaudin exact equations to derive the ground-state energy of $N$ composite bosons (cobosons) interacting via a potential which acts between fermion pairs having zero center-of-mass momentum, that is, a potential similar to the reduced BCS potential used in conventional superconductivity. Through a density expansion, we show that while, for 2D systems, the $N$-coboson correlation energy undergoes a surprising cancellation which leaves the interaction part with a $N(N-1)$ dependence only, such a cancellation does not exist in 1D, 3D, and 4D systems --- which corresponds to 2D parabolic traps --- nor when the cobosons interact via a similar short-range potential but between pairs having an arbitrary center-of-mass momentum. This shows that the previously-found cancellation which exists for the Cooper-pair correlation energy results not only from the very peculiar form of the reduced BCS potential, but also from a quite mysterious dimensionality effect, the density of states for Cooper pairs feeling the BCS potential being essentially constant, as for 2D systems.

cond-mat.quant-gas↗

arXiv2015

Coboson many-body formalism for cold atom dimers with attraction between different fermion species only

Unlike the Coulomb potential that acts between all semiconductor carriers, the potential commonly used for BCS superconductors and cold atom gases acts between different fermion species only, these species differing by their spin or hyperfine index. The coboson formalism we here develop evidences that such composite bosons interact through fermion exchange only, thus rendering the structure of the Shiva diagrams that visualize their many-body effects far simpler. A separable potential is used to obtain analytical results for the $N$-coboson normalization factor and the $N$-coboson ground-state energy within the Born approximation, in terms of the Born dimer-dimer scattering length. This formalism opens the route toward approaching complex many-body effects, such as Bose-Einstein condensation, through a new perspective.

cond-mat.quant-gas↗

arXiv2015

Correlation Energy for Elementary Bosons: Physics of the Singularity

We propose a compact perturbative approach that reveals the physical origin of the singularity occurring in the density dependence of correlation energy: like fermions, elementary bosons have a singular correlation energy which comes from the accumulation, through Feynman "bubble" diagrams, of the same non-zero momentum transfer excitations from the free particle ground state, that is, the Fermi sea for fermions and the Bose-Einstein condensate for bosons. This understanding paves the way toward deriving the correlation energy of composite bosons like atomic dimers and semiconductor excitons, by suggesting Shiva diagrams that have similarity with Feynman "bubble" diagrams, the previous elementary boson approaches, which hide this physics, being difficult to do so.

cond-mat.quant-gas↗

arXiv2015

Coboson many-body approach to the $N$-exciton ground-state energy

We derive the ground-state energy of $N$ composite bosons made of fermion pairs using the recently developed composite boson many-body formalism. We concentrate on the $N$-pair energy linear in density. We show that the scattering relevant for scattering length contains not only direct and exchange interaction scatterings but also the dimensionless "Pauli scattering" for fermion exchange in the absence of fermion-fermion interaction. Numerical resolution of the resulting "ladder" integral equation for fermions interacting through long-range Coulomb forces --- which act as effective repulsion between excitons made of same-spin electrons and same-spin holes --- shows that the prefactor of the $N$-exciton energy linear in density is substantially decreased from its Born approximation value, $13π/3$, by a factor $\simeq0.38$ for equal electron and hole effective masses. Interestingly, this factor goes to zero when the hole mass goes to infinity, making the triplet-exciton gas unstable in this limit.

cond-mat.str-el↗

arXiv2014

Evidence for a Bose-Einstein condensate of excitons

The demonstration of Bose-Einstein condensation in atomic gases at micro-Kelvin temperatures is a striking landmark while its evidence for semiconductor excitons still is a long-awaited milestone. This situation was not foreseen because excitons are light-mass boson-like particles with a condensation expected to occur around a few Kelvins. An explanation can be found in the underlying fermionic nature of excitons which rules their condensation. Precisely, it was recently predicted that, at accessible experimental conditions, the exciton condensate shall be "gray" with a dominant dark part coherently coupled to a weak bright component through fermion exchanges. This counter-intuitive quantum condensation, since excitons are mostly known for their optical activity, directly follows from the excitons internal structure which has an optically inactive, i.e., dark, ground state. Here, we report compelling evidence for such a "gray" condensate. We use an all-optical approach in order to produce microscopic traps which confine a dense exciton gas that yet exhibits an anomalously weak photo-emission at sub-Kelvin temperatures. This first fingerprint for a "gray" condensate is then confirmed by the macroscopic spatial coherence and the linear polarization of the weak excitonic photoluminescence emitted from the trap, as theoretically predicted.

cond-mat.quant-gas↗

arXiv2013

Partition function of N composite bosons

The partition function of composite bosons ("cobosons" for short) is calculated in the canonical ensemble, with the Pauli exclusion principle between their fermionic components included in an exact way through the finite temperature many-body formalism for composite quantum particles we recently developed. To physically understand the very compact result we obtain, we first present a diagrammatic approach to the partition function of $N$ elementary bosons. We then show how to extend this approach to cobosons with Pauli blocking and interaction between their fermions. These diagrams provide deep insights on the structure of a coboson condensate, paving the way toward the determination of the critical parameters for their quantum condensation.

cond-mat.stat-mech↗

arXiv2013

Electronic structure and absorption spectrum of biexciton obtained by using exciton basis

We approach the biexciton Schrödinger equation not through the free-carrier basis as usually done, but through the free-exciton basis, exciton-exciton interactions being treated according to the recently developed composite boson many-body formalism which allows an exact handling of carrier exchange between excitons, as induced by the Pauli exclusion principle. We numerically solve the resulting biexciton Schrödinger equation with the exciton levels restricted to the ground state and we derive the biexciton ground state as well as the bound and unbound excited states as a function of hole-to-electron mass ratio. The biexciton ground-state energy we find, agrees reasonably well with variational results. Next, we use the obtained biexciton wave functions to calculate optical absorption in the presence of a dilute exciton gas in quantum well. We find a small asymmetric peak with a characteristic low-energy tail, identified with the biexciton ground state, and a set of large peaks associated with biexciton unbound states, i.e., exciton-exciton scattering states.

cond-mat.str-el↗

arXiv2012

Trion ground state, excited states and absorption spectrum using electron-exciton basis

We solve the Schrödinger equation for two electrons plus one hole by writing it in the electron-exciton basis. The main advantage of this basis is to eliminate the exciton contribution from the trion energy in a natural way. The interacting electron-exciton system is treated using the recently developed composite boson many-body formalism which allows an exact handling of electron exchange. We numerically solve the resulting electron-exciton Schrödinger equation, with the exciton levels restricted to the lowest $1s, 2s$ and $3s$ states, and we derive the trion ground state energy as a function of the electron-to-hole mass ratio. While our results are in reasonable agreement with those obtained through the best variational methods using free carrier basis, this electron-exciton basis is mostly suitable to easily reach the bound and unbound trion excited states. Through their wave functions, we here calculate the optical absorption spectrum in the presence of hot carriers for 2D quantum wells. We find large peaks located at the exciton levels, which are attributed to electron-exciton (unbound) scattering states, and small peaks identified with trion bound states.

cond-mat.str-el↗

arXiv2011

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 $N$ pairs via $N$ parameters coupled through $N$ 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 $N$-pair energy depends on $N$ as $N(N-1)$ only from N=1 to the dense regime, a result which evidences that Cooper pairs interact via Pauli blocking only.

cond-mat.supr-con↗

arXiv2011

"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 $N$ pairs through the requirement that their number operator mean value must stay close to $N$. 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.

cond-mat.mes-hall↗

arXiv2011

Competition between BCS-pairing and "moth-eaten effect" in BEC-BCS crossover

We study the change in condensation energy from a single pair of fermionic atoms to a large number of pairs interacting via the reduced BCS potential. We find that the energy-saving due to correlations decreases when the pair number increases because the number of empty states available for pairing gets smaller ("moth-eaten effect"). However, this decrease dominates the 3D kinetic energy increase of the same amount of noninteracting atoms only when the pair number is a sizeable fraction of the number of states available for pairing. As a result, in BEC-BCS crossover of 3D systems, the condensation energy per pair first increases and then decreases with pair number while in 2D, it always is controlled by the "moth-eaten effect" and thus simply decreases.

cond-mat.supr-con↗

arXiv2010

Fundamental collapse of the exciton-exciton effective scattering

The exciton-exciton effective scattering which rules the time evolution of two excitons is studied as a function of initial momentum difference, scattering angle and electron-to-hole mass ratio. We show that this effective scattering can collapse for energy-conserving configurations provided that the difference between the two initial exciton momenta is larger than a threshold value. Sizeable scatterings then exist in the forward direction only. We even find that, for an electron-to-hole mass ratio close to 1/2, the exciton-exciton effective scattering stays close to zero in all directions when the difference between the initial exciton momenta has a very specific value. This unexpected but quite remarkable collapse comes from tricky compensation between direct and exchange Coulomb processes which originates from the fundamental undistinguishability of the exciton fermionic components.

cond-mat.mes-hall↗

arXiv2010

Coboson formalism for Cooper pairs used to derive Richardson's equations

We propose a many-body formalism for Cooper pairs which has similarities to the one we recently developed for composite boson excitons (coboson in short). Its Shiva diagram representation evidences that $N$ Cooper pairs differ from $N$ single pairs through electron exchange only: no direct coupling exists due to the very peculiar form of the BCS potential. As a first application, we here use this formalism to derive Richardson's equations for the exact eigenstates of $N$ Cooper pairs. This gives hints on why the $N(N-1)$ dependence of the $N$-pair ground state energy we recently obtained by solving Richardson's equations analytically in the low density limit, stays valid up to the dense regime, no higher order dependence exists even under large overlap, a surprising result hard to accept at first. We also briefly question the BCS wave function ansatz compared to Richardson's exact form, in the light of our understanding of coboson many-body effects.

cond-mat.supr-con↗

arXiv2008

On the dark nature of exciton Bose-Einstein condensate

We show that for the very same reason that excitons are bright, i.e. coupled to photons, they have a higher energy than dark excitons, even for electrons spatially separated from holes, such as in a double quantum well. Indeed, the same channel which produces the finite electron-hole effective overlap responsible for the absorption and emission of photon allows for Coulomb interband exchange processes, which are nothing but a sequence of virtual recombination and creation of one electron-hole pair. Consequently, this additional repulsive electron-hole Coulomb exchange interaction exists for bright excitons, but not for dark excitons. If we now remember that dark excitons with spins $\pm 2$ are formed in a natural way through carrier exchange between two opposite spin bright excitons, we are led to predict that in a double quantum well sample with one trap -- a configuration appropriate to get high density -- exciton Bose-Einstein condensation should appear when cooling down the sample as a dark spot made of $(\pm 2)$ excitons at the center of the trap.

cond-mat.str-el↗