Spin 1/2 fermions in the unitary regime: a superfluid of a new type

Thermodynamics of spin-1/2 fermions on coarse temporal lattices using automated algebra

Recent advances in automated algebra for dilute Fermi gases in the virial expansion, where coarse temporal lattices were found advantageous, motivate the study of more general computational schemes that could be applied to arbitrary densities, beyond the dilute limit where the virial expansion is physically reasonable. We propose here such an approach by developing what we call the Quantum Thermodynamics Computational Engine (QTCE). In QTCE, the imaginary-time direction is discretized and the interaction is accounted for via a quantum cumulant expansion, where the coefficients are expressed in terms of non-interacting expectation values. The aim of QTCE is to enable the systematic resolution of interaction effects at fixed temporal discretization, as in lattice Monte Carlo calculations, but here in an algebraic rather than numerical fashion. Using this approach, in combination with numerical integration techniques (both known and alternative ones proposed here), we explore the thermodynamics of spin-1/2 fermions across spatial dimensions, focusing on the unitary limit. We find that, remarkably, extremely coarse temporal lattices, when suitably renormalized using known results from the virial expansion, yield stable partial sums for QTCE's cumulant expansion that are qualitatively and quantitatively correct in wide regions (when compared with known experimental results). This article is part of the theme issue 'The liminal position of Nuclear Physics: from hadrons to neutron stars'.

Perturbative Quantum Monte Carlo Method for Nuclear Physics

While first order perturbation theory is routinely used in quantum Monte Carlo (QMC) calculations, higher-order terms present significant numerical challenges. We present a new approach for computing perturbative corrections in projection QMC calculations. We demonstrate the method by computing nuclear ground state energies up to second order for a realistic chiral interaction. We calculate the binding energies of several light nuclei up to ^{16}O by expanding the Hamiltonian around the Wigner SU(4) limit and find good agreement with data. In contrast to the natural ordering of the perturbative series, we find remarkably large second-order energy corrections. This occurs because the perturbing interactions break the symmetries of the unperturbed Hamiltonian. Our method is free from the sign problem and can be applied to QMC calculations for many-body systems in nuclear physics, condensed matter physics, ultracold atoms, and quantum chemistry.

Ab Initio Nuclear Thermodynamics

We propose a new Monte Carlo method called the pinhole trace algorithm for ab initio calculations of the thermodynamics of nuclear systems. For typical simulations of interest, the computational speedup relative to conventional grand-canonical ensemble calculations can be as large as a factor of one thousand. Using a leading-order effective interaction that reproduces the properties of many atomic nuclei and neutron matter to a few percent accuracy, we determine the location of the critical point and the liquid-vapor coexistence line for symmetric nuclear matter with equal numbers of protons and neutrons. We also present the first ab initio study of the density and temperature dependence of nuclear clustering.

Contact in the Unitary Fermi Gas across the Superfluid Phase Transition

A quantity known as the contact is a fundamental thermodynamic property of quantum many-body systems with short-range interactions. Determination of the temperature dependence of the contact for the unitary Fermi gas of infinite scattering length has been a major challenge, with different calculations yielding qualitatively different results. Here we use finite-temperature auxiliary-field quantum Monte Carlo (AFMC) methods on the lattice within the canonical ensemble to calculate the temperature dependence of the contact for the homogeneous spin-balanced unitary Fermi gas. We extrapolate to the continuum limit for 40, 66, and 114 particles, eliminating systematic errors due to finite-range effects. We observe a dramatic decrease in the contact as the superfluid critical temperature is approached from below, followed by a gradual weak decrease as the temperature increases in the normal phase. Our theoretical results are in excellent agreement with the most recent precision ultracold atomic gas experiments. We also present results for the energy as a function of temperature in the continuum limit.

Finite-Temperature Equation of State of Polarized Fermions at Unitarity

We study in a nonperturbative fashion the thermodynamics of a unitary Fermi gas over a wide range of temperatures and spin polarizations. To this end, we use the complex Langevin method, a first principles approach for strongly coupled systems. Specifically, we show results for the density equation of state, the magnetization, and the magnetic susceptibility. At zero polarization, our results agree well with state-of-the-art results for the density equation of state and with experimental data. At finite polarization and low fugacity, our results are in excellent agreement with the third-order virial expansion. In the fully quantum mechanical regime close to the balanced limit, the critical temperature for superfluidity appears to depend only weakly on the spin polarization.

Equation of state of non-relativistic matter from automated perturbation theory and complex Langevin

We calculate the pressure and density of polarized non-relativistic systems of two-component fermions coupled via a contact interaction at finite temperature. For the unpolarized one-dimensional system with an attractive interaction, we perform a thirdorder lattice perturbation theory calculation and assess its convergence by comparing with hybrid Monte Carlo. In that regime, we also demonstrate agreement with real Langevin. For the repulsive unpolarized one-dimensional system, where there is a so-called complex phase problem, we present lattice perturbation theory as well as complex Langevin calculations. For our studies, we employ a Hubbard-Stratonovich transformation to decouple the interaction and automate the application of Wick’s theorem for perturbative calculations, which generates the diagrammatic expansion at any order. We find excellent agreement between the results from our perturbative calculations and stochastic studies in the weakly interacting regime. In addition, we show predictions for the strong coupling regime as well as for the polarized one-dimensional system. Finally, we show a first estimate for the equation of state in three dimensions where we focus on the polarized unitary Fermi gas.

Review of pseudogaps in strongly interacting Fermi gases

A central challenge in modern condensed matter physics is developing the tools for understanding nontrivial yet unordered states of matter. One important idea to emerge in this context is that of a 'pseudogap': the fact that under appropriate circumstances the normal state displays a suppression of the single particle spectral density near the Fermi level, reminiscent of the gaps seen in ordered states of matter. While these concepts arose in a solid state context, they are now being explored in cold gases. This article reviews the current experimental and theoretical understanding of the normal state of strongly interacting Fermi gases, with particular focus on the phenomonology which is traditionally associated with the pseudogap.

Effect of the particle-hole channel on BCS-Bose-Einstein condensation crossover in atomic Fermi gases

BCS-Bose-Einstein condensation (BEC) crossover is effected by increasing pairing strength between fermions from weak to strong in the particle-particle channel, and has attracted a lot of attention since the experimental realization of quantum degenerate atomic Fermi gases. Here we study the effect of the (often dropped) particle-hole channel on the zero T gap Δ(0), superfluid transition temperature Tc, the pseudogap at Tc, and the mean-field ratio 2Δ(0)/, from BCS through BEC regimes, using a pairing fluctuation theory which includes self-consistently the contributions of finite-momentum pairs and features a pseudogap in single particle excitation spectrum. Summing over the infinite particle-hole ladder diagrams, we find a complex dynamical structure for the particle-hole susceptibility χph, and conclude that neglecting the self-energy feedback causes a serious over-estimate of χph. While our result in the BCS limit agrees with Gor'kov et al., the particle-hole channel effect becomes more complex and pronounced in the crossover regime, where χph is reduced by both a smaller Fermi surface and a big (pseudo)gap. Deep in the BEC regime, the particle-hole channel contributions drop to zero. We predict a density dependence of the magnetic field at the Feshbach resonance, which can be used to quantify χph and test different theories.

Transition and Damping of Collective Modes in a Trapped Fermi Gas between BCS and Unitary Limits near the Phase Transition

We investigate the transition and damping of low-energy collective modes in a trapped unitary Fermi gas by solving the Boltzmann-Vlasov kinetic equation in a scaled form, which is combined with both the T-matrix fluctuation theory in normal phase and the mean-field theory in order phase. In order to connect the microscopic and kinetic descriptions of many-body Feshbach scattering, we adopt a phenomenological two-fluid physical approach, and derive the coupling constants in the order phase. By solving the Boltzmann-Vlasov steady-state equation in a variational form, we calculate two viscous relaxation rates with the collision probabilities of fermion's scattering including fermions in the normal fluid and fermion pairs in the superfluid. Additionally, by considering the pairing and depairing of fermions, we get results of the frequency and damping of collective modes versus temperature and s-wave scattering length. Our theoretical results are in a remarkable agreement with the experimental data, particularly for the sharp transition between collisionless and hydrodynamic behaviour and strong damping between BCS and unitary limits near the phase transition. The sharp transition originates from the maximum of viscous relaxation rate caused by fermion-fermion pair collision at the phase transition point when the fermion depair, while the strong damping due to the fast varying of the frequency of collective modes from BCS limit to unitary limit.

Pressure, compressibility, and contact of the two-dimensional attractive fermi gas

Using ab initio lattice methods, we calculate the finite temperature thermodynamics of homogeneous two-dimensional spin-1/2 fermions with attractive short-range interactions. We present results for the density, pressure, compressibility, and quantum anomaly (i.e., Tan's contact) for a wide range of temperatures (mostly above the superfluid phase, including the pseudogap regime) and coupling strengths, focusing on the unpolarized case. Within our statistical and systematic uncertainties, our prediction for the density equation of state differs quantitatively from the prediction by Luttinger-Ward theory in the strongly coupled region of parameter space, but otherwise agrees well with it. We also compare our calculations with the second- and third-order virial expansion, with which they are in excellent agreement in the low-fugacity regime.

Zero-temperature equation of state of mass-imbalanced resonant Fermi gases

We calculate the zero-temperature equation of state of mass-imbalanced resonant Fermi gases in an ab initio fashion, by implementing the recent proposal of imaginary-valued mass difference to bypass the sign problem in lattice Monte Carlo calculations. The fully nonperturbative results thus obtained are analytically continued to real mass-imbalance to yield the physical equation of state, providing predictions for upcoming experiments with mass-imbalanced atomic Fermi gases. In addition, we present an exact relation for the rate of change of the equation of state at small mass imbalances, showing that it is fully determined by the energy of the mass-balanced system.

Imaginary polarization as a way to surmount the sign problem in ab initio calculations of spin-imbalanced Fermi gases

From ultracold atoms to quantum chromodynamics, reliable ab initio studies of strongly interacting fermions require numerical methods, typically in some form of quantum Monte Carlo calculation. Unfortunately, (non)relativistic systems at finite density (spin polarization) generally have a sign problem, such that those ab initio calculations are impractical. It is well-known, however, that in the relativistic case imaginary chemical potentials solve this problem, assuming the data can be analytically continued to the real axis. Is this feasible for nonrelativistic systems? Are the interesting features of the phase diagram accessible in this manner? By introducing complex chemical potentials, for real total particle number and imaginary polarization, the sign problem is avoided in the nonrelativistic case. To give a first answer to the above questions, we perform a mean-field study of the finite-temperature phase diagram of spin-1/2 fermions with imaginary polarization.

Complexity of quantum states in the two-dimensional pairing model

It is known that many-fermion systems, such as complex atoms and nuclei, reveal (at some level of excitation energy) local signatures of quantum chaos similar to the predictions of random matrix theory. Here, we study the gradual development of such signatures in a model system of up to 16 fermions interacting through short-range pairing-type forces in a two-dimensional harmonic trap. We proceed from the simplest characteristics of the level spacing distribution to the complexity of eigenstates, strength, and correlation functions. For increasing pairing strength, at first, chaotic signatures gradually appear. However, when the pairing force dominates the Hamiltonian, we see a regression towards regularity. We introduce a "phase correlator" that allows us to distinguish the complexity of a quantum state that originates from its collective nature, from the complexity originating from quantum chaos.

Shear viscosity of a unitary Fermi gas

We present an ab initio determination of the shear viscosity η of the unitary Fermi gas, based on finite temperature quantum Monte Carlo calculations and the Kubo linear-response formalism. We determine the temperature dependence of the shear viscosity-to-entropy density ratio η/s. The minimum of η/s appears to be located above the critical temperature for the superfluid-to-normal phase transition with the most probable value being (η/s)min≈0.2ℏ/k(B), which is close the Kovtun-Son-Starinets universal value ℏ/(4πk(B)).

Few-body physics with ultracold atomic and molecular systems in traps

Few-body physics has played a prominent role in atomic, molecular and nuclear physics since the early days of quantum mechanics. It is now possible-thanks to tremendous progress in cooling, trapping and manipulating ultracold samples-to experimentally study few-body phenomena in trapped atomic and molecular systems with unprecedented control. This review summarizes recent studies of few-body phenomena in trapped atomic and molecular gases, with an emphasis on small trapped systems. We start by introducing the free-space scattering properties and then investigate what happens when two particles, bosons or fermions, are placed in an external confinement. Next, various three-body systems are treated analytically in limiting cases. Our current understanding of larger two-component Fermi systems and Bose systems is reviewed, and connections with the corresponding bulk systems are established. Lastly, future prospects and challenges are discussed. Throughout this review, commonalities with other systems such as nuclei or quantum dots are highlighted.

Properties of the nuclear medium

We review our knowledge on the properties of the nuclear medium that have been studied, over many years, on the basis of many-body theory, laboratory experiments and astrophysical observations. Throughout the presentation particular emphasis is placed on the possible relationship and links between the nuclear medium and the structure of nuclei, including the limitations of such an approach. First we consider the realm of phenomenological laboratory data and astrophysical observations and the hints they can give on the characteristics that the nuclear medium should possess. The analysis is based on phenomenological models, that however have a strong basis on physical intuition and an impressive success. More microscopic models are also considered, and it is shown that they are able to give invaluable information on the nuclear medium, in particular on its equation of state. The interplay between laboratory experiments and astrophysical observations is particularly stressed, and it is shown how their complementarity enormously enriches our insights into the structure of the nuclear medium. We then introduce the nucleon-nucleon interaction and the microscopic many-body theory of nuclear matter, with a critical discussion about the different approaches and their results. The Landau-Fermi liquid theory is introduced and briefly discussed, and it is shown how fruitful it can be in discussing the macroscopic and low-energy properties of the nuclear medium. As an illustrative example, we discuss neutron matter at very low density, and it is shown how it can be treated within the many-body theory. The general bulk properties of the nuclear medium are reviewed to indicate at which stage of our knowledge we stand, taking into account the most recent developments both in theory and experiments. A section is dedicated to the pairing problem. The connection with nuclear structure is then discussed, on the basis of the energy density functional method. The possibility of linking the physics of exotic nuclei and the astrophysics of neutron stars is particularly stressed. Finally, we discuss the thermal properties of the nuclear medium, in particular the liquid-gas phase transition and its connection with the phenomenology on heavy ion reactions and the cooling evolution of neutron stars. The presentation has been taken for non-specialists and possibly for non-nuclear physicists.

Onset of a pseudogap regime in ultracold Fermi gases

We show, using an ab initio approach based on Quantum Monte Carlo technique, that the pseudogap regime emerges in ultracold Fermi gases close to the unitary point. We locate the onset of this regime at a value of the interaction strength corresponding to (k(F)a)(-1)≈-0.05 (a-scattering length). We determine the evolution of the gap as a function of temperature and interaction strength in the Fermi gas around the unitary limit and show that our results exhibit a remarkable agreement with the recent wave-vector resolved radio frequency spectroscopy data. Our results indicate that a finite temperature structure of the Fermi gas around unitarity is more complicated and involves the presence of the phase with preformed Cooper pairs, which, however, do not contribute to the long range order.

Functional renormalization for the Bardeen-Cooper-Schrieffer to Bose-Einstein condensation crossover

We review the functional renormalization group (RG) approach to the Bardeen-Cooper-Schrieffer to Bose-Einstein condensation (BCS-BEC) crossover for an ultracold gas of fermionic atoms. Formulated in terms of a scale-dependent effective action, the functional RG interpolates continuously between the atomic or molecular microphysics and the macroscopic physics on large length scales. We concentrate on the discussion of the phase diagram as a function of the scattering length and the temperature, which is a paradigm example for the non-perturbative power of the functional RG. A systematic derivative expansion provides for both a description of the many-body physics and its expected universal features as well as an accurate account of the few-body physics and the associated BEC and BCS limits.

Momentum distribution and contact of the unitary Fermi gas

We calculate the momentum distribution n(k) of the unitary Fermi gas by using quantum Monte Carlo calculations at finite temperature T/ϵ(F) as well as in the ground state. At large momenta k/k(F), we find that n(k) falls off as C/k⁴, in agreement with the Tan relations. From the asymptotics of n(k), we determine the contact C as a function of T/ϵ(F) and present a comparison with theory. At low T/ϵ(F), we find that C increases with temperature, and we tentatively identify a maximum around T/ϵ(F) ≃ 0.4. Our calculations are performed on lattices of spatial extent up to N(x) = 14 with a particle number per unit volume of ≃ 0.03-0.07.

Evolution of the normal state of a strongly interacting Fermi gas from a pseudogap phase to a molecular Bose gas

Wave-vector resolved radio frequency spectroscopy data for an ultracold trapped Fermi gas are reported for several couplings at T(c), and extensively analyzed in terms of a pairing-fluctuation theory. We map the evolution of a strongly interacting Fermi gas from the pseudogap phase into a fully gapped molecular Bose gas as a function of the interaction strength, which is marked by a rapid disappearance of a remnant Fermi surface in the single-particle dispersion. We also show that our theory of a pseudogap phase is consistent with a recent experimental observation as well as with quantum Monte Carlo data of thermodynamic quantities of a unitary Fermi gas above T(c).

First and second sound in cylindrically trapped gases

We investigate the propagation of density and temperature waves in a cylindrically trapped gas with radial harmonic confinement. Starting from two-fluid hydrodynamic theory we derive effective 1D equations for the chemical potential and the temperature which explicitly account for the effects of viscosity and thermal conductivity. Differently from quantum fluids confined by rigid walls, the harmonic confinement allows for the propagation of both first and second sound in the long wavelength limit. We provide quantitative predictions for the two sound velocities of a superfluid Fermi gas at unitarity. For shorter wavelengths we discover a new surprising class of excitations continuously spread over a finite interval of frequencies. This results in a nondissipative damping in the response function which is analytically calculated in the limiting case of a classical ideal gas.

Collective coordinate description of anisotropically trapped degenerate Fermi gases

The solution of the many-body Schrödinger equation using an adiabatic treatment of the hyperradius is generalized to treat two components of a hyperspherical vector adiabatically. This treatment has advantages in certain physical situations, such as the description of a degenerate Fermi gas or Bose-Einstein condensate in an anisotropic trapping potential. A first application to the zero-temperature anisotropic Fermi gas is compared with predictions of the Hartree-Fock method.

Finite-temperature pairing gap of a unitary fermi gas by quantum monte carlo calculations

We calculate the one-body temperature Green's (Matsubara) function of the unitary Fermi gas via quantum Monte Carlo, and extract the spectral weight function A(p,omega) using the methods of maximum entropy and singular value decomposition. From A(p,omega) we determine the quasiparticle spectrum, which can be accurately parametrized by three functions of temperature: an effective mass m{*}, a mean-field potential U, and a gap Delta. Below the critical temperature T{c}=0.15 epsilon{F} the results for m{*}, U, and Delta can be accurately reproduced using an independent quasiparticle model. We find evidence of a pseudogap in the fermionic excitation spectrum for temperatures up to T{*} approximately 0.20 epsilon{F}> T{c}.

Virial expansion for a strongly correlated Fermi gas

Using a high temperature virial expansion, we present a controllable study of the thermodynamics of strongly correlated Fermi gases near the BEC-BCS crossover region. We propose a practical way to determine the expansion coefficients for both harmonically trapped and homogeneous cases, and calculate the third order coefficient b{3}(T) at finite temperatures T. At resonance, a T-independent coefficient b{3,infinity};{hom} approximately -0.290 952 95 is determined in free space. These results are compared with a recent thermodynamic measurement of 6Li atoms, at temperatures below the degeneracy temperature, and with Monte Carlo simulations.

Superfluidity in a gas of strongly interacting fermions

After an introduction into 100 years of research on superfluidity and the concept of the BCS-BEC crossover, we describe recent experimental studies of a spin-polarized Fermi gas with strong interactions. Tomographically resolving the spatial structure of an inhomogeneous trapped sample, we have mapped out the superfluid phases in the parameter space of temperature, spin polarization, and interaction strength. Phase separation between the superfluid and the normal component occurs at low temperatures, showing spatial discontinuities in the spin polarization. The critical polarization of the normal gas increases with stronger coupling. Beyond a critical interaction strength all minority atoms pair with majority atoms, and the system can be effectively described as a boson-fermion mixture. Pairing correlations have been studied by rf spectroscopy, determining the fermion pair size and the pairing gap energy in a resonantly interacting superfluid.

Cold fermionic atoms in two-dimensional traps: pairing versus Hund's rule

The microscopic properties of few interacting cold fermionic atoms confined in a two-dimensional (2D) harmonic trap are studied by numerical diagonalization. For repulsive interactions, a strong shell structure dominates, with Hund's rule acting at its extreme for the midshell configurations. In the attractive case, odd-even oscillations due to pairing occur simultaneously with deformations in the internal structure of the ground states, as seen from pair correlation functions.

Critical temperature curve in BEC-BCS crossover

The strongly correlated regime of the crossover from Bardeen-Cooper-Schrieffer pairing to Bose-Einstein condensation can be realized by diluting a system of two-component fermions with a short-range attractive interaction. We investigate this system via a novel continuous-space-time diagrammatic determinant Monte Carlo method and determine the universal curve Tc/epsilonF for the transition temperature between the normal and the superfluid states as a function of the scattering length with the maximum on the Bose-Einstein condensation side. At unitarity, we confirm that Tc/epsilonF=0.152(7).

New effective interaction for the trapped fermi gas

We apply the configuration-interaction method to calculate the spectra of two-component Fermi systems in a harmonic trap, studying the convergence of energies at the unitary interaction limit. We find that for a fixed regularization of the two-body interaction the convergence is exponential or better in the truncation parameter of the many-body space. However, the conventional regularization is found to have poor convergence in the regularization parameter, with an error that scales as a low negative power of this parameter. We propose a new regularization of the two-body interaction that produces exponential convergence for systems of three and four particles. We estimate the ground-state energy of the four-particle system to be (5.045 +/- 0.003) variant Planck's constant over 2 pi omega.

Thermodynamics of a trapped unitary Fermi gas

We present the first model-independent comparison of recent measurements of the entropy and of the critical temperature of a unitary Fermi gas, performed by Luo et al., with the most complete results currently available from finite temperature Monte Carlo calculations. The measurement of the critical temperature in a cold fermionic atomic cloud is consistent with a value T(c) = 0.23(2)epsilon(F) in the bulk, as predicted by the present authors in their Monte Carlo calculations.

First-order transition from superfluid to bose-metal state in systems with resonant pairing

Systems showing resonant superfluidity, driven by an exchange coupling of strength g between uncorrelated pairs of itinerant fermions and tightly bound ones, undergo a first-order phase transition as g increases beyond some critical value gc. The superfluid phase for g<or=gc is characterized by a gap in the fermionic single-particle spectrum and an acoustic sound-wave-like collective mode of the bosonic resonating fermion pairs inside this gap. For g>gc this state gives way to a phase-uncorrelated bosonic liquid with a q2 spectrum.

Universality in a 2-component fermi system at finite temperature

Thermodynamic properties of a Fermi system close to the unitarity limit, where the 2-body scattering length a approaches +/-infinity, are studied in the high temperature Boltzmann regime. For dilute systems the virial expansion coefficients in the Boltzmann regime are expected, from general arguments, to be universal. A model independent finite temperature T calculation of the third virial coefficient b3(T) is presented. At the unitarity limit, b3infinity approximately 1.11 is a universal number. The energy density up to the third virial expansion is derived. These calculations are of interest in dilute neutron matter and could be tested in current atomic experiments on dilute Fermi gases near the Feshbach resonance.

Measurement of the entropy and critical temperature of a strongly interacting Fermi gas

We report a model-independent measurement of the entropy, energy, and critical temperature of a degenerate, strongly interacting Fermi gas of atoms. The total energy is determined from the mean square cloud size in the strongly interacting regime, where the gas exhibits universal behavior. The entropy is measured by sweeping a bias magnetic field to adiabatically tune the gas from the strongly interacting regime to a weakly interacting regime, where the entropy is known from the cloud size after the sweep. The dependence of the entropy on the total energy quantitatively tests predictions of the finite-temperature thermodynamics.

Superfluid expansion of a rotating Fermi gas

We study the expansion of a rotating, superfluid Fermi gas. The presence and absence of vortices in the rotating gas are used to distinguish the superfluid and normal parts of the expanding cloud. We find that the superfluid pairs survive during the expansion until the density decreases below a critical value. Our observation of superfluid flow in the expanding gas at 1/kFa=0 extends the range where fermionic superfluidity has been studied to densities of 1.2x10(11) cm(-3), about an order of magnitude lower than any previous study.

Potential energy of a 40K Fermi gas in the BCS-BEC crossover

We present a measurement of the potential energy of an ultracold trapped gas of 40K atoms in the BCS-BEC crossover and investigate the temperature dependence of this energy at a wide Feshbach resonance, where the gas is in the unitarity limit. In particular, we study the ratio of the potential energy in the region of the unitarity limit to that of a noninteracting gas, and in the T=0 limit we extract the universal many-body parameter beta. We find beta=-0.54_{-0.12};{+0.05}; this value is consistent with previous measurements using 6Li atoms and also with recent theory and Monte Carlo calculations. This result demonstrates the universality of ultracold Fermi gases in the strongly interacting regime.

Generic phase diagram of Fermion superfluids with population imbalance

It is shown by microscopic calculations for trapped imbalanced Fermi superfluids that the gap function always has sign changes, i.e., the Fulde-Ferrell-Larkin-Ovchinnikov (FFLO)-like state, up to a critical imbalance P(c), beyond which normal state becomes stable, at temperature T=0. A temperature-versus-pressure phase diagram is constructed, where the BCS state without sign change is stable only at T not equal to 0. We reproduce the observed bimodality in the density profile to identify its origin and evaluate P(c) as functions of T and the coupling strength. These dependencies match with the recent experiments.

Critical temperature and thermodynamics of attractive fermions at unitarity

The unitarity regime of the BCS-BEC crossover can be realized by diluting a system of two-component lattice fermions with an on-site attractive interaction. We perform a systematic-error-free finite-temperature simulation of this system by diagrammatic determinant Monte Carlo method. The critical temperature in units of Fermi energy is found to be T(C)/epsilonF=0.152(7). We also report the behavior of the thermodynamic functions, and discuss the issues of thermometry of ultracold Fermi gases.

Density profile of a trapped strongly interacting Fermi gas with unbalanced spin populations

We present a theoretical study of the density profile of a trapped strongly interacting Fermi gas with unbalanced spin populations. Making the assumption of the existence of a first order phase transition between an unpolarized superfluid phase and a fully polarized normal phase, we show good agreement with a recent experiment presented by Partridge et al.