We investigate fermion pairing in the unitary regime for a mass ratio corresponding to a 6Li-40K mixture using Quantum Monte Carlo methods. The ground-state energy and the average light and heavy particle excitation spectrum for the unpolarized superfluid state are nearly independent of the mass ratio. In the majority light system, the polarized superfluid is close to the energy of a phase separated mixture of nearly fully polarized normal and unpolarized superfluid. For a majority of heavy particles, we find an energy minimum for a normal state with a ratio of ~ 3:1 heavy to light particles. A slight increase in attraction to kF*a ~ 2.5 yields a ground state energy of nearly zero for this ratio. A cold unpolarized system in a harmonic trap at unitarity should phase separate into three regions, with a shell of unpolarized superfluid in the middle.
We investigate the zero-temperature properties of a superfluid Bose-Fermi mixture by introducing a set of coupled Galilei-invariant nonlinear Schrödinger equations valid from weak-coupling to unitarity. The Bose dynamics is described by a Gross-Pitaevskii-type equation including beyond-mean-field corrections possessing the correct weak-coupling and unitarity limits. The dynamics of the two-component Fermi superfluid is described by a density-functional equation including beyond-mean-field terms with correct weak-coupling and unitarity limits. The present set of equations is equivalent to the e…
We consider a polarized Fermi gas in the unitarity limit. Results are calculated analytically up to next-to-leading order in an expansion about d=4 spatial dimensions. We find a first order transition from superfluid to normal phase. The critical chemical potential asymmetry for this phase transition is delta_mu_c= 2/(mu epsilon)*(1-0.467ε), where epsilon=4-d is the expansion parameter and 'mu' is the average chemical potential of the two fermion species. Stability of the superfluid phase in the presence of supercurrents is also studied.
We extract the shear viscosity to entropy density ratio η/s of cold fermionic atoms in the unitarity limit from experimental data on the damping of collective excitations. We find that near the critical temperature η/s is roughly equal to 1/2 in units of \hbar/k_B. With the possible exception of the quark gluon plasma, this value is closer to the conjectured lower bound 1/(4π) than any other known liquid.
We derive an energy density functional for non-relativistic spin one-half fermions in the limit of a divergent two-body scattering length. Using an epsilon expansion around d=4-epsilon spatial dimensions we compute the coefficient of the leading correction beyond the local density approximation (LDA). In the case of N fermionic atoms trapped in a harmonic potential this correction has the form E=E_(LDA)(1+c_s (3N)^(-2/3)), where E_(LDA) is the total energy in LDA approximation. At next-to-leading order in the epsilon expansion we find c_s=1.68, which is significantly larger than the result for…
We consider a few-particle system of trapped neutral fermionic atoms at ultra-low temperatures, with the attractive interaction tuned to Feshbach resonance. We calculate the energies and the spatial densities of the few-body systems using a generalisation of the extended Thomas-Fermi (ETF) method, and assuming the particles obey the Haldane-Wu fractional exclusion statistics (FES) at unitarity. This method is different from the scaled ETF version given by Chang and Bertsch (Phys. Rev. A76,021603(R) (2007)). Our semiclassical FES results are consistent with the Monte-Carlo calculations of the a…
We consider two-component fermions on the lattice in the unitarity limit. This is an idealized limit of attractive fermions where the range of the interaction is zero and the scattering length is infinite. Using Euclidean time projection, we compute the ground state energy using four computationally different but physically identical auxiliary-field methods. The best performance is obtained using a bounded continuous auxiliary field and a non-local updating algorithm called hybrid Monte Carlo. With this method we calculate results for 10 and 14 fermions at lattice volumes 4^3, 5^3, 6^3, 7^3, 8…
From an extensive calculation of static properties of a trapped Fermi superfluid at zero temperature using a density-functional formulation, we demonstrate a universal behavior of its observables, such as energy, chemical potential, radius etc., over the crossover from the BCS limit to unitarity leading to scaling over many orders of magnitude in fermion number. This scaling allows to predict the static properties of the system, with a large number ($\sim 10^5$) of fermions, over the crossover with an error of 1-2%, from the knowledge of those for a small number ($\sim 10$) of fermions.
We consider a gas of neutral fermionic atoms at ultra-low temperatures, with the attractive interaction tuned to Feshbach resonance. We calculate, the variation of the chemical potential and the energy per particle as a function of temperature by assuming the system to be an ideal gas obeying the Haldane-Wu fractional exclusion statistics. Our results for the untrapped gas compare favourably with the recently published Monte Carlo calculations of two groups. For a harmonically trapped gas, the results agree with experiment, and also with other published work.
Using many-body results available from diagrammatic and {\it ab initio} Monte Carlo calculations we analyze the phase diagram $μ=(μ_{\uparrow}+μ_{\downarrow})/2$ versus $h=(μ_{\uparrow}-μ_{\downarrow})/2$ of a unitary Fermi gas at zero temperature with population imbalance and unequal masses. We identify different regions where the gas is superfluid, partially polarized or fully polarized and determine the corresponding coexistence conditions. The asymmetry in the phase diagram, caused by the mass imbalance, and its effect on the Chandrasekhar-Clogston limit for the critical polarization are e…
We investigate a two-species Fermi gas with a large mass ratio interacting by an interspecies short-range interaction. Using the Born-Oppenheimer approximation, we determine the interaction energy of two heavy fermions immersed in the Fermi sea of light fermions as a function of the s-wave scattering length. In the BCS limit, we recover the perturbative calculation of the effective interaction between heavy fermions. The p-wave projection of the effective interaction is attractive in the BCS limit while it turns out to be repulsive near the unitarity limit. We find that the p-wave attraction r…
We analyze the dynamical response of a ultracold binary gas mixture in presence of strong boson-fermion couplings. Mapping the problem onto that of the optical response of a metal/semiconductor electronic degrees of freedom to electromagnetic perturbation we calculate the corresponding dynamic linear response susceptibility in the non-perturbative regimes of strong boson-fermion coupling using diagrammatic resummation technique as well as quantum Monte Carlo simulations. We evaluate the Bragg spectral function as well as the optical conductivity and find a pseudogap, which forms in certain par…
We numerically investigated the mixing-demixing transition of the boson-fermion mixture on a 1D lattice at an incommensurate filling with the fermion density being kept below the boson density. The phase diagram we obtained suggested that the decrease of the number of the fermions drove the system into the demixing phase.
We construct a Galilean invariant low-energy effective field theory of boson-fermion mixtures and study bound fermion states on a vortex of boson superfluid. We derive a simple criterion to determine for which values of the fermion angular momentum l there exist an infinite number of bound energy levels. We apply our formalism to two boson-fermion mixed systems: the dilute solution of He3 in He4 superfluid and the cold polarized Fermi gas on the BEC side of the "splitting point". For the He3-He4 mixture, we determine parameters of the effective theory from experimental data as functions of pre…
Boson-fermion pairing is considered in a discrete environment of bosons and fully spin-polarized fermions, coupled via an attractive Bose-Fermi Hubbard Hamiltonian in one dimension. The results of the T-matrix approximation for particles of equal mass and at double half filling are compared with the results of exact diagonalization and with Quantum Monte Carlo results. Satisfactory agreement for most quantities is found. The appearance of a stable, weak-coupling pairing mode is also confirmed.
Mixing-demixing transitions in one-dimensional mixtures of fermions and bosons are numerically investigated. With Monte Carlo simulations, we searched the transitions by changing various parameters such as number densities of each component, fermion-boson interactions, boson-boson interactions, and hopping energies. In most cases we found clear evidences of the mixing-demixing transitions. We also identified the roles of each microscopic parameter in the transitions.
We treat the trapped two-component Fermi system, in which unlike fermions interact through a two-body short-range potential having no bound state but an infinite scattering length. By accurately solving the Schroedinger equation for up to N=6 fermions, we show that no many-body bound states exist other than those bound by the trapping potential, and we demonstrate unique universal properties of the system: Certain excitation frequencies are separated by $2\hbarω$, the wavefunctions agree with analytical predictions and a virial theorem is fulfilled. Further calculations up to N=30 determine th…
We numerically investigated Mott transitions and mixing-demixing transitions in one-dimensional boson-fermion mixtures at a commensurate filling. The mixing-demixing transition occurred in a qualitatively similar manner to the incommensurate filling case. We also found the Mott insulator phase appeared in both the mixing and the demixing states as the fermion-boson interaction or the boson-boson interaction increased. Phase diagrams were obtained in the interaction parameter space.
The ground state phase diagram of fermion mixtures in optical lattices is analyzed as a function of interaction strength, fermion filling factor and tunneling parameters. In addition to standard superfluid, phase-separated or coexisting superfluid/excess-fermion phases found in homogeneous or harmonically trapped systems, fermions in optical lattices have several insulating phases, including a molecular Bose-Mott insulator (BMI), a Fermi-Pauli (band) insulator (FPI), a phase-separated BMI/FPI mixture or a Bose-Fermi checkerboard (BFC). The molecular BMI phase is the fermion mixture counterpart…
We use a time-dependent dynamical hydrodynamic model to study a collapse in a degenerate fermion-fermion mixture (DFFM) of different atoms. Due to a strong Pauli-blocking repulsion among identical spin-polarized fermions at short distances there cannot be a collapse for repulsive interspecies fermion-fermion interaction. However, there can be a collapse for a sufficiently attractive interspecies fermion-fermion interaction in a DFFM of different atoms. Using a variational analysis and numerical solution of the hydrodynamic model we study different aspects of collapse in such a DFFM initiated b…
We use a time-dependent dynamical mean-field-hydrodynamic model to predict and study bright solitons in a degenerate fermion-fermion mixture in a quasi-one-dimensional cigar-shaped geometry using variational and numerical methods. Due to a strong Pauli-blocking repulsion among identical spin-polarized fermions at short distances there cannot be bright solitons for repulsive interspecies fermion-fermion interactions. However, stable bright solitons can be formed for a sufficiently attractive interspecies interaction. We perform a numerical stability analysis of these solitons and also demonstra…
We use a time-dependent dynamical mean-field-hydrodynamic model to study the formation of fermionic bright solitons in a trapped degenerate Fermi gas mixed with a Bose-Einstein condensate in a quasi-one-dimensional cigar-shaped geometry. Due to a strong Pauli-blocking repulsion among spin-polarized fermions at short distances there cannot be bright fermionic solitons in the case of repulsive boson-fermion interactions. However, we demonstrate that stable bright fermionic solitons can be formed for a sufficiently attractive boson-fermion interaction in a boson-fermion mixture. We also consider …
We study fermionic superfluidity in a boson-single-species-fermion cold atom mixture. We argue that apart from the standard p-wave fermion pairing mediated by the phonon field of the boson gas, the system also exhibits s-wave pairing with the anomalous correlator being an odd function of time or frequency. We show that such a superfluid phase can have a much higher transition temperature than the p-wave and may exist for sufficiently strong couplings between fermions and bosons. These conditions for odd-frequency pairing are favorable close to the value of the coupling at which the mixture pha…
We present mean-field calculations of the equilibrium state in a gaseous mixture of bosonic and spin-polarized fermionic atoms with repulsive or attractive interspecies interactions, confined inside a cigar-shaped trap under conditions such that the radial thickness of the two atomic clouds is approaching the magnitude of the s-wave scattering lengths. In this regime the kinetic pressure of the fermionic component is dominant. Full demixing under repulsive boson-fermion interactions can occur only when the number of fermions in the trap is below a threshold, and collapse under attractive inter…
The phase diagrams of low density Fermi-Fermi mixtures with equal or unequal masses and equal or unequal populations are described at zero and finite temperatures in the strong attraction limit. In this limit, the Fermi-Fermi mixture can be described by a weakly interacting Bose-Fermi mixture, where the bosons correspond to Feshbach molecules and the fermions correspond to excess atoms. First, we discuss the three and four fermion scattering processes, and use the exact boson-fermion and boson-boson scattering lengths to generate the phase diagrams in terms of the underlying fermion-fermion sc…
By minimizing the coupled mean-field energy functionals, we investigate the ground-state properties of a rotating atomic boson-fermion mixture in a two-dimensional parabolic trap. At high angular frequencies in the mean-field-lowest-Landau-level regime, quantized vortices enter the bosonic condensate, and a finite number of degenerate fermions form the maximum-density-droplet state. As the boson-fermion coupling constant increases, the maximum density droplet develops into a lower-density state associated with the phase separation, revealing characteristics of a Landau-level structure.
We consider the phase separation of a trapped atomic mixture of fermions with unequal spin populations near a Feshbach resonance. In particular, we determine the density profile of the two spin states and compare with the recent experiments of Partridge et al. (cond-mat/0511752). Overall we find quite good agreement. We identify the remaining discrepancies and pose them as open problems.
We use the Bogoliubov-de Gennes formalism to analyze the ground state phases of harmonically trapped two-species fermion mixtures with unequal masses. In the weakly attracting limit and around unitarity, we find that the superfluid order parameter is spatially modulated around the trap center, and that its global maximum occurs at a finite distance away from the trap center where the mixture is locally unpolarized. As the attraction strength increases towards the molecular limit, the spatial modulations gradually disappear while the Bardeen-Cooper-Schrieffer (BCS) type nonmodulated superfluid …
We employ a time-dependent mean-field-hydrodynamic model to study the generation of bright solitons in a degenerate fermion-fermion mixture in a cigar-shaped geometry using variational and numerical methods. Due to a strong Pauli-blocking repulsion among identical spin-polarized fermions at short distances there cannot be bright solitons for repulsive interspecies interactions. Employing a linear stability analysis we demonstrate the formation of stable solitons due to modulational instability of a constant-amplitude solution of the model equations for a sufficiently attractive interspecies in…
We consider a strongly interacting one-dimensional (1D) Bose-Fermi mixture confined in a harmonic trap. It consists of a Tonks-Girardeau (TG) gas (1D Bose gas with repulsive hard-core interactions) and of a non-interacting Fermi gas (1D spin-aligned Fermi gas), both species interacting through hard-core repulsive interactions. Using a generalized Bose-Fermi mapping, we determine the exact particle density profiles, momentum distributions and behaviour of the mixture under 1D expansion when opening the trap. In real space, bosons and fermions do not display any phase separation: the respective …
We study the density-wave states of quasi-one-dimensional atomic gas mixture of one- and two-component boson and fermion using the mean-field approximation. Owing to the Peierls instability in the quasi-one-dimensional fermion system, the ground state of the system shows the fermion density wave and the periodic Bose-Einstein condensation induced by the boson-fermion interatomic interaction. For the two-component fermions, two density waves appear in these components, and the phase difference between them distinguishes two types of ground states, the in-phase and the out-phase density-waves. I…
We analyze the ground state phases of two-component ($σ\equiv \lbrace \uparrow, \downarrow \rbrace$) population- and mass-balanced ($N_\uparrow = N_\downarrow$ and $m_\uparrow = m_\downarrow$) but trap-imbalanced ($ω_\uparrow \ne ω_\downarrow$) fermion mixtures as a function of interaction strength from the weak attraction Bardeen-Cooper-Schrieffer (BCS) to the strong attraction Bose-Einstein condensation (BEC) limit. In the BCS limit, we find that the unpolarized superfluid (UPS) fermions exist away from the central core of the trapping potentials, and are surrounded by partially polarized no…
We analyze the phase diagram of uniform superfluidity for two-species fermion mixtures from the Bardeen-Cooper-Schrieffer (BCS) to Bose-Einstein condensation (BEC) limit as a function of the scattering parameter and population imbalance. We find at zero temperature that the phase diagram of population imbalance versus scattering parameter is asymmetric for unequal masses, having a larger stability region for uniform superfluidity when the lighter fermions are in excess. In addition, we find topological quantum phase transitions associated with the disappearance or appearance of momentum space …
We study the transition to fermion pair superfluidity in a mixture of interacting bosonic and fermionic atoms. The fermion interaction induced by the bosons and the dynamical screening of the condensate phonons due to fermions are included using the nonperturbative Hamiltonian flow equations. We determine the bosonic spectrum near the transition towards phase separation and find that the superfluid transition temperature may be increased substantially due to phonon damping.
We suggest a time-dependent dynamical mean-field-hydrodynamic model for the collapse of a trapped boson-fermion condensate and perform numerical simulation based on it to understand some aspects of the experiment by Modugno et al. [Science 297, 2240 (2002)] on the collapse of the fermionic condensate in the 40K-87Rb mixture. We show that the mean-field model explains the formation of a stationary boson-fermion condensate at zero temparature with relative sizes compatible with experiment. This model is also found to yield a faithful representation of the collapse dynamics in qualitative agreeme…
We propose a setup with ultracold atomic gases that can be used to make a nonrelativistic superstring in four spacetime dimensions. In particular, we consider for the creation of the superstring a fermionic atomic gas that is trapped in the core of a vortex in a Bose-Einstein condensate. We explain the required tuning of experimental parameters to achieve supersymmetry between the fermionic atoms and the bosonic modes describing the oscillations in the vortex position. Furthermore, we discuss the experimental consequences of supersymmetry.
