Dynamical mean-field approximation with explicit pairing is utilized to study the properties of a two-component Fermi gas at unitarity. The problem is approximated by the lattice Hubbard Hamiltonian, and the continuum limit is realized by diluting the lattice. We have found that at zero temperature the predictions of this theory for the energy and the pairing gap agree remarkably well with the results of full numerical Monte-Carlo simulations. Investigating the evolution of the system with temperature we identify the existence of a second order phase transition associated with a jump in the heat capacity and the collapse of the pairing gap.
We study the evolution of the energy gap in a unitary Fermi gas as a function of temperature. To this end we approximate the Fermi gas by the Hubbard lattice Hamiltonian and solve using the dynamical mean-field approximation. We have found that below the critical temperature, Tc, the system is a superfluid and the energy gap is decreasing monotonously. For temperatures above Tc the system is an insulator and the corresponding energy gap is monotonously increasing.
We calculate the oscillation frequencies of trapped Fermi condensate with particular emphasis on the equation of state of the interacting Fermi system. We confirm Stringari's finding that the frequencies are independent of the interaction in the unitary limit, and we extend the theory away from that limit, where the interaction does affect the frequencies of the compressional modes only.
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 in Partridge et al.
We have performed a fully non-perturbative calculation of the thermal properties of a system of spin 1/2 fermions in 3D in the unitary regime. We have determined the critical temperature for the superfluid-normal phase transition. The thermodynamic behavior of this system presents a number of unexpected features, and we conclude that spin 1/2 fermions in the BCS-BEC crossover should be classified as a new type of superfluid.
We propose a phenomenological approach for the equation of state of a unitary Fermi gas. The universal equation of state is parametrised in terms of Fermi-Dirac integrals. This reproduces the experimental data over the accessible range of fugacity and normalised temperature, but cannot describe the superfluid phase transition found in the MIT experiment \cite{ku}. The most sensitive data for compressibility and specific heat at phase transition can, however, befitted by introducing into the grand partition function a pair of complex conjugate zeros lying in the complex fugacity plane slightly …
Thermodynamic properties of an ultracold Fermi gas in a harmonic trap are calculated within a local density approximation, using a conserving many-body formalism for the BCS to BEC crossover problem, which has been developed by Haussmann et al. [Phys. Rev. A 75, 023610 (2007)]. We focus on the unitary regime near a Feshbach resonance and determine the local density and entropy profiles and the global entropy S(E) as a function of the total energy E. Our results are in good agreement with both experimental data and previous analytical and numerical results for the thermodynamics of the unitary …
It is suggested that for a fermi gas at unitarity, the two-body bond plays a special role. We propose an equation of state using an ansatz relating the interaction part of the $l$-body cluster to its two-body counterpart. This allows a parameter-free comparison with the recently measured equation of state by the ENS group. The agreement between the two over a range of fugacity ($z<5$ for a homogeneous gas, and $z<10$ for the trapped gas) leads us to perform the calculations of more sensitive quantities measured recently by the MIT group.
We measure the temperature dependence of the radial breathing mode in an optically trapped, strongly-interacting Fermi gas of $^6$Li, just above the center of a broad Feshbach resonance. The frequency remains close to the unitary hydrodynamic value, while the damping rate reveals transitions at two well-separated temperatures, consistent with the existence of atom pairs above a superfluid transition.
We present theoretical predictions for the equation of state of a harmonically-trapped Fermi gas in the unitary limit. Our calculations rest on a study of the equation of state of a uniform gas using three distinct perturbation schemes, compared to Monte-Carlo results. We show that in experiments the temperature can be usefully calibrated by making use of the entropy, which is invariant during an adiabatic conversion into the weakly-interacting limit of molecular BEC. We predict the entropy dependence of the equation of state.
Although recent theoretical and experimental progress have considerably clarified pairing mechanisms in spin 1/2 fermionic superfluid with equally populated internal states, many open questions remain when the two spin populations are mismatched. We show here that, taking advantage of the universal behavior characterizing the regime of infinite scattering length, the macroscopic properties of these systems can be simply and quantitatively understood in the regime of strong interactions.
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.
We have studied, in a fully non-perturbative calculation, a dilute system of spin 1/2 interacting fermions, characterized by an infinite scattering length at finite temperatures. Various thermodynamic properties and the condensate fraction were calculated and we have also determined the critical temperature for the superfluid-normal phase transition in this regime. The thermodynamic behavior appears as a rather surprising and unexpected melange of fermionic and bosonic features. The thermal response of a spin 1/2 fermion at the BCS-BEC crossover should be classified as that of a new type of su…
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 $A(p,ω)$ using the methods of maximum entropy and singular value decomposition. From $A(p,ω)$ 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 $Δ$. Below the critical temperature $T_c=0.15\varepsilon_F$ the results for $m^*$, $U$ and $Δ$ can be accurately reproduced using an independent quasiparticle model. We fin…
We present lattice results for the ground state energy of a spin-1/2 fermion system in the unitary limit, where the effective range of the interaction is zero and the scattering length is infinite. We compute the ground state energy for a system of 6, 10, 14, 18, and 22 particles, with equal numbers of up and down spins in a periodic cube. We estimate that in the limit of large number of particles, the ground state energy is 0.25(3) times the ground state energy of the free Fermi system.
We calculate the damping of the Bogoliubov-Anderson mode in a one-dimensional two-component attractive Fermi gas for arbitrary coupling strength within a quantum hydrodynamic approach. Using the Bethe-Ansatz solution of the 1D BCS-BEC crossover problem, we derive analytic results for the viscosity covering the full range from a Luther-Emery liquid of weakly bound pairs to a Lieb-Liniger gas of strongly bound bosonic dimers. At the unitarity point, the system is a Tonks-Girardeau gas with a universal constant $α_ζ=0.38$ in the viscosity $ζ=α_ζ\hbar n$ for T=0. For the trapped case, we calculate…
We calculate the momentum distribution n(k) of the Unitary Fermi Gas 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/k^4, 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 \simeq 0.4. Our calculations are performed on lattices of spatial extent up to N_x = 14 with a particle num…
The density of states of a quantum system can be calculated from its definition but, in some cases, this approach is quite cumbersome. Alternatively, the density of states can be deduced from the microcanonical entropy or from the canonical partition function. After discussing the relationship among these procedures, we suggest a simple numerical method, which is equivalent in the thermodynamic limit to perform a Legendre transformation, to obtain the density of states from the Helmholtz free energy. We apply this method to determine the many-body density of states of the unitary Fermi gas, a …
We study the thermal evolution of a highly spin-imbalanced, homogeneous Fermi gas with unitarity limited interactions, from a Fermi liquid of polarons at low temperatures to a classical Boltzmann gas at high temperatures. Radio-frequency spectroscopy gives access to the energy, lifetime, and short-range correlations of Fermi polarons at low temperatures $T$. In this regime, we observe a characteristic $T^2$ dependence of the spectral width, corresponding to the quasiparticle decay rate expected for a Fermi liquid. At high $T$, the spectral width decreases again towards the scattering rate of t…
A unitary Fermi gas has a surprisingly rich spectrum of large amplitude modes of the pairing field alone, which defies a description within a formalism involving only a reduced set of degrees of freedom, such as quantum hydrodynamics or a Landau-Ginzburg-like description. These modes are very slow, with oscillation frequencies well below the pairing gap, which makes their damping through quasiparticle excitations quite ineffective. In atomic traps these modes couple naturally with the density oscillations, and the corresponding oscillations of the atomic cloud are an example of a new type of c…
We investigate the superfluid transition of the Unitary Fermi Gas by means of the Functional Renormalization Group, aiming at quantitative precision. We extract $T_{\rm c}/μ=0.38(2)$ and $Δ/μ=1.04(15)$ for the critical temperature and the superfluid gap at zero temperature, respectively, within a systematic improvement of the truncation for the effective average action. The key new ingredient in comparison to previous approaches consists in the use of regulators which cut off both frequencies and momenta. We incorporate renormalization effects on both the bosonic and the fermionic propagator, …
The dimensionless universal coefficient $ξ$ defines the ratio of the unitary fermions energy density to that for the ideal non-interacting ones in the non-relativistic limit with T=0. The classical Thomson Problem is taken as a nonperturbative quantum many-body arm to address the ground state energy including the low energy nonlinear quantum fluctuation/correlation effects. With the relativistic Dirac continuum field theory formalism, the concise expression for the energy density functional of the strongly interacting limit fermions at both finite temperature and density is obtained. Analytica…
We study the roles of the dynamical high order perturbation and statistically non-linear infrared fluctuation/correlation in the virial equation of state for the Fermi gas in the unitary limit. Incorporating the quantum level crossing rearrangement effects, the spontaneously generated entropy departing from the mean-field theory formalism leads to concise thermodynamical expressions. The dimensionless virial coefficients with complex non-local correlations are calculated up to the fourth order for the first time. The virial coefficients of unitary Fermi gas are found to be proportional to thos…
