Cooper pairing above the critical temperature in a unitary Fermi gas

Pseudogap Effects in the Strongly Correlated Regime of the Two-Dimensional Fermi Gas

The two-species Fermi gas with attractive short-range interactions in two spatial dimensions provides a paradigmatic system for the understanding of strongly correlated Fermi superfluids in two dimensions. It is known to exhibit a BEC to BCS crossover as a function of ln(k_{F}a), where a is the scattering length, and to undergo a Berezinskii-Kosterlitz-Thouless superfluid transition below a critical temperature T_{c}. However, the extent of a pseudogap regime in the strongly correlated regime of ln(k_{F}a)∼1, in which pairing correlations persist above T_{c}, remains largely unexplored with controlled theoretical methods. Here, we use finite-temperature auxiliary-field quantum Monte Carlo methods on discrete lattices in the canonical ensemble formalism to calculate thermodynamical observables in the strongly correlated regime. We extrapolate to continuous time and the continuum limit to eliminate systematic errors and present results for particle numbers ranging from N=42 to N=162. We estimate T_{c} by a finite-size scaling analysis, and observe clear pseudogap signatures above T_{c} and below a temperature T^{*} in both the spin susceptibility and free-energy gap. We also present results for the contact, a fundamental thermodynamic property of quantum many-body systems with short-range interactions.

Spin Susceptibility above the Superfluid Onset in Ultracold Fermi Gases

Ultracold atomic Fermi gases can be tuned to interact strongly, which produces a display of spectroscopic signatures above the superfluid transition reminiscent of the pseudogap in cuprates. However, the extent of the analogy can be questioned since many thermodynamic quantities in the low temperature spin-imbalanced normal state can be described successfully using Fermi liquid theory. Here we present spin susceptibility measurements across the interaction strength-temperature phase diagram using a novel radio frequency technique with ultracold ^{6}Li gases. For all significant interaction strengths and at all temperatures we find the spin susceptibility is reduced compared to the equivalent value for a noninteracting Fermi gas. At unitarity, we can use the local density approximation to extract the integrated spin susceptibility for the uniform gas as a function of temperature, which at high temperatures is generally less than theoretically predicted. At low temperatures, our data lie within the range of theoretical predictions, although we can also describe the entire curve using a very simple one-parameter mean field model with monotonically increasing spin susceptibility.

Emergence of a Pseudogap in the BCS-BEC Crossover

Strongly correlated Fermi systems with pairing interactions become superfluid below a critical temperature T_{c}. The extent to which such pairing correlations alter the behavior of the liquid at temperatures T>T_{c} is a subtle issue that remains an area of debate, in particular regarding the appearance of the so-called pseudogap in the BCS-BEC crossover of unpolarized spin-1/2 nonrelativistic matter. To shed light on this, we extract several quantities of crucial importance at and around the unitary limit, namely, the odd-even staggering of the total energy, the spin susceptibility, the pairing correlation function, the condensate fraction, and the critical temperature T_{c}, using a nonperturbative, constrained-ensemble quantum Monte Carlo algorithm.

Pairing Correlations across the Superfluid Phase Transition in the Unitary Fermi Gas

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.

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.

Suppressed Solitonic Cascade in Spin-Imbalanced Superfluid Fermi Gas

Cold atoms experiments offer invaluable information on superfluid dynamics, including decay cascades of topological defects. While the cascade properties are well established for Bose systems, our understanding of their behavior in Fermi counterparts is very limited, in particular in spin-imbalanced systems, where superfluid (paired) and normal (unpaired) particles naturally coexist giving rise to complex spatial structure of the atomic cloud. Here we show, based on a newly developed microscopic approach, that the decay cascades of topological defects are dramatically modified by the spin polarization. We demonstrate that decay cascades end up at different stages: "dark soliton," "vortex ring," or "vortex line," depending on the polarization. We reveal that it is caused by sucking of unpaired particles into the soliton's internal structure. As a consequence vortex reconnections are hindered and we anticipate that quantum turbulence phenomenon can be significantly affected, indicating new physics induced by polarization effects.

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.

Momentum-resolved spectroscopy of a Fermi liquid

We consider a recent momentum-resolved radio-frequency spectroscopy experiment, in which Fermi liquid properties of a strongly interacting atomic Fermi gas were studied. Here we show that by extending the Brueckner-Goldstone model, we can formulate a theory that goes beyond basic mean-field theories and that can be used for studying spectroscopies of dilute atomic gases in the strongly interacting regime. The model hosts well-defined quasiparticles and works across a wide range of temperatures and interaction strengths. The theory provides excellent qualitative agreement with the experiment. Comparing the predictions of the present theory with the mean-field Bardeen-Cooper-Schrieffer theory yields insights into the role of pair correlations, Tan's contact, and the Hartree mean-field energy shift.

Auxiliary-field quantum Monte Carlo simulations of neutron matter in chiral effective field theory

We present variational Monte Carlo calculations of the neutron matter equation of state using chiral nuclear forces. The ground-state wave function of neutron matter, containing nonperturbative many-body correlations, is obtained from auxiliary-field quantum Monte Carlo simulations of up to about 340 neutrons interacting on a 10(3) discretized lattice. The evolution Hamiltonian is chosen to be attractive and spin independent in order to avoid the fermion sign problem and is constructed to best reproduce broad features of the chiral nuclear force. This is facilitated by choosing a lattice spacing of 1.5 fm, corresponding to a momentum-space cutoff of Λ=414  MeV/c, a resolution scale at which strongly repulsive features of nuclear two-body forces are suppressed. Differences between the evolution potential and the full chiral nuclear interaction (Entem and Machleidt Λ=414  MeV [L. Coraggio et al., Phys. Rev. C 87, 014322 (2013).