laboratoire de physique statistique
laboratoire de physique statistique


Second-order virial expansion for an atomic gas in a harmonic waveguide - Kristensen, Tom and Leyronas, Xavier and Pricoupenko, Ludovic

Abstract : The virial expansion for cold two-component Fermi and Bose atomic gases is considered in the presence of a waveguide and in the vicinity of a Feshbach resonance. The interaction between atoms and the coupling with the Feshbach molecules is modeled using a quantitative separable two-channel model. The scattering phase shift in an atomic waveguide is defined. This permits us to extend the Beth-Uhlenbeck formula for the second-order virial coefficient to this inhomogeneous case.
High-temperature expansion for interacting fermions - Sun, Mingyuan and Leyronas, Xavier

Abstract : We present a general method for the high-temperature expansion of the self-energy of interacting particles. Although the method is valid for fermions and bosons, we illustrate it for spin-one-half fermions interacting via a zero range potential, in the Bose-Einstein-condensate-Bardeen-Cooper-Schrieffer (BEC-BCS) crossover. The small parameter of the expansion is the fugacity z. Our results include terms of order z and z(2), which take into account, respectively, two-and three-body correlations. We give results for the high-temperature expansion of Tan's contact at order z(3) in the whole BEC-BCS crossover. We apply our method to calculate the spectral function at the unitary limit. We find structures that are different from those discussed in previous approaches, which included only two-body correlations. This shows that including three-body correlations can play an important role in the structures of the spectral function.
Momentum Distribution of a Dilute Unitary Bose Gas with Three-Body Losses - Laurent, Sebastien and Leyronas, Xavier and Chevy, Frederic

Abstract : Using a combination of Boltzmann's equation and virial expansion, we study the effect of three-body losses and interactions on the momentum distribution of a homogeneous unitary Bose gas in the dilute limit where quantum correlations are negligible. The comparison of our results to the recent measurement made at JILA on a unitary gas of Rb-85 allows us to determine an experimental fugacity z = 0.5(1).
Dimer-dimer scattering length for fermions with different masses: Analytical study for large mass ratio - Alzetto, F. and Combescot, R. and Leyronas, X.

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
Condensation energy of a spin-1/2 strongly interacting Fermi gas - Navon, N. and Nascimbene, S. and Leyronas, X. and Chevy, F. and Salomon, C.

Abstract : We report a measurement of the condensation energy of a two-component Fermi gas with tunable interactions. From the equation of state of the gas, we infer the properties of the normal phase in the zero-temperature limit. By comparing the pressure of the normal phase at T = 0 to that of the low-temperature superfluid phase, we deduce the condensation energy, i.e., the energy gain of the system upon being in the superfluid rather than the normal state. We compare our measurements to a ladder approximation description of the normal phase and to a fixed-node Monte Carlo approach, finding excellent agreement. We discuss the relationship between condensation energy and pairing gap in the BEC-BCS crossover.
Atom-dimer scattering amplitude for fermionic mixtures with different masses: s-wave and p-wave contributions - Alzetto, F. and Combescot, R. and Leyronas, X.

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
Virial expansion with Feynman diagrams - Leyronas, X.

Abstract : We present a field theoretic method for the calculation of the second and third virial coefficients b(2) and b(3) of two-species fermions interacting via a contact interaction. The method is mostly analytic. We find a closed expression for b(3) in terms of the two- and three-body T matrices. We recover numerically, at unitarity, and also in the whole Bose-Einstein-condensate-BCS crossover, previous numerical results for the third virial coefficient b(3).
Normal state of highly polarized Fermi gases: The bound state - Combescot, R. and Giraud, S. and Leyronas, X.
LASER PHYSICS 20678-682 (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.
Equation of state of a polarized Fermi gas in the Bose-Einstein-condensate limit - Alzetto, F. and Leyronas, X.

Abstract : We present a theoretical study of the BEC-BCS crossover in the Bose-Einstein-condensate (BEC) regime in the case of an unequal number of fermions of two species. We take full account of the composite nature of the dimers made of fermions. In the limit of low densities, we calculate the ground-state energy of the system, or equivalently the chemical potentials of each species, as well as the one-particle gap and the energy of an ``impurity'' immersed in a Fermi sea. For the chemical potentials we go up to order (density)(4/3). The results found involve the exact atom-dimer a(AD) and dimer-dimer a(DD) scattering lengths and therefore include the three-and four-body problems in the many-body problem. We briefly comment on the importance of the different mean-field corrections for recent experiments.
Atom-dimer scattering length for fermions with different masses: Analytical study of limiting cases - Alzetto, F. and Combescot, R. and Leyronas, X.

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.
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 19599-601 (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).
Particle distribution tail and related energy formula - Combescot, R. and Alzetto, F. and Leyronas, X.

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.
Theory of nonequilibrium transport in the SU(N) Kondo regime - Mora, Christophe and Vitushinsky, Pavel and Leyronas, Xavier and Clerk, Aashish A. and Le Hur, Karyn

Abstract : Using a Fermi-liquid approach, we provide a comprehensive treatment of the current and current noise through a quantum dot whose low-energy behavior corresponds to an SU(N) Kondo model, focusing on the case N=4 relevant to carbon nanotube dots. We show that for general N, one needs to consider the effects of higher-order Fermi-liquid corrections even to describe low-voltage current and noise. We also show that the noise exhibits complex behavior due to the interplay between coherent shot noise, and noise arising from interaction-induced scattering events. We also treat various imperfections relevant to experiments, such as the effects of asymmetric dot-lead couplings.
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
Current noise through a kondo quantum dot in a SU(N) fermi liquid state - Mora, Christophe and Leyronas, Xavier and Regnault, Nicolas

Abstract : The current noise through a mesoscopic quantum dot is calculated and analyzed in the Fermi liquid regime of the SU(N) Kondo model. The results connect the Johnson-Nyquist noise to the shot noise for an arbitrary ratio of voltage and temperature, and show that temperature corrections are sizable in the usual experiments. For the experimentally relevant SU(4) case, quasiparticle interactions are shown to increase the shot noise.
Superfluid equation of state of cold fermionic gases in the Bose-Einstein regime - Combescot, R. and Leyronas, X.

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).
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 17523-526 (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.
Superfluid equation of state of dilute composite bosons - Leyronas, X. and Combescot, R.

Abstract : We present an exact theory of the BEC-BCS crossover in the Bose-Einstein-condensate (BEC) regime, which treats explicitly dimers as made of two fermions. We apply our framework, 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).