Session T3: Fermi Gases and Imbalanced Fermi Gases

Time-resolved measurement of the contact parameter in a strongly interacting Fermi gas

Two-component Fermi gases with strong interactions play an important role in different physical scenarios ranging from atomic nuclei to neutron stars. A number of universal relations for these systems built around a central parameter called the ``contact'' have been developed in 2005 by S. Tan. Neutral fermionic atoms cooled to quantum degeneracy provide a highly controllable test bed for such relations. We use ultracold samples of $^{40}$K in two different Zeeman states to study the time-evolution of the contact parameter by means of radiofrequency spectroscopy to a third weakly-interacting state. Starting with a spin-polarized gas of atoms in a coherent superposition of the two interacting internal states, we observe a build-up of contact as the sample evolves towards an incoherent, fully interacting mixture. Our observations connect single-particle coherence dynamics with the evolution of the contact. We are able to affect the latter deterministically by controlling the single particle coherence via spin echoes. Once the sample has fully decohered, atom loss dominates the contact dynamics. We investigate the time-evolution of the Fermi gas over a wide range of interactions using a Feshbach resonance.   

Measurement of the Homogenous Contact in a Strongly Interacting Fermi Gas

The contact, proposed originally by Shina Tan, is a thermodynamic parameter that has been shown, both theoretically and experimentally, to connect to a large number of measurable properties of a Fermi gas. For a strongly interacting Fermi gas in the BCS-BEC crossover, a measurement of the temperature-dependence of the contact in the vicinity of the superfluid transition has the potential to distinguish among different theories of this system. However, as with any quantity that depends on density, averaging over a trapped gas can wash out essential features. We perform measurements of the homogeneous gas contact as a function of temperature by employing a technique to probe only the center of a trapped gas of potassium-40 atoms. We compare our results to theories of strongly interacting Fermi gases.   

Obtaining the thermodynamics of harmonically trapped gases from their column density

We present a procedure to obtain the equation of state (EoS) of a harmonically trapped atomic gas directly from its column density. We show that the column density of a harmonically trapped gas is a thermodynamic quantity, and its variation with respect to the external trapping potential encodes the EoS. This procedure also prescribes a powerful tool to perform thermometry for trapped atomic gases. We demonstrate the procedure on the unitary Fermi gas, where the column density is directly related to the trap-averaged heat capacity. This trap-averaged quantity shows evidently only a benign rise above its normal value around the superfluid transition, in contrast to the sharp rise in the homogeneous case. We also report on the progress to measure the temperature dependence of the spin susceptibility in spin-imbalanced Fermi gases at unitarity.   

Lee-Yang cluster expansion approach to BCS-BEC crossover

A dilute gas of spin-1/2 Fermi atoms can continuously evolve from Cooper pairing to Bose-Einstein condensation (BEC) of tightly-bound dimers by changing the strength of interaction between them. This is called BCS-BEC crossover and has realized by using a ultracold atomic gases. In this work, we propose a new systematic approach to describe the BCS-BEC crossover based on a cluster expansion method of Lee and Yang. Here, the cluster expansion is a systematic expansion of the equation of state in terms of the fugacity $z:=e^{\beta \mu}$ as $\beta \lambda^3 p =2z+b_2 z^2 + b_3 z^3 + \dots$, with inverse temperature $\beta=(k_B T)^{-1}$, chemical potential $\mu$, pressure $p$, and thermal de Broglie length $\lambda := (2\pi \hbar \beta/m)^{1/2}$. We show the following results: (i) in the weak-coupling limit, the Thouless criterion and the number equation of Nozieres and Schmitt-Rink are derived, and thereby the critical temperature is identical with that of the BCS theory; (ii) in the strong-coupling limit, the critical temperature is identical with that of the BEC of non-interacting dimers; (iii) The exact second cluster integral $b_2$, which is dominant in the high-temperature region, is also included in the expansion for any value of an s-wave scattering length $a$.   

Spin-Imbalanced Fermi Gases from 1D to 3D

A spin-imbalanced Fermi gas confined to 1D tubes using a 2D optical lattice exhibits phase separation; a partially polarized superfluid core adjoins fully polarized or fully paired wings in each 1D tube, depending on the overall spin polarization\footnote{Y.A. Liao et~al., Nature 467, 567 (2010)}. By decreasing the strength of the optical lattice, we vary the tunneling rate between the tubes and decrease the cloud's 1D character. In the absence of a lattice, the 3D cloud separates into a fully paired core surrounded by excess unpaired spins\footnote{G. B. Partridge et~al., Science 311, 503 (2006); Y. Shin et~al., Phys. Rev. Lett. 97, 030401 (2006)}. We report investigations of the spin density in spin-imbalanced Fermi gases confined in a range of lattice depths such that the character of the gas varies from 1D to 3D.   

Parametric dimensional evolution of the Fulde-Ferrell-Larkin-Ovchinnikov state of imbalanced fermionic-atom superfluids in an optical lattice of coupled tubes

We study two-species imbalanced fermionic superfluids in an array of one-dimensional tubes that are coupled via particle tunneling between nearest neighbors. Incorporating the interplay of Cooper pairing, spin imbalance (or magnetization), and single-particle tunneling, we obtain imbalance profiles accompanied with oscillatory pairing reminiscent of a Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) state, and show that the magnetization of the system can undergo an incompressible-compressible transition by the tuning of the magnetic field as well as tunneling strength [Phys. Rev. A 85, 051607 (2012)]. The system's phase diagram is well described by an effective extended Bose-Hubbard model. In addition, we discuss another viable process of pair tunneling that strongly affects the evolution of the FFLO profiles. With this new element, one can build a model describing the development of signatures characteristic of the incipience of the dimensional crossover and in partial agreement with preliminary experimental data.   

Thermal and colliding solitons in fermionic superfluids.

We study solitons in strongly interacting Fermi gases of $^6$Li in an elongated axisymmetric geometry. We investigate the formation of thermal solitons which spontaneously emerge at finite temperature as a consequence of phase fluctuations of the order parameter in the axial direction of the clouds. Using a rapid-ramp technique, we convert phase fluctuations into density fluctuations, which can be directly imaged. While the recorded density distribution is very smooth for the coldest clouds, we observe the formation of stripes along the radial direction, whose number and visibility increase with temperature. We interpret strong phase variations as thermal solitons. When temperature is increased even more, the radial phase stiffness is progressively lost and stripes are no longer observed. We also describe progress towards the study of colliding solitons across the BEC-BCS crossover. In this case two solitons are created by the mean of phase-imprinting. While solitons collide elastically in the BEC regime, it has been predicted that such collisions become more and more inelastic toward the BCS side, which is thought to be in part due to the occupation of localized Andreev bound states in the solitons.   

Attractive atom-dimer interaction in a mass-imbalanced Fermi-Fermi mixture

Mass imbalance in strongly interacting mixtures of ultracold fermions is predicted to lead to new pairing phenomena and quantum phases. We report on a striking phenomenon that appears as a unique consequence of mass imbalance, having no counterpart in a mass-balanced case. We investigate a $^{6}$Li-$^{40}$K Fermi-Fermi mixture in the regime of strong interactions on the repulsive side of an interspecies Feshbach resonance. Using radio-frequency spectroscopy we find that, for a sufficiently strong repulsive {\it s}-wave interaction, the $^{40}$K atoms and the $^{6}$Li$^{40}$K dimers interact attractively, which is in strong contrast to the mass-balanced case. This surprising behavior is related to the existence of a $\uparrow \uparrow \downarrow$ trimer state in $\uparrow \downarrow$ Fermi-Fermi mixtures with a mass ratio m$_{\uparrow}$/m$_{\downarrow} > 8.2 $. For our mass ratio of m$_{\rm K}$/m$_{\rm Li} = 6.64$, this trimer state turns into a {\it p}-wave atom-dimer scattering resonance, giving rise to an attractive interaction.