We present an ab initio determination of the spin response 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 spin susceptibility and the spin conductivity. We show that both quantities exhibit suppression above the critical temperature of the superfluid-to-normal phase transition due to Cooper pairing. The spin diffusion transport coefficient does not display a minimum in the vicinity of the critical temperature and drops to very low values D(s)≈0.8ħ/m in the superfluid phase. All these spin observables show a smooth and monotonic behavior with temperature when crossing the critical temperature T(c), until the Fermi liquid regime is attained at the temperature T(*), above which the pseudogap regime disappears.
We present an ab initio determination of the spin response 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 spin susceptibility and the spin conductivity. We show that both quantities exhibit suppression above the critical temperature of the superfluid-to-normal phase transition due to Cooper pairing. The spin diffusion transport coefficient does not display a minimum in the vicinity of the critical temperature and drops to very low values D(s)≈0.8ħ/m in the superfluid phase. All these spin observables show a smooth and monotonic behavior with temperature when crossing the critical temperature T(c), until the Fermi liquid regime is attained at the temperature T(*), above which the pseudogap regime disappears.
In the two-component Fermi gas with a contact interaction, a pseudogap regime can exist at temperatures between the superfluid critical temperature T_{c} and a temperature T^{*}>T_{c}. This regime is characterized by pairing correlations without superfluidity. However, in the unitary limit of infinite scattering length, the existence of this regime is still debated. To help address this, we have applied finite-temperature auxiliary-field quantum Monte Carlo (AFMC) methods to study the thermodynamics of the superfluid phase transition and signatures of the pseudogap in the spin-balanced homogeneous unitary Fermi gas. We present results at finite filling factor ν≃0.06 for the condensate fraction, an energy-staggering pairing gap, the spin susceptibility, and the heat capacity, and compare them to experimental data when available. In contrast to previous AFMC simulations, our model space consists of the complete first Brillouin zone of the lattice, and our calculations are performed in the canonical ensemble of fixed particle number. The canonical ensemble AFMC framework enables the calculation of a model-independent gap, providing direct information on pairing correlations without the need for numerical analytic continuation. We use finite-size scaling to estimate T_{c} at the corresponding filling factor. We find that the energy-staggering pairing gap vanishes above T_{c}, showing no pseudogap effects, and that the spin susceptibility shows a substantially reduced signature of a spin gap compared to previously reported AFMC simulations.
The unitary Fermi gas (UFG) is a strongly correlated system of two-species (spin-1/2) fermions with a short-range attractive interaction modeled by a contact interaction and has attracted much interest across different disciplines. The UFG is considered a paradigm for strongly correlated superfluids and has been investigated extensively, with generally good agreement found between theory and experiment. However, the extent of a pseudogap regime above the critical temperature Tc for superfluidity is still debated both theoretically and experimentally. Here we study thermodynamic properties of the UFG across the superfluid phase transition using finite-temperature lattice auxiliary-field quantum Monte Carlo (AFMC) methods in the canonical ensemble of fixed particle numbers. We extrapolate our lattice AFMC results to the continuous time and continuum limits, thus removing the systematic error associated with the finite filling factor of previous AFMC studies. We determine the critical temperature to be Tc=0.16(1)TF. For the largest particle number studied N=114, the energy-staggering pairing gap is suppressed above a pairing scale temperature of T∗≈0.2TF. The spin susceptibility displays moderate suppression above Tc with a spin gap temperature of Ts≈0.2TF. We also calculate a free energy-staggering pairing gap, which shows substantially reduced statistical errors when compared with the energy-staggering gap, allowing for a clear signature of pairing correlations in the finite-size system. All results indicate that the pseudogap regime is narrow, with pseudogap signatures emerging at temperatures below T∗≈0.2TF. The reduced statistical errors of the free energy gap enable an extrapolation at low temperatures, allowing an estimate of the zero-temperature pairing gap ΔE=0.576(24)εF.
We investigate the uniform spin susceptibility ${\ensuremath{\chi}}_{\mathrm{s}}$ in the BCS (Bardeen-Cooper-Schrieffer)-BEC (Bose-Einstein condensation) crossover regime of an ultracold Fermi gas. Including pairing fluctuations within the framework of an extended T-matrix approximation, we show that ${\ensuremath{\chi}}_{\mathrm{s}}$ exhibits nonmonotonic temperature dependence in the normal state. In particular, ${\ensuremath{\chi}}_{\mathrm{s}}$ is suppressed near the superfluid phase transition temperature Tc due to strong pairing fluctuations. To characterize this anomalous behavior, we introduce the spin-gap temperature Ts as the temperature at which ${\ensuremath{\chi}}_{\mathrm{s}}$ takes a maximum value. Determining Ts in the whole BCS-BEC crossover region, we identify the spin-gap regime in the phase diagram of a Fermi gas in terms of the temperature and the strength of a pairing interaction. We also clarify how the spin-gap phenomenon is related to the pseudogap phenomenon appearing in the single-particle density of states. Our results indicate that an ultracold Fermi gas in the BCS-BEC crossover region is a very useful system to examine the pseudogap phenomenon and the spin-gap phenomenon in a unified manner.
In the two-component Fermi gas with contact interactions a pseudogap regime, in which pairing correlations are present without superfluidity, can exist at temperatures between the superfluid critical temperature Tc and a temperature T∗>Tc. However, the existence of a pseudogap in the unitary limit of infinite scattering length is debated. To help address this issue, we have used finite-temperature auxiliary-field quantum Monte Carlo (AFMC) methods to study the thermodynamics of the spin-balanced homogeneous unitary Fermi gas on a lattice. We present results for the thermal energy, heat capacity, condensate fraction, a model-independent pairing gap, and spin susceptibility, and compare them to experimental data when available. Our model space consists of the complete first Brillouin zone of the lattice, and our calculations are performed in the canonical ensemble of fixed particle number. We find that the energy-staggering pairing gap vanishes above Tc and that T∗ at unitarity, as determined from the spin susceptibility, is lower than previously reported in AFMC simulations.
We theoretically investigate the uniform spin susceptibility $\ensuremath{\chi}$ in the superfluid phase of an ultracold Fermi gas in the region of the Bardeen-Cooper-Schrieffer--Bose-Einstein-condensate (BCS-BEC) crossover. In our previous paper [H. Tajima et al., Phys. Rev. A 89, 033617 (2014)], including pairing fluctuations within an extended T-matrix approximation (ETMA), we showed that strong pairing fluctuations cause the so-called spin-gap phenomenon, where $\ensuremath{\chi}$ is anomalously suppressed even in the normal state near the superfluid phase transition temperature Tc. In this paper, we extend this work to the superfluid phase below Tc, to clarify how this many-body phenomenon is affected by the superfluid order. From the comparison of the ETMA $\ensuremath{\chi}$ with the Yosida function describing the spin susceptibility in a weak-coupling BCS superfluid, we identify the region where pairing fluctuations crucially affect this magnetic quantity below Tc in the phase diagram with respect to the strength of a pairing interaction and the temperature. This spin-gap regime is found to be consistent with the previous pseudogap regime determined from the pseudogapped density of states. We also compare our results with a recent experiment on a 6Li Fermi gas. Since the spin susceptibility is sensitive to the formation of spin-singlet preformed pairs, our results would be useful for the study of pseudogap physics in an ultracold Fermi gas on the viewpoint of the spin degrees of freedom.
Superfluidity in the cold atomic two-species Fermi gas system in the unitary limit of infinite scattering length remains incompletely understood. In particular, a pseudogap phase has been proposed to exist above the superfluid critical temperature. Here we apply the auxiliary-field quantum Monte Carlo method to perform ab initio calculations of the temperature dependence of three quantities---the energy-staggering pairing gap, the condensate fraction, and the heat capacity---in a trapped finite-size cold atom system in the unitary limit of infinite scattering length. As the calculations of the energy-staggering pairing gap require the use of the canonical ensemble, we employ an efficient algorithm for the stabilization of particle-number projection that is essential for reaching convergence in the size of the model space. We observe clear signatures of the superfluid phase transition in all three quantities, including a signature of the recently measured $\ensuremath{\lambda}$ peak in the heat capacity. We also find that the energy-staggering gap does not lead the condensate fraction as the temperature decreases.