DOI

1

Effects of Fermion Exchange on the Polarization of Exciton Condensates - Combescot, Monique and Combescot, Roland and Alloing, Mathieu and Dubin, Francois

PHYSICAL REVIEW LETTERS 114, (2015)

Abstract : Exchange interaction is responsible for the stability of elementary boson condensates with respect to momentum fragmentation. This remains true for composite bosons when single fermion exchanges are included but spin degrees of freedom are ignored. Here, we show that their inclusion can produce a spin fragmentation of the dark exciton condensate, i.e., an unpolarized condensate with an equal amount of spin (+2) and (-2) excitons not coupled to light. The composite boson many-body formalism allows us to predict that, for spatially indirect excitons, the condensate polarization switches from unpolarized to fully polarized when the distance between the layers confining electrons and holes increases. Importantly, the threshold distance for this switch lies in a regime fully accessible to experiments.

PHYSICAL REVIEW LETTERS 114, (2015)

LPS

Abstract : Exchange interaction is responsible for the stability of elementary boson condensates with respect to momentum fragmentation. This remains true for composite bosons when single fermion exchanges are included but spin degrees of freedom are ignored. Here, we show that their inclusion can produce a spin fragmentation of the dark exciton condensate, i.e., an unpolarized condensate with an equal amount of spin (+2) and (-2) excitons not coupled to light. The composite boson many-body formalism allows us to predict that, for spatially indirect excitons, the condensate polarization switches from unpolarized to fully polarized when the distance between the layers confining electrons and holes increases. Importantly, the threshold distance for this switch lies in a regime fully accessible to experiments.

DOI

2

Optical signatures of a fully dark exciton condensate - Combescot, Monique and Combescot, Roland and Alloing, Mathieu and Dubin, Francois

EPL 105, (2014)

Abstract : We propose optical means to reveal the presence of a dark exciton condensate that does not yield any photoluminescence at all. We show that i) the dark exciton density can be obtained from the blueshift of the excitonic absorption line induced by dark excitons; ii) the polarization of the dark condensate can be obtained from the blueshift dependence on the probe photon polarization as well as from the Faraday effect. All these effects result from carrier exchanges between dark and bright states. Copyright (C) EPLA, 2014

EPL 105, (2014)

LPS

Abstract : We propose optical means to reveal the presence of a dark exciton condensate that does not yield any photoluminescence at all. We show that i) the dark exciton density can be obtained from the blueshift of the excitonic absorption line induced by dark excitons; ii) the polarization of the dark condensate can be obtained from the blueshift dependence on the probe photon polarization as well as from the Faraday effect. All these effects result from carrier exchanges between dark and bright states. Copyright (C) EPLA, 2014

DOI

3

Evidence for a Bose-Einstein condensate of excitons - Alloing, Mathieu and Beian, Mussie and Lewenstein, Maciej and Fuster, David and Gonzalez, Yolanda and Gonzalez, Luisa and Combescot, Roland and Combescot, Monique and Dubin, Francois

EPL 107, (2014)

Abstract : We report compelling evidence for a ``gray'' condensate of dipolar excitons, electrically polarised in a 25 nm wide GaAs quantum well. The condensate is composed by a macroscopic population of dark excitons coherently coupled to a lower population of bright excitons. To create the exciton condensate we use an all-optical approach in order to produce microscopic traps which confine a dense exciton gas (similar to 10(10) cm(-2)) that yet exhibits an anomalously weak photoemission at sub-kelvin temperatures. This is the first fingerprint for the ``gray'' condensate. It is then confirmed by the macroscopic spatial coherence and the linear polarization of the weak excitonic photoluminescence emitted from the trap, as theoretically predicted. Copyright (C) EPLA, 2014

EPL 107, (2014)

LPS

Abstract : We report compelling evidence for a ``gray'' condensate of dipolar excitons, electrically polarised in a 25 nm wide GaAs quantum well. The condensate is composed by a macroscopic population of dark excitons coherently coupled to a lower population of bright excitons. To create the exciton condensate we use an all-optical approach in order to produce microscopic traps which confine a dense exciton gas (similar to 10(10) cm(-2)) that yet exhibits an anomalously weak photoemission at sub-kelvin temperatures. This is the first fingerprint for the ``gray'' condensate. It is then confirmed by the macroscopic spatial coherence and the linear polarization of the weak excitonic photoluminescence emitted from the trap, as theoretically predicted. Copyright (C) EPLA, 2014

4

The BEC-BCS Crossover in Ultracold Fermi Gases - Combescot, R.

in FIFTY YEARS OF NUCLEAR BCS: PAIRING IN FINITE SYSTEMS edited by Broglia, RA and Zelevinsky, V (2013),

Abstract : We provide an introduction to the matter of ultracold Fermi gases and the observation of the BEC-BCS crossover in these systems. We discuss in particular the simple modelisation of these gases, the Fano-Feshbach resonance, the simple BCS model of the crossover, the equation of state at T = 0, experiments on superfluid vortices and on critical velocity, results with the T-matrix approximation, and the Fermi polaron.

in FIFTY YEARS OF NUCLEAR BCS: PAIRING IN FINITE SYSTEMS edited by Broglia, RA and Zelevinsky, V (2013),

LPS

Abstract : We provide an introduction to the matter of ultracold Fermi gases and the observation of the BEC-BCS crossover in these systems. We discuss in particular the simple modelisation of these gases, the Fano-Feshbach resonance, the simple BCS model of the crossover, the equation of state at T = 0, experiments on superfluid vortices and on critical velocity, results with the T-matrix approximation, and the Fermi polaron.

DOI

5

Dimer-dimer scattering length for fermions with different masses: Analytical study for large mass ratio - Alzetto, F. and Combescot, R. and Leyronas, X.

PHYSICAL REVIEW A 87, (2013)

Abstract : We study the dimer-dimer scattering length a(4) for a two-component Fermi mixture in which the different fermions have different masses m(up arrow) and m(down arrow). This is made in the framework of the exact field-theoretic method. In the large mass ratio domain the equations are simplified enough to lead to an analytical solution. In particular we link a(4) to the fermion-dimer scattering length a(3) for the same fermions and obtain the very simple relation a(4) = a(3)/2. The result a(4) similar or equal to a(3)/2 is actually valid whatever the mass ratio with quite good precision. As a result we find an analytical expression providing a(4) with fairly good precision for any mass. To dominant orders for large mass ratio it agrees with the literature. We show that in this large mass ratio domain, the dominant processes are the repeated dimer-dimer Born scatterings, considered earlier by Pieri and Strinati [Phys Rev. B 61, 15370 (2000)]. We conclude that their approximation of retaining only these processes is a fairly good one whatever the mass ratio. DOI: 10.1103/PhysRevA.87.022704

PHYSICAL REVIEW A 87, (2013)

LPS

Abstract : We study the dimer-dimer scattering length a(4) for a two-component Fermi mixture in which the different fermions have different masses m(up arrow) and m(down arrow). This is made in the framework of the exact field-theoretic method. In the large mass ratio domain the equations are simplified enough to lead to an analytical solution. In particular we link a(4) to the fermion-dimer scattering length a(3) for the same fermions and obtain the very simple relation a(4) = a(3)/2. The result a(4) similar or equal to a(3)/2 is actually valid whatever the mass ratio with quite good precision. As a result we find an analytical expression providing a(4) with fairly good precision for any mass. To dominant orders for large mass ratio it agrees with the literature. We show that in this large mass ratio domain, the dominant processes are the repeated dimer-dimer Born scatterings, considered earlier by Pieri and Strinati [Phys Rev. B 61, 15370 (2000)]. We conclude that their approximation of retaining only these processes is a fairly good one whatever the mass ratio. DOI: 10.1103/PhysRevA.87.022704

DOI

6

Interaction between polarons and analogous effects in polarized Fermi gases - Giraud, S. and Combescot, R.

PHYSICAL REVIEW A 85, (2012)

Abstract : We consider an imbalanced mixture of two different ultracold Fermi gases, which are strongly interacting. Calling spin-down the minority component and spin-up the majority component, the limit of small relative density x = n(down arrow)/n(up arrow) is usually considered as a gas of noninteracting polarons. This allows us to calculate, in the expansion of the total energy of the system in powers of x, the terms proportional to x (corresponding to the binding energy of the polaron) and to x(5/3) (corresponding to the kinetic energy of the polaron Fermi sea). We investigate in this paper terms physically due to an interaction between polarons and which are proportional to x(2) and x(7/3). We find three such terms. The first one corresponds to the overlap between the clouds dressing two polarons. The two other ones are due to the modification of the single polaron binding energy caused by the nonzero density of polarons. The second term is due to the restriction of the polaron momentum by the Fermi sea formed by the other polarons. The last one results from the modification of the spin-up Fermi sea brought by the other polarons. The calculation of all these terms is made at the simplest level of a single particle-hole excitation. It is performed for all the possible interaction strengths within the stability range of the polaron. At unitarity the last two terms give a fairly weak contribution while the first one is strong and leads to a marked disagreement with Monte Carlo results. The possible origins of this discrepancy are discussed.

PHYSICAL REVIEW A 85, (2012)

LPS

Abstract : We consider an imbalanced mixture of two different ultracold Fermi gases, which are strongly interacting. Calling spin-down the minority component and spin-up the majority component, the limit of small relative density x = n(down arrow)/n(up arrow) is usually considered as a gas of noninteracting polarons. This allows us to calculate, in the expansion of the total energy of the system in powers of x, the terms proportional to x (corresponding to the binding energy of the polaron) and to x(5/3) (corresponding to the kinetic energy of the polaron Fermi sea). We investigate in this paper terms physically due to an interaction between polarons and which are proportional to x(2) and x(7/3). We find three such terms. The first one corresponds to the overlap between the clouds dressing two polarons. The two other ones are due to the modification of the single polaron binding energy caused by the nonzero density of polarons. The second term is due to the restriction of the polaron momentum by the Fermi sea formed by the other polarons. The last one results from the modification of the spin-up Fermi sea brought by the other polarons. The calculation of all these terms is made at the simplest level of a single particle-hole excitation. It is performed for all the possible interaction strengths within the stability range of the polaron. At unitarity the last two terms give a fairly weak contribution while the first one is strong and leads to a marked disagreement with Monte Carlo results. The possible origins of this discrepancy are discussed.

DOI

7

``Gray'' BCS Condensate of Excitons and Internal Josephson Effect - Combescot, Roland and Combescot, Monique

PHYSICAL REVIEW LETTERS 109, (2012)

Abstract : It has been recently suggested that the Bose-Einstein condensate formed by excitons in the dilute limit must be dark, i.e., not coupled to photons. Here, we show that, under a density increase, the dark exciton condensate must acquire a bright component due to carrier exchange in which dark excitons turn bright. This, however, requires a density larger than a threshold which seems to fall in the forbidden region of the phase separation between a dilute exciton gas and a dense electron-hole plasma. The BCS-like condensation which is likely to take place on the dense side, must then have a dark and a bright component-which makes it ``gray.'' It should be possible to induce an internal Josephson effect between these two coherent components, with oscillations of the photoluminescence as a strong proof of the existence for this ``gray'' BCS-like exciton condensate.

PHYSICAL REVIEW LETTERS 109, (2012)

LPS

Abstract : It has been recently suggested that the Bose-Einstein condensate formed by excitons in the dilute limit must be dark, i.e., not coupled to photons. Here, we show that, under a density increase, the dark exciton condensate must acquire a bright component due to carrier exchange in which dark excitons turn bright. This, however, requires a density larger than a threshold which seems to fall in the forbidden region of the phase separation between a dilute exciton gas and a dense electron-hole plasma. The BCS-like condensation which is likely to take place on the dense side, must then have a dark and a bright component-which makes it ``gray.'' It should be possible to induce an internal Josephson effect between these two coherent components, with oscillations of the photoluminescence as a strong proof of the existence for this ``gray'' BCS-like exciton condensate.

DOI

8

Atom-dimer scattering amplitude for fermionic mixtures with different masses: s-wave and p-wave contributions - Alzetto, F. and Combescot, R. and Leyronas, X.

PHYSICAL REVIEW A 86, (2012)

Abstract : We study near a Feshbach resonance, as a function of the mass ratio, the fermion-dimer scattering amplitude in fermionic mixtures of two fermion species. When masses are equal the physical situation is known to be quite simple. We show that, when the mass ratio is increased, the situation becomes much more complex. For the s-wave contribution we obtain an analytical solution in the asymptotic limit of very large mass ratio. In this regime the s-wave scattering amplitude displays a large number of zeros, essentially linked to the known large value of the fermion-dimer scattering length in this regime. We find by an exact numerical calculation that a zero is still present for a mass ratio of 15. For the p-wave contribution we make our study below the mass ratio of 8.17, where a fermion-dimer bound state appears. We find that a strong p-wave resonance is present at low energy, due to a virtual bound state, in the fermion-dimer system, which is a forerunner of the real bound state. This resonance becomes prominent in the mass ratio range around the one corresponding to the K-40-Li-6 mixtures, much studied experimentally. This resonance should affect a number of physical properties. These include the equation of state of unbalanced mixtures at very low temperature but also the equation of state of balanced mixtures at moderate or high temperature. The frequency and the damping of collective modes should also provide a convenient way to evidence this resonance. Finally it should be possible to modify the effective mass of one of the fermionic species by making use of an optical lattice. This would allow one to study the strong dependence of the resonance as a function of the mass ratio of the two fermionic elements. In particular one could check if the virtual bound state is relevant for the instabilities of these mixtures. DOI: 10.1103/PhysRevA.86.062708

PHYSICAL REVIEW A 86, (2012)

LPS

Abstract : We study near a Feshbach resonance, as a function of the mass ratio, the fermion-dimer scattering amplitude in fermionic mixtures of two fermion species. When masses are equal the physical situation is known to be quite simple. We show that, when the mass ratio is increased, the situation becomes much more complex. For the s-wave contribution we obtain an analytical solution in the asymptotic limit of very large mass ratio. In this regime the s-wave scattering amplitude displays a large number of zeros, essentially linked to the known large value of the fermion-dimer scattering length in this regime. We find by an exact numerical calculation that a zero is still present for a mass ratio of 15. For the p-wave contribution we make our study below the mass ratio of 8.17, where a fermion-dimer bound state appears. We find that a strong p-wave resonance is present at low energy, due to a virtual bound state, in the fermion-dimer system, which is a forerunner of the real bound state. This resonance becomes prominent in the mass ratio range around the one corresponding to the K-40-Li-6 mixtures, much studied experimentally. This resonance should affect a number of physical properties. These include the equation of state of unbalanced mixtures at very low temperature but also the equation of state of balanced mixtures at moderate or high temperature. The frequency and the damping of collective modes should also provide a convenient way to evidence this resonance. Finally it should be possible to modify the effective mass of one of the fermionic species by making use of an optical lattice. This would allow one to study the strong dependence of the resonance as a function of the mass ratio of the two fermionic elements. In particular one could check if the virtual bound state is relevant for the instabilities of these mixtures. DOI: 10.1103/PhysRevA.86.062708

DOI

9

Normal state of highly polarized Fermi gases: The bound state - Combescot, R. and Giraud, S. and Leyronas, X.

LASER PHYSICS 20, 678-682 (2010)

Abstract : We consider a highly polarized Fermi gas with a single a dagger'' atom within a Fermi sea of a dagger atoms. We extend a preceding many-body analysis to the case where a bound state is formed between the a dagger'' atom and an a dagger atom.

LASER PHYSICS 20, 678-682 (2010)

LPS

Abstract : We consider a highly polarized Fermi gas with a single a dagger'' atom within a Fermi sea of a dagger atoms. We extend a preceding many-body analysis to the case where a bound state is formed between the a dagger'' atom and an a dagger atom.

DOI

10

Comment on ``Motion of an impurity particle in an ultracold quasi-one-dimensional gas of hard-core bosons'' - Giraud, S. and Combescot, R.

PHYSICAL REVIEW A 82, (2010)

Abstract : Very recently Girardeau and Minguzzi [Phys. Rev. A 79, 033610 (2009)] have studied an impurity in a one-dimensional gas of hard-core bosons. In particular they dealt with the general case where the mass of the impurity is different from the mass of the bosons and the impurity-boson interaction is not necessarily infinitely repulsive. We show that one of their initial steps is unjustified, contradicting known exact results. Their results in the general case apply only actually when the mass of the impurity is infinite.

PHYSICAL REVIEW A 82, (2010)

LPS

Abstract : Very recently Girardeau and Minguzzi [Phys. Rev. A 79, 033610 (2009)] have studied an impurity in a one-dimensional gas of hard-core bosons. In particular they dealt with the general case where the mass of the impurity is different from the mass of the bosons and the impurity-boson interaction is not necessarily infinitely repulsive. We show that one of their initial steps is unjustified, contradicting known exact results. Their results in the general case apply only actually when the mass of the impurity is infinite.

DOI

11

Atom-dimer scattering length for fermions with different masses: Analytical study of limiting cases - Alzetto, F. and Combescot, R. and Leyronas, X.

PHYSICAL REVIEW A 82, (2010)

Abstract : We consider the problem of obtaining the scattering length for a fermion colliding with a dimer, formed from a fermion identical to the incident one and another different fermion. This is done in the universal regime where the range of interactions is short enough that the scattering length a for nonidentical fermions is the only relevant quantity. This is the generalization to fermions with different masses of the problem solved long ago by Skorniakov and Ter-Martirosian for particles with equal masses. We solve this problem analytically in the two limiting cases where the mass of the solitary fermion is very large or very small compared to the mass of the two other identical fermions. This is done for both the value of the scattering length and the function entering the Skorniakov-Ter-Martirosian integral equation, for which simple explicit expressions are obtained.

PHYSICAL REVIEW A 82, (2010)

LPS

Abstract : We consider the problem of obtaining the scattering length for a fermion colliding with a dimer, formed from a fermion identical to the incident one and another different fermion. This is done in the universal regime where the range of interactions is short enough that the scattering length a for nonidentical fermions is the only relevant quantity. This is the generalization to fermions with different masses of the problem solved long ago by Skorniakov and Ter-Martirosian for particles with equal masses. We solve this problem analytically in the two limiting cases where the mass of the solitary fermion is very large or very small compared to the mass of the two other identical fermions. This is done for both the value of the scattering length and the function entering the Skorniakov-Ter-Martirosian integral equation, for which simple explicit expressions are obtained.

DOI

12

Highly polarized Fermi gases: One-dimensional case - Giraud, S. and Combescot, R.

PHYSICAL REVIEW A 79, (2009)

Abstract : We consider the problem of a single particle interacting with N identical fermions, at zero temperature and in one dimension. We calculate the binding energy as well as the effective mass of the single particle. We use an approximate method developed in the three-dimensional case, where the Hilbert space for the excited states of the N fermions is restricted to have at most two particle-hole pairs. When the mass of the single particle is equal to the fermion mass, we find excellent agreement with the exact results of McGuire. When the mass of the single particle is infinite, we solve exactly the problem and find again excellent agreement between approximate results and exact ones. This overall agreement in one dimension gives a strong validation for the approximate method applied in three dimensions. Moreover it shows that our approximate treatment is excellent for the one-dimensional problem in the general case with respect to the mass of the single particle.

PHYSICAL REVIEW A 79, (2009)

LPS

Abstract : We consider the problem of a single particle interacting with N identical fermions, at zero temperature and in one dimension. We calculate the binding energy as well as the effective mass of the single particle. We use an approximate method developed in the three-dimensional case, where the Hilbert space for the excited states of the N fermions is restricted to have at most two particle-hole pairs. When the mass of the single particle is equal to the fermion mass, we find excellent agreement with the exact results of McGuire. When the mass of the single particle is infinite, we solve exactly the problem and find again excellent agreement between approximate results and exact ones. This overall agreement in one dimension gives a strong validation for the approximate method applied in three dimensions. Moreover it shows that our approximate treatment is excellent for the one-dimensional problem in the general case with respect to the mass of the single particle.

DOI

13

Superfluid equation of state of dilute composite bosons or how to include 3-and 4-body problems in the many body problem - Leyronas, X. and Combescot, R.

LASER PHYSICS 19, 599-601 (2009)

Abstract : We show how the 3 and 4-body problems emerge in the BEC limit of the BEC-BCS crossover, where we treat explicitly dimers as made of two fermions. We give the argument leading, at zero temperature, to the calculation of the equation of state. We find that, when expanding the chemical potential in powers of the density n up to the Lee-Huang-Yang order, proportional to n (3/2), the result is identical to the one of elementary bosons in terms of the dimer-dimer scattering length a (M) , the composite nature of the dimers appearing only in the next order term proportional to n (2).

LASER PHYSICS 19, 599-601 (2009)

LPS

Abstract : We show how the 3 and 4-body problems emerge in the BEC limit of the BEC-BCS crossover, where we treat explicitly dimers as made of two fermions. We give the argument leading, at zero temperature, to the calculation of the equation of state. We find that, when expanding the chemical potential in powers of the density n up to the Lee-Huang-Yang order, proportional to n (3/2), the result is identical to the one of elementary bosons in terms of the dimer-dimer scattering length a (M) , the composite nature of the dimers appearing only in the next order term proportional to n (2).

DOI

14

Normal state of highly polarized Fermi gases: Full many-body treatment - Giraud, S. and Combescot, R.

LASER PHYSICS 19, 583-587 (2009)

Abstract : We present a full many-body analysis of the problem of a single a dagger'' atom resonantly interacting with a Fermi sea of a dagger atoms. A series of successive approximations permits us to clarify the quite mysterious agreement between Monte Carlo results and approximate calculations taking only into account single particle-hole excitations. We show that it results from a nearly perfect destructive interference of the contributions of states with more than one particle-hole pair. Our treatment provides, at the same time, an essentially exact solution to this problem.

LASER PHYSICS 19, 583-587 (2009)

LPS

Abstract : We present a full many-body analysis of the problem of a single a dagger'' atom resonantly interacting with a Fermi sea of a dagger atoms. A series of successive approximations permits us to clarify the quite mysterious agreement between Monte Carlo results and approximate calculations taking only into account single particle-hole excitations. We show that it results from a nearly perfect destructive interference of the contributions of states with more than one particle-hole pair. Our treatment provides, at the same time, an essentially exact solution to this problem.

DOI

15

Particle distribution tail and related energy formula - Combescot, R. and Alzetto, F. and Leyronas, X.

PHYSICAL REVIEW A 79, (2009)

Abstract : We present a simple derivation of the energy formula found by Tan, relative to the single-channel Hamiltonian relevant for ultracold Fermi gases. This derivation is generalized to particles with different masses, to arbitrary mixtures, and to two-dimensional space. We show how in a field-theoretic approach, the 1/k(4) tail in the momentum distribution and the energy formula arise in a natural way. As a specific example, we consider quantitative calculations of the energy from different formulas within the ladder diagram approximation in the normal state. The comparison of the results provides an indication on the quality of the approximation.

PHYSICAL REVIEW A 79, (2009)

LPS

Abstract : We present a simple derivation of the energy formula found by Tan, relative to the single-channel Hamiltonian relevant for ultracold Fermi gases. This derivation is generalized to particles with different masses, to arbitrary mixtures, and to two-dimensional space. We show how in a field-theoretic approach, the 1/k(4) tail in the momentum distribution and the energy formula arise in a natural way. As a specific example, we consider quantitative calculations of the energy from different formulas within the ladder diagram approximation in the normal state. The comparison of the results provides an indication on the quality of the approximation.

DOI

16

Analytical theory of the dressed bound state in highly polarized Fermi gases - Combescot, R. and Giraud, S. and Leyronas, X.

EPL 88, (2009)

Abstract : We present an analytical treatment of a single down arrow-atom within a Fermi sea of up arrow-atoms, when the interaction is strong enough to produce a bound state, dressed by the Fermi sea. Our method makes use of a diagrammatic analysis, with the involved diagrams taking only into account at most two particle-hole pairs excitations. The agreement with existing Monte Carlo results is excellent. In the BEC limit our equation reduces exactly to the Skorniakov and Ter-Martirosian equation. We present results for up arrow-and down arrow-atoms with different masses, which is of interest for experiments in progress. Copyright (C) EPLA, 2009

EPL 88, (2009)

LPS

Abstract : We present an analytical treatment of a single down arrow-atom within a Fermi sea of up arrow-atoms, when the interaction is strong enough to produce a bound state, dressed by the Fermi sea. Our method makes use of a diagrammatic analysis, with the involved diagrams taking only into account at most two particle-hole pairs excitations. The agreement with existing Monte Carlo results is excellent. In the BEC limit our equation reduces exactly to the Skorniakov and Ter-Martirosian equation. We present results for up arrow-and down arrow-atoms with different masses, which is of interest for experiments in progress. Copyright (C) EPLA, 2009

DOI

17

Normal state of highly polarized Fermi gases: Full many-body treatment - Combescot, R. and Giraud, S.

PHYSICAL REVIEW LETTERS 101, (2008)

Abstract : We consider a single down arrow atom within a Fermi sea of up arrow atoms. We elucidate by a full many-body analysis the quite mysterious agreement between Monte Carlo results and approximate calculations taking only into account single particle-hole excitations. It results from a nearly perfect destructive interference of the contributions of states with more than one particle-hole pair. This is linked to the remarkable efficiency of the expansion in powers of hole wave vectors, the lowest order leading to perfect interference. Going up to two particle-hole pairs gives an essentially perfect agreement with known exact results. Hence our treatment amounts to an exact solution of this problem.

PHYSICAL REVIEW LETTERS 101, (2008)

LPS

Abstract : We consider a single down arrow atom within a Fermi sea of up arrow atoms. We elucidate by a full many-body analysis the quite mysterious agreement between Monte Carlo results and approximate calculations taking only into account single particle-hole excitations. It results from a nearly perfect destructive interference of the contributions of states with more than one particle-hole pair. This is linked to the remarkable efficiency of the expansion in powers of hole wave vectors, the lowest order leading to perfect interference. Going up to two particle-hole pairs gives an essentially perfect agreement with known exact results. Hence our treatment amounts to an exact solution of this problem.

DOI

18

Superfluid equation of state of cold fermionic gases in the Bose-Einstein regime - Combescot, R. and Leyronas, X.

PHYSICAL REVIEW A 78, (2008)

Abstract : We present an exact many-body theory of ultracold fermionic gases for the Bose-Einstein condensation (BEC) regime of the BEC-BCS crossover. This is a purely fermionic approach which treats explicitly and systematically the dimers formed in the BEC regime as made of two fermions. We consider specifically the zero temperature case and calculate the first terms of the expansion of the chemical potential in powers of the density n. We derive first the mean-field contribution, which has the expected standard expression when it is written in terms of the dimer-dimer scattering length a(M). We go next in the expansion to the Lee-Huang-Yang order, proportional to n(3/2). We find the far less obvious result that it retains also the same expression in terms of a(M) as for elementary bosons. The composite nature of the dimers appears only in the next term proportional to n(2).

PHYSICAL REVIEW A 78, (2008)

LPS

Abstract : We present an exact many-body theory of ultracold fermionic gases for the Bose-Einstein condensation (BEC) regime of the BEC-BCS crossover. This is a purely fermionic approach which treats explicitly and systematically the dimers formed in the BEC regime as made of two fermions. We consider specifically the zero temperature case and calculate the first terms of the expansion of the chemical potential in powers of the density n. We derive first the mean-field contribution, which has the expected standard expression when it is written in terms of the dimer-dimer scattering length a(M). We go next in the expansion to the Lee-Huang-Yang order, proportional to n(3/2). We find the far less obvious result that it retains also the same expression in terms of a(M) as for elementary bosons. The composite nature of the dimers appears only in the next term proportional to n(2).

DOI

19

Four-particle problem using Feynman diagrams - Brodsky, I. V. and Kagan, M. Yu. and Klaptsov, A. V. and Combescot, R. and Leyronas, X.

LASER PHYSICS 17, 523-526 (2007)

Abstract : We present an exact diagrammatic approach for the problem of dimer-dimer scattering in 3D for dimers being a resonant bound state of two fermions in a spin singlet state, with corresponding scattering length a. We recover exactly the previously known result a(B) = 0.60a, where a(B) is the dimer-dimer scattering length. A detailed discussion of how one can ``sum all the diagrams'' in this case is presented. Applications to the study of 4-particle bound states of various complexes in 2D are briefly presented.

LASER PHYSICS 17, 523-526 (2007)

LPS

Abstract : We present an exact diagrammatic approach for the problem of dimer-dimer scattering in 3D for dimers being a resonant bound state of two fermions in a spin singlet state, with corresponding scattering length a. We recover exactly the previously known result a(B) = 0.60a, where a(B) is the dimer-dimer scattering length. A detailed discussion of how one can ``sum all the diagrams'' in this case is presented. Applications to the study of 4-particle bound states of various complexes in 2D are briefly presented.

DOI

20

Exciton-exciton scattering: Composite boson versus elementary boson - Combescot, M. and Betbeder-Matibet, O. and Combescot, R.

PHYSICAL REVIEW B 75, (2007)

Abstract : This paper shows the necessity of introducing a quantum object, the ``coboson,'' to properly describe, through a fermion scheme, any composite particle, such as the exciton, which is made of two fermions. Although commonly dealt 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. As a direct consequence of this composite nature, there is no correct way to describe the interaction between cobosons as a potential V. This is rather dramatic because, with the Hamiltonian not written as H=H-0+V, all the usual approaches to many-body effects fail. In particular, the standard form of the Fermi golden rule, written in terms of V, cannot be used to obtain the transition rates of two cobosons. To get them, we have had to construct an unconventional expression for this Fermi golden rule in which H only appears. Making use of this expression, we give here 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 Hamiltonian in which the excitons are considered as elementary bosons with effective scatterings between them, these scatterings resulting from an elaborate mapping between the two-fermion space and the ideal boson space. We show that the relation between the inverse lifetime and the sum of the transition rates for elementary bosons differs from the one of the composite bosons by a factor of 1/2, so that it is impossible to find effective scatterings between bosonic excitons giving these two physical quantities correctly, 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.

PHYSICAL REVIEW B 75, (2007)

LPS

Abstract : This paper shows the necessity of introducing a quantum object, the ``coboson,'' to properly describe, through a fermion scheme, any composite particle, such as the exciton, which is made of two fermions. Although commonly dealt 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. As a direct consequence of this composite nature, there is no correct way to describe the interaction between cobosons as a potential V. This is rather dramatic because, with the Hamiltonian not written as H=H-0+V, all the usual approaches to many-body effects fail. In particular, the standard form of the Fermi golden rule, written in terms of V, cannot be used to obtain the transition rates of two cobosons. To get them, we have had to construct an unconventional expression for this Fermi golden rule in which H only appears. Making use of this expression, we give here 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 Hamiltonian in which the excitons are considered as elementary bosons with effective scatterings between them, these scatterings resulting from an elaborate mapping between the two-fermion space and the ideal boson space. We show that the relation between the inverse lifetime and the sum of the transition rates for elementary bosons differs from the one of the composite bosons by a factor of 1/2, so that it is impossible to find effective scatterings between bosonic excitons giving these two physical quantities correctly, 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.