DOI

1

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

PHYSICAL REVIEW A 93, (2016)

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.

PHYSICAL REVIEW A 93, (2016)

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.

DOI

2

Quantum walks and non-Abelian discrete gauge theory - Arnault, Pablo and Di Molfetta, Giuseppe and Brachet, Marc and Debbasch, Fabrice

PHYSICAL REVIEW A 94, (2016)

Abstract : A family of discrete-time quantum walks (DTQWs) on the line with an exact discrete U(N) gauge invariance is introduced. It is shown that the continuous limit of these DTQWs, when it exists, coincides with the dynamics of a Dirac fermion coupled to usual U(N) gauge fields in two-dimensional spacetime. A discrete generalization of the usual U(N) curvature is also constructed. An alternate interpretation of these results in terms of superimposed U(1) Maxwell fields and SU(N) gauge fields is discussed in the Appendix. Numerical simulations are also presented, which explore the convergence of the DTQWs towards their continuous limit and which also compare the DTQWs with classical (i.e., nonquantum) motions in classical SU(2) fields. The results presented in this paper constitute a first step towards quantum simulations of generic Yang-Mills gauge theories through DTQWs.

PHYSICAL REVIEW A 94, (2016)

Abstract : A family of discrete-time quantum walks (DTQWs) on the line with an exact discrete U(N) gauge invariance is introduced. It is shown that the continuous limit of these DTQWs, when it exists, coincides with the dynamics of a Dirac fermion coupled to usual U(N) gauge fields in two-dimensional spacetime. A discrete generalization of the usual U(N) curvature is also constructed. An alternate interpretation of these results in terms of superimposed U(1) Maxwell fields and SU(N) gauge fields is discussed in the Appendix. Numerical simulations are also presented, which explore the convergence of the DTQWs towards their continuous limit and which also compare the DTQWs with classical (i.e., nonquantum) motions in classical SU(2) fields. The results presented in this paper constitute a first step towards quantum simulations of generic Yang-Mills gauge theories through DTQWs.

DOI

3

Helicity, topology, and Kelvin waves in reconnecting quantum knots - Clark di Leoni, P. and Mininni, P. D. and Brachet, M. E.

PHYSICAL REVIEW A 94, (2016)

Abstract : Helicity is a topological invariant that measures the linkage and knottedness of lines, tubes, and ribbons. As such, it has found myriads of applications in astrophysics, fluid dynamics, atmospheric sciences, and biology. In quantum flows, where topology-changing reconnection events are a staple, helicity appears as a key quantity to study. However, the usual definition of helicity is not well posed in quantum vortices, and its computation based on counting links and crossings of centerline vorticity can be downright impossible to apply in complex and turbulent scenarios. We present a definition of helicity which overcomes these problems and which gives the expected result in the large-scale limit. With it, we show that certain reconnection events can excite Kelvin waves and other complex motions of the centerline vorticity, which slowly deplete helicity as they interact nonlinearly, thus linking the theory of vortex knots with observations of quantum fluids. This process also results in the depletion of helicity in a fully turbulent quantum flow, in a way reminiscent of the decay of helicity in classical fluids.

PHYSICAL REVIEW A 94, (2016)

Abstract : Helicity is a topological invariant that measures the linkage and knottedness of lines, tubes, and ribbons. As such, it has found myriads of applications in astrophysics, fluid dynamics, atmospheric sciences, and biology. In quantum flows, where topology-changing reconnection events are a staple, helicity appears as a key quantity to study. However, the usual definition of helicity is not well posed in quantum vortices, and its computation based on counting links and crossings of centerline vorticity can be downright impossible to apply in complex and turbulent scenarios. We present a definition of helicity which overcomes these problems and which gives the expected result in the large-scale limit. With it, we show that certain reconnection events can excite Kelvin waves and other complex motions of the centerline vorticity, which slowly deplete helicity as they interact nonlinearly, thus linking the theory of vortex knots with observations of quantum fluids. This process also results in the depletion of helicity in a fully turbulent quantum flow, in a way reminiscent of the decay of helicity in classical fluids.

DOI

4

Sticking transition in a minimal model for the collisions of active particles in quantum fluids - Shukla, Vishwanath and Brachet, Marc and Pandit, Rahul

PHYSICAL REVIEW A 94, (2016)

Abstract : Particles of low velocity, traveling without dissipation in a superfluid, can interact and emit sound when they collide. We propose a minimal model in which the equations of motion of the particles, including a short-range repulsive force, are self-consistently coupled with the Gross-Pitaevskii equation. We show that this model generates naturally an effective superfluid-mediated attractive interaction between the particles; and we study numerically the collisional dynamics of particles as a function of their incident kinetic energy and the length scale of the repulsive force. We find a transition from almost elastic to completely inelastic (sticking) collisions as the parameters are tuned. We find that aggregation and clustering result from this sticking transition in multiparticle systems.

PHYSICAL REVIEW A 94, (2016)

Abstract : Particles of low velocity, traveling without dissipation in a superfluid, can interact and emit sound when they collide. We propose a minimal model in which the equations of motion of the particles, including a short-range repulsive force, are self-consistently coupled with the Gross-Pitaevskii equation. We show that this model generates naturally an effective superfluid-mediated attractive interaction between the particles; and we study numerically the collisional dynamics of particles as a function of their incident kinetic energy and the length scale of the repulsive force. We find a transition from almost elastic to completely inelastic (sticking) collisions as the parameters are tuned. We find that aggregation and clustering result from this sticking transition in multiparticle systems.

DOI

5

High-temperature expansion for interacting fermions - Sun, Mingyuan and Leyronas, Xavier

PHYSICAL REVIEW A 92, (2015)

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.

PHYSICAL REVIEW A 92, (2015)

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.

DOI

6

Spatiotemporal detection of Kelvin waves in quantum turbulence simulations - Clark di Leoni, P. and Mininni, P. D. and Brachet, M. E.

PHYSICAL REVIEW A 92, (2015)

Abstract : We present evidence of Kelvin excitations in space-time resolved spectra of numerical simulations of quantum turbulence. Kelvin waves are transverse and circularly polarized waves that propagate along quantized vortices, for which the restitutive force is the tension of the vortex line, and which play an important role in theories of superfluid turbulence. We use the Gross-Pitaevskii equation to model quantum flows, letting an initial array of well-organized vortices develop into a turbulent bundle of intertwined vortex filaments. By achieving high spatial and temporal resolution we are able to calculate space-time resolved mass density and kinetic energy spectra. Evidence of Kelvin and sound waves is clear in both spectra. Identification of the waves allows us to extract the spatial spectrum of Kelvin waves, clarifying their role in the transfer of energy.

PHYSICAL REVIEW A 92, (2015)

Abstract : We present evidence of Kelvin excitations in space-time resolved spectra of numerical simulations of quantum turbulence. Kelvin waves are transverse and circularly polarized waves that propagate along quantized vortices, for which the restitutive force is the tension of the vortex line, and which play an important role in theories of superfluid turbulence. We use the Gross-Pitaevskii equation to model quantum flows, letting an initial array of well-organized vortices develop into a turbulent bundle of intertwined vortex filaments. By achieving high spatial and temporal resolution we are able to calculate space-time resolved mass density and kinetic energy spectra. Evidence of Kelvin and sound waves is clear in both spectra. Identification of the waves allows us to extract the spatial spectrum of Kelvin waves, clarifying their role in the transfer of energy.

DOI

7

Wetting Heterogeneities in Porous Media Control Flow Dissipation - Murison, Julie and Semin, Benoit and Baret, Jean-Christophe and Herminghaus, Stephan and Schroeter, Matthias and Brinkmann, Martin

PHYSICAL REVIEW APPLIED 2, (2014)

Abstract : Pressure-controlled displacement of an oil-water interface is studied in dense packings of functionalized glass beads with well-defined spatial wettability correlations. An enhanced dissipation is observed if the typical extension xi of the same-type wetting domains is smaller than the average bead diameter d. Three-dimensional imaging using x-ray microtomography shows that the frequencies n(s) of residual droplet volumes s for different xi collapse onto the same curve. This indicates that the additional dissipation for small xi is due to contact line pinning rather than an increase of capillary break-up and coalescence events.

PHYSICAL REVIEW APPLIED 2, (2014)

Abstract : Pressure-controlled displacement of an oil-water interface is studied in dense packings of functionalized glass beads with well-defined spatial wettability correlations. An enhanced dissipation is observed if the typical extension xi of the same-type wetting domains is smaller than the average bead diameter d. Three-dimensional imaging using x-ray microtomography shows that the frequencies n(s) of residual droplet volumes s for different xi collapse onto the same curve. This indicates that the additional dissipation for small xi is due to contact line pinning rather than an increase of capillary break-up and coalescence events.

DOI

8

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)

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

9

Quantum walks as massless Dirac fermions in curved space-time - Di Molfetta, Giuseppe and Brachet, M. and Debbasch, Fabrice

PHYSICAL REVIEW A 88, (2013)

Abstract : A particular family of time- and space-dependent discrete-time quantum walks (QWs) is considered in one-dimensional physical space. The continuous limit of these walks is defined through a procedure discussed here and computed in full detail. In this limit, the walks coincide with the propagation of a massless Dirac fermion in an arbitrary gravitational field. A QW mimicking the radial propagation of a fermion outside and inside the event horizon of a Schwarzschild black hole is explicitly constructed and simulated numerically. Thus, the family of QWs considered in our manuscript provides an analog system to study experimentally coherent quantum propagation in curved spacetime.

PHYSICAL REVIEW A 88, (2013)

Abstract : A particular family of time- and space-dependent discrete-time quantum walks (QWs) is considered in one-dimensional physical space. The continuous limit of these walks is defined through a procedure discussed here and computed in full detail. In this limit, the walks coincide with the propagation of a massless Dirac fermion in an arbitrary gravitational field. A QW mimicking the radial propagation of a fermion outside and inside the event horizon of a Schwarzschild black hole is explicitly constructed and simulated numerically. Thus, the family of QWs considered in our manuscript provides an analog system to study experimentally coherent quantum propagation in curved spacetime.

DOI

10

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.

PHYSICAL REVIEW A 88, (2013)

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.

PHYSICAL REVIEW A 88, (2013)

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.

DOI

11

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)

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

12

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)

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

13

Modulated solutions and superfluid fraction for the Gross-Pitaevskii equation with a nonlocal potential at T not equal 0 - Sepulveda, Nestor

PHYSICAL REVIEW A 83, (2011)

Abstract : Modulated solutions of the nonlocal Gross-Pitaevskii equation are studied at T not equal 0. Stationary states are computed by constructing a stochastic process consisting of a noisy Ginzburg-Landau equation. An order parameter is introduced to quantify the superfluid fraction as a function of the temperature. When the temperature increases the superfluid fraction is shown to vanish. This is explained qualitatively by the thermal appearance of defects that disconnect the system wave function. We also deduce an explicit formula for the introduced order parameter in terms of an Arrhenius law. This allow us to estimate the ``energy of activation'' to create a disconnection in the wave function.

PHYSICAL REVIEW A 83, (2011)

Abstract : Modulated solutions of the nonlocal Gross-Pitaevskii equation are studied at T not equal 0. Stationary states are computed by constructing a stochastic process consisting of a noisy Ginzburg-Landau equation. An order parameter is introduced to quantify the superfluid fraction as a function of the temperature. When the temperature increases the superfluid fraction is shown to vanish. This is explained qualitatively by the thermal appearance of defects that disconnect the system wave function. We also deduce an explicit formula for the introduced order parameter in terms of an Arrhenius law. This allow us to estimate the ``energy of activation'' to create a disconnection in the wave function.

DOI

14

Classification of the ground states and topological defects in a rotating two-component Bose-Einstein condensate - Mason, Peter and Aftalion, Amandine

PHYSICAL REVIEW A 84, (2011)

Abstract : We classify the ground states and topological defects of a rotating two-component condensate when varying several parameters: the intracomponent coupling strengths, the intercomponent coupling strength, and the particle numbers. No restriction is placed on the masses or trapping frequencies of the individual components. We present numerical phase diagrams which show the boundaries between the regions of coexistence, spatial separation, and symmetry breaking. Defects such as triangular coreless vortex lattices, square coreless vortex lattices, and giant skyrmions are classified. Various aspects of the phase diagrams are analytically justified thanks to a nonlinear sigma model that describes the condensate in terms of the total density and a pseudo-spin representation.

PHYSICAL REVIEW A 84, (2011)

Abstract : We classify the ground states and topological defects of a rotating two-component condensate when varying several parameters: the intracomponent coupling strengths, the intercomponent coupling strength, and the particle numbers. No restriction is placed on the masses or trapping frequencies of the individual components. We present numerical phase diagrams which show the boundaries between the regions of coexistence, spatial separation, and symmetry breaking. Defects such as triangular coreless vortex lattices, square coreless vortex lattices, and giant skyrmions are classified. Various aspects of the phase diagrams are analytically justified thanks to a nonlinear sigma model that describes the condensate in terms of the total density and a pseudo-spin representation.

DOI

15

Virial expansion with Feynman diagrams - Leyronas, X.

PHYSICAL REVIEW A 84, (2011)

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).

PHYSICAL REVIEW A 84, (2011)

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).

DOI

16

Universal correlations and coherence in quasi-two-dimensional trapped Bose gases - Holzmann, Markus and Chevallier, Maguelonne and Krauth, Werner

PHYSICAL REVIEW A 81, (2010)

Abstract : We study the quasi-two-dimensional Bose gas in harmonic traps at temperatures above the Kosterlitz-Thouless transition, where the gas is in the normal phase. We show that mean-field theory takes into account the dominant interaction effects for experimentally relevant trap geometries. Comparing with quantum Monte Carlo calculations, we quantify the onset of the fluctuation regime, where correlations beyond mean-field become important. Although the density profile depends on the microscopic parameters of the system, we show that the correlation density (the difference between the exact and the mean-field density) is accurately described by a universal expression, obtained from classical-field calculations of the homogeneous strictly two-dimensional gas. Deviations from universality, due to the finite value of the interaction or to the trap geometry, are shown to be small for current experiments. We further study coherence and pair correlations on a microscopic scale. Finite-size effects in the off-diagonal density matrix allow us to characterize the crossover from Kosterlitz-Thouless to Bose-Einstein behavior for small particle numbers. Bose-Einstein condensation occurs below a characteristic number of particles which rapidly diverges with vanishing interactions.

PHYSICAL REVIEW A 81, (2010)

Abstract : We study the quasi-two-dimensional Bose gas in harmonic traps at temperatures above the Kosterlitz-Thouless transition, where the gas is in the normal phase. We show that mean-field theory takes into account the dominant interaction effects for experimentally relevant trap geometries. Comparing with quantum Monte Carlo calculations, we quantify the onset of the fluctuation regime, where correlations beyond mean-field become important. Although the density profile depends on the microscopic parameters of the system, we show that the correlation density (the difference between the exact and the mean-field density) is accurately described by a universal expression, obtained from classical-field calculations of the homogeneous strictly two-dimensional gas. Deviations from universality, due to the finite value of the interaction or to the trap geometry, are shown to be small for current experiments. We further study coherence and pair correlations on a microscopic scale. Finite-size effects in the off-diagonal density matrix allow us to characterize the crossover from Kosterlitz-Thouless to Bose-Einstein behavior for small particle numbers. Bose-Einstein condensation occurs below a characteristic number of particles which rapidly diverges with vanishing interactions.

DOI

17

Equation of state of a polarized Fermi gas in the Bose-Einstein-condensate limit - Alzetto, F. and Leyronas, X.

PHYSICAL REVIEW A 81, (2010)

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.

PHYSICAL REVIEW A 81, (2010)

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.

DOI

18

Equilibrium state of a trapped two-dimensional Bose gas - Rath, Steffen P. and Yefsah, Tarik and Guenter, Kenneth J. and Cheneau, Marc and Desbuquois, Remi and Holzmann, Markus and Krauth, Werner and Dalibard, Jean

PHYSICAL REVIEW A 82, (2010)

Abstract : We study experimentally and numerically the equilibrium density profiles of a trapped two-dimensional (87)Rb Bose gas and investigate the equation of state of the homogeneous system using the local density approximation. We find a clear discrepancy between in situ measurements and quantum Monte Carlo simulations, which we attribute to a nonlinear variation of the optical density of the atomic cloud with its spatial density. However, good agreement between experiment and theory is recovered for the density profiles measured after time of flight, taking advantage of their self-similarity in a two-dimensional expansion.

PHYSICAL REVIEW A 82, (2010)

Abstract : We study experimentally and numerically the equilibrium density profiles of a trapped two-dimensional (87)Rb Bose gas and investigate the equation of state of the homogeneous system using the local density approximation. We find a clear discrepancy between in situ measurements and quantum Monte Carlo simulations, which we attribute to a nonlinear variation of the optical density of the atomic cloud with its spatial density. However, good agreement between experiment and theory is recovered for the density profiles measured after time of flight, taking advantage of their self-similarity in a two-dimensional expansion.

DOI

19

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)

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

20

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)

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.