Local observation of pair condensation in a Fermi gas at unitarity

We present measurements of the local (homogeneous) density-density response function of a Fermi gas at unitarity using spatially resolved Bragg spectroscopy. By analyzing the Bragg response across one axis of the cloud, we extract the response function for a uniform gas which shows a clear signature of the Bose-Einstein condensation of pairs of fermions when the local temperature drops below the superfluid transition temperature. The method we use for local measurement generalizes a scheme for obtaining the local pressure in a harmonically trapped cloud from the line density and can be adapted to provide any homogeneous parameter satisfying the local density approximation.

Observation of conformal symmetry breaking and scale invariance in expanding Fermi gases

We precisely test scale invariance and examine local thermal equilibrium in the hydrodynamic expansion of a Fermi gas of atoms as a function of interaction strength. After release from an anisotropic optical trap, we observe that a resonantly interacting gas obeys scale-invariant hydrodynamics, where the mean square cloud size <r2>=<x2+y2+z2> expands ballistically (like a noninteracting gas) and the energy-averaged bulk viscosity is consistent with zero, 0.00(0.04)ℏn, with n the density. In contrast, the aspect ratios of the cloud exhibit anisotropic "elliptic" flow with an energy-dependent shear viscosity. Tuning away from resonance, we observe conformal symmetry breaking, where <r2> deviates from ballistic flow.

Quantum Joule-Thomson effect in a saturated homogeneous Bose gas

We study the thermodynamics of Bose-Einstein condensation in a weakly interacting quasihomogeneous atomic gas, prepared in an optical-box trap. We characterize the critical point for condensation and observe saturation of the thermal component in a partially condensed cloud, in agreement with Einstein's textbook picture of a purely statistical phase transition. Finally, we observe the quantum Joule-Thomson effect, namely isoenthalpic cooling of an (essentially) ideal gas. In our experiments this cooling occurs spontaneously, due to energy-independent collisions with the background gas in the vacuum chamber. We extract a Joule-Thomson coefficient μJT>10(9)  K/bar, about 10 orders of magnitude larger than observed in classical gases.

Wilson ratio of fermi gases in one dimension

We calculate the Wilson ratio of the one-dimensional Fermi gas with spin imbalance. The Wilson ratio of attractively interacting fermions is solely determined by the density stiffness and sound velocity of pairs and of excess fermions for the two-component Tomonaga-Luttinger liquid phase. The ratio exhibits anomalous enhancement at the two critical points due to the sudden change in the density of states. Despite a breakdown of the quasiparticle description in one dimension, two important features of the Fermi liquid are retained; namely, the specific heat is linearly proportional to temperature, whereas the susceptibility is independent of temperature. In contrast to the phenomenological Tomonaga-Luttinger liquid parameter, the Wilson ratio provides a powerful parameter for testing universal quantum liquids of interacting fermions in one, two, and three dimensions.

Bulk viscosity and conformal symmetry breaking in the dilute Fermi gas near unitarity

The dilute Fermi gas at unitarity is scale invariant and its bulk viscosity vanishes. We compute, in the high temperature limit, the leading contribution to the bulk viscosity when the scattering length is not infinite. A measure of scale breaking is provided by the ratio (P-2πħ/3ε)/P, where P is the pressure and E is the energy density. At high temperature this ratio scales as zλ/a, where z is the fugacity, λ is the thermal wavelength, and a is the scattering length. We show that the bulk viscosity ζ scales as the second power of this parameter, ζ~(zλ/a)(2)λ(-3).

Bose-Einstein condensation of atoms in a uniform potential

We have observed the Bose-Einstein condensation of an atomic gas in the (quasi)uniform three-dimensional potential of an optical box trap. Condensation is seen in the bimodal momentum distribution and the anisotropic time-of-flight expansion of the condensate. The critical temperature agrees with the theoretical prediction for a uniform Bose gas. The momentum distribution of a noncondensed quantum-degenerate gas is also clearly distinct from the conventional case of a harmonically trapped sample and close to the expected distribution in a uniform system. We confirm the coherence of our condensate in a matter-wave interference experiment. Our experiments open many new possibilities for fundamental studies of many-body physics.

Precise characterization of 6Li Feshbach resonances using trap-sideband-resolved RF spectroscopy of weakly bound molecules

We perform radio-frequency dissociation spectroscopy of weakly bound 6Li2 Feshbach molecules using low-density samples of about 30 molecules in an optical dipole trap. Combined with a high magnetic field stability, this allows us to resolve the discrete trap levels in the radio-frequency dissociation spectra. This novel technique allows the binding energy of Feshbach molecules to be determined with unprecedented precision. We use these measurements as an input for a fit to the 6Li scattering potential using coupled-channel calculations. From this new potential, we determine the pole positions of the broad 6Li Feshbach resonances with an accuracy better than 7×10(-4) of the resonance widths. This eliminates the dominant uncertainty for current precision measurements of the equation of state of strongly interacting Fermi gases. As an important consequence, our results imply a corrected value for the Bertsch parameter ξ measured by Ku et al. [Science 335, 563 (2012)], which is ξ=0.370(5)(8).

Cooper pairing above the critical temperature in a unitary Fermi gas

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.

Collective modes in a unitary Fermi gas across the superfluid phase transition

We provide a joint theoretical and experimental investigation of the temperature dependence of the collective oscillations of first sound nature exhibited by a highly elongated harmonically trapped Fermi gas at unitarity, including the region below the critical temperature for superfluidity. Differently from the lowest axial breathing mode, the hydrodynamic frequencies of the higher-nodal excitations show a temperature dependence, which is calculated starting from Landau two-fluid theory and using the available experimental knowledge of the equation of state. The experimental results agree with high accuracy with the predictions of theory and provide the first evidence for the temperature dependence of the collective frequencies near the superfluid phase transition.

Precise determination of the structure factor and contact in a unitary Fermi gas

We present a high-precision determination of the universal contact parameter in a strongly interacting Fermi gas. In a trapped gas at unitarity, we find the contact to be 3.06±0.08 at a temperature of 0.08 of the Fermi temperature in a harmonic trap. The contact governs the high-momentum (short-range) properties of these systems, and this low-temperature measurement provides a new benchmark for the zero-temperature homogeneous contact. The experimental measurement utilizes Bragg spectroscopy to obtain the dynamic and static structure factors of ultracold Fermi gases at high momentum in the unitarity and molecular Bose-Einstein condensate regimes. We have also performed quantum Monte Carlo calculations of the static properties, extending from the weakly coupled BCS regime to the strongly coupled Bose-Einstein condensate case, that show agreement with experiment at the level of a few percent.

Observing the drop of resistance in the flow of a superfluid Fermi gas

The ability of particles to flow with very low resistance is characteristic of superfluid and superconducting states, leading to their discovery in the past century. Although measuring the particle flow in liquid helium or superconducting materials is essential to identify superfluidity or superconductivity, no analogous measurement has been performed for superfluids based on ultracold Fermi gases. Here we report direct measurements of the conduction properties of strongly interacting fermions, observing the well-known drop in resistance that is associated with the onset of superfluidity. By varying the depth of the trapping potential in a narrow channel connecting two atomic reservoirs, we observed variations of the atomic current over several orders of magnitude. We related the intrinsic conduction properties to the thermodynamic functions in a model-independent way, by making use of high-resolution in situ imaging in combination with current measurements. Our results show that, as in solid-state systems, current and resistance measurements in quantum gases provide a sensitive probe with which to explore many-body physics. Our method is closely analogous to the operation of a solid-state field-effect transistor and could be applied as a probe for optical lattices and disordered systems, paving the way for modelling complex superconducting devices.

Universal contact for a Tonks-Girardeau gas at finite temperature

We determine the finite-temperature momentum distribution of a strongly interacting 1D Bose gas in the Tonks-Girardeau (impenetrable-boson) limit under harmonic confinement and explore its universal properties associated to the scale invariance of the model. We show that, at difference from the unitary Fermi gas in three dimensions, the weight of its large-momentum tails--given by Tan's contact--increases with temperature and calculate the high-temperature universal second contact coefficient using a virial expansion.

Transdimensional equivalence of universal constants for Fermi gases at unitarity

I present lattice Monte Carlo calculations for a universal four-component Fermi gas confined to a finite box and to a harmonic trap in one spatial dimension. I obtain the values ξ(1D) = 0.370(4) and ξ(1D) = 0.372(1), respectively, for the Bertsch parameter, a nonperturbative universal constant defined as the (square of the) energy of the untrapped (trapped) system measured in units of the free gas energy. The Bertsch parameter obtained for the one-dimensional system is consistent to within ~1% uncertainties with the most recent numerical and experimental estimates of the analogous Bertsch parameter for a three-dimensional spin-1/2 Fermi gas at unitarity. The finding suggests the intriguing possibility that there exists a universality between two conformal theories in different dimensions. To lend support to this study, I also compute ground state energies for four and five fermions confined to a harmonic trap and demonstrate the restoration of a virial theorem in the continuum limit. The continuum few-body energies obtained are consistent with exact analytical calculations to within ~1.0% and ~0.3% statistical uncertainties, respectively.

Signatures of fermion pairing with unconventional symmetry around the BCS-BEC crossover in a quasi-2D lattice

We consider fermions on a 2D square lattice with a finite-range pairing interaction, and obtain signatures for unconventional pair-symmetry states, d(x(2)-y(2)) and extended-s (s(*)), in the Bardeen-Cooper-Schrieffer-Bose-Einstein Condensation crossover region. We find that the fermion momentum distribution function, v(k)(2), the ratio of the Bogoliubov coefficients, v(k)/u(k), and the Fourier transform of v(k)(2) are strikingly different for d and s(*) symmetries in the crossover region. The chemical potential and the gap functions for both pairing symmetries show several interesting features as a function of interaction. Fermionic atoms in 2D optical lattices may provide a way to test these signatures. We discuss current generation cold atom experiments that may be utilized.

Measurement of the homogeneous contact of a unitary Fermi gas

By selectively probing the center of a trapped gas, we measure the local, or homogeneous, contact of a unitary Fermi gas as a function of temperature. Tan's contact, C, is proportional to the derivative of the energy with respect to the interaction strength and is thus an essential thermodynamic quantity for a gas with short-range correlations. Theoretical predictions for the temperature dependence of C differ substantially, especially near the superfluid transition, T(c), where C is predicted to either sharply decrease, sharply increase, or change very little. For T/T(F)>0.4, our measurements of the homogeneous gas contact show a gradual decrease of C with increasing temperature, as predicted by theory. We observe a sharp decrease in C at T/T(F)=0.16, which may be due to the superfluid phase transition. While a sharp decrease in C below T(c) is predicted by some many-body theories, we find that none of the predictions fully account for the data.

Quantum mechanical limitations to spin diffusion in the unitary Fermi gas

We compute spin transport in the unitary Fermi gas using the strong-coupling Luttinger-Ward theory. In the quantum degenerate regime the spin diffusivity attains a minimum value of D(s) Symbol: see text] 1.3 ħ/m approaching the quantum limit of diffusion for a particle of mass m. Conversely, the spin drag rate reaches a maximum value of Γ(sd) [Symbol: see text] 1.2k(B)T(F)/ħ in terms of the Fermi temperature T(F). The frequency-dependent spin conductivity σ(s)(ω) exhibits a broad Drude peak, with spectral weight transferred to a universal high-frequency tail σ(s) (ω → ∞) = ħ(1/2)C/3π(mω)(3/2) proportional to the Tan contact density C. For the spin susceptibility χ(s)(T) we find no downturn in the normal phase.

Increasing quantum degeneracy by heating a superfluid

We consider a uniform superfluid confined in two compartments connected by a superleak and initially held at equal temperatures. If one of the two compartments is heated, a fraction of the superfluid will flow through the superleak. We show that, under certain thermodynamic conditions, the atoms flow from the hotter to the colder compartment, contrary to what happens in the fountain effect observed in superfluid helium. This flow causes quantum degeneracy to increase in the colder compartment. In superfluid helium, this novel thermomechanical effect takes place in the phonon regime of very low temperatures. In dilute quantum gases, it occurs at all temperatures below T(c). The increase in quantum degeneracy reachable through the adiabatic displacement of the wall separating the two compartments is also discussed.

Virial expansion coefficients in the harmonic approximation

The virial expansion method is applied within a harmonic approximation to an interacting N-body system of identical fermions. We compute the canonical partition functions for two and three particles to get the two lowest orders in the expansion. The energy spectrum is carefully interpolated to reproduce ground-state properties at low temperature and the noninteracting high-temperature limit of constant virial coefficients. This resembles the smearing of shell effects in finite systems with increasing temperature. Numerical results are discussed for the second and third virial coefficients as functions of dimension, temperature, interaction, and transition temperature between low- and high-energy limits.

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)).

Universal equation of state of a unitary fermionic gas

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.

Seeing the Superfluid Transition of a Gas

The universal thermodynamic functions of a superfluid formed from a fermion gas of strongly interacting lithium atoms have been measured precisely.