Session W4: Strongly Interacting Fermi Gases

Revealing the Superfluid Lambda Transition in the Universal Thermodynamics of a Unitary Fermi Gas

We have observed the superfluid phase transition in a strongly interacting Fermi gas via high-precision measurements of the local compressibility, density and pressure down to near-zero entropy. We perform the measurements by in-situ imaging of ultracold $^6$Li at a Feshbach resonance. Our data completely determine the universal thermodynamics of strongly interacting fermions without any fit or external thermometer. The onset of superfluidity is observed in the compressibility, the chemical potential, the entropy, and the heat capacity. In particular, the heat capacity displays a characteristic lambda-like feature at the critical temperature of $T_c/T_F = 0.167(13)$. This is the first clear thermodynamic signature of the superfluid transition in a spin-balanced atomic Fermi gas. We provide a new value of the Bertsch parameter $\xi_S$. The experimental results are compared to recent Monte-Carlo calculations. Our measurements provide a benchmark for many-body theories on strongly interacting fermions, relevant for problems ranging from high-temperature superconductivity to the equation of state of neutron stars.   

Probing upper branch physics in strongly interacting Fermi gases

Motivated by a recent experiment at MIT, we consider the collision of two clouds of spin-polarized atomic Fermi gases close to a Feshbach resonance. We explain why two dilute gas clouds, with attractive interactions between its constituents, bounce off each other as if they were billiard balls. Our hydrodynamic analysis, in excellent agreement with experiment, gives strong evidence for a novel metastable many-body state, the so-called upper branch, with repulsive effective interactions. We also propose another experiment, measuring spin decoherence rates, to study the physics of the upper branch.   

Strongly interacting atomic Fermi gases in a trap with mass and population imbalances at finite temperature

A great advantage of studying atomic Fermi gases is the easy tunability of multiple physical parameters, including interaction strength, mass and population imbalances, as well as species dependent trapping potential. Indeed, the mixture of $^6$Li and $^{40}$K gases has been of great interest, with and without population imbalance. In this talk, we will address the finite temperature phase diagrams of two component atomic Fermi gases with both mass and population imbalances in a trap, using a pairing fluctuation theory. We show that in certain parameter ranges, there exist intermediate temperature superfluids as well as phase separation with exotic sandwich-like shell structure with superfluid or pseudogapped normal state in the middle. We consider pairing strength over the entire range of BCS-BEC crossover. Our result is relevant to future experiment on mixtures of $^6$Li and $^{40}$K and possibly other Fermi atoms. References: H. Guo, C.-C. Chien, Q.J. Chen, Y. He, and K. Levin, Phys. Rev. A 80, 011601(R) (2009); C.-C. Chien, Q.J. Chen, Y. He, and K. Levin, Phys. Rev. Lett. 98, 110404 (2007); C.-C. Chien, Q.J. Chen, Y. He, and K. Levin, Phys. Rev. Lett. 97, 090402 (2006); Q.J. Chen, I. Kosztin, B. Janko, and K. Levin, Phys. Rev. Lett. 81, 4708 (1998).   

Two-particle current from Superfluid Fermi Gases in the BCS-BEC Crossover

In recent years, the crossover from the BCS-type superfluid to the Bose-Einstein condensation (BEC) of tightly-bound molecules has been realized in ultracold atomic Fermi gases using a tunable pairing interaction associated with a Feshbach resonance.In the BCS-BEC crossover it will be important to reveal the nature of fermion pairs. In this paper, we propose that two-particle (double photoemission) current (DPE current) is a powerful technics to provide direct insight into the pair-correlations. The DPE from superconductors has been studied both theoretically and experimentally, where a pair of electrons is emitted from the system upon the absorption of one photon. In this study, we consider an analogous situation in ultracold atomic gases, and derive a general expression for DPE current from superfluid Fermi gases in the BCS-BEC crossover.We show DPE current as a function of energy and momentum transfers, and identify the contributions of the condensed pair components and uncorrelated pair states, and discuss the possibility of distinguishing between weakly-bound Cooper pairs and tightly-bound molecules.   

Feshbach resonances and BCS-BEC crossover in optical lattices

In this talk we study Feshbach resonances of fermionic atoms placed in a periodic potential. We investigate the criteria when such a system can be described by a Hubbard model with variable interaction strength in case of broad resonance, or by a tight binding model of atoms and molecules with can convert into each other on sites of the lattice in case of narrow resonances. Assuming the applicability of these models, we first study the BCS-BEC crossover for broad resonance. We find that while below half filling the system undergoes the conventional crossover from a BCS superconductor to a Bose condensate of molecules, above half filling the nature of the BEC phase changes to that of a condensate of molecules made of holes. Switching our attention to the case of narrow resonance, we find that the crossover takes the system from a BCS to hole-BEC regime, than back to BCS, and finally to a conventional BEC of atomic molecules. In the latter crossover, we find that the size of Cooper pairs/molecules changes non-monotonously, being larger in the BCS and smaller in the BEC regimes. Finally, at a unity filling we find a quantum phase transition from a band insulator to a BCS-BEC superfluid replacing the crossover.   

Resonant enhancement of the FFLO state in 3D by an optical potential

In a two component Fermi gas, spin-imbalance leads to a competition between Cooper-pairing with zero momentum and with nonzero momentum. The latter gives rise to the Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) state. Hitherto this state has not been observed in a 3D Fermi gas. We propose a new way to enhance the presence of the FFLO state, by adding a 1D periodic potential. To investigate the effect of this potential, we study the ground state properties of the system, starting from the partition sum of an imbalanced Fermi gas in path-integral representation. To describe the FFLO state, a saddle point is chosen in which the pairs can have nonzero momentum. Minimizing the resulting free energy leads to the phase diagram of the system. The stability region of the FFLO state is found to be greatly enlarged due to the presence of the periodic potential, compared to the ordinary 3D case. We find that the FFLO state can exist at higher spin imbalance if the wavelength of the optical potential becomes smaller. We propose that this concept can be used experimentally to enhance the FFLO state.\\[4pt] [1] Jeroen P.A. Devreese, S.N. Klimin, and J. Tempere, Phys. Rev. A 83, 013606 (2011).\\[0pt] [2] Jeroen P.A. Devreese, M. Wouters, and J. Tempere, J. Phys. B 44, 115302 (2011); Phys. Rev. A 84, 043623 (2011).   

Single magnetic impurity in a spin-imbalanced superfluid Fermi gas

A spin-imbalanced superfluid Fermi gas harmonically trapped in a two-dimensional optical lattice with a single classical magnetic impurity is investigated by Bogoliubov-de Gennes equations. In spin-balanced and weak spin-imbalanced case, we show that a strong magnetic impurity can change sign of the pairing order parameter. The amplitude of the sign-changed order parameter caused by impurity is affected by the strength of impurity potential, temperature and particle density. Compared to spin-balanced case, we find that an additional in-gap bound state can be induced by a strong magnetic impurity in weak spin-imbalanced case. In strong spin-imbalanced case where the Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) state is established as the ground state, the impurity induces wide spatial oscillations of pairing order parameters and can enhance the order parameters by suppressing the local spin-imbalance. Our results can be used to create and manipulate the FFLO state with magnetic impurities in spin-imbalanced Fermi gases.   

Proposal for interferometric detection of the topological character of modulated superfluidity in ultracold Fermi gases

A system with unequal populations of up and down fermions may exhibit a Larkin-Ovchinnikov (LO) phase characterized by periodic domain walls across which the order parameter changes sign and the excess polarization is localized. Despite fifty years of theoretical and experimental work, there has so far been no unambiguous observation of an LO phase. We propose an experiment in which two fermion clouds, prepared with unequal population imbalances, are allowed to expand and interfere. We show that a pattern of staggered fringes in the interference is unequivocal evidence of LO physics. The resilience of these interference signatures against thermal and quantum fluctuations is also discussed, and our results are supported with time-of-flight simulations of the experiment. Y.-L. Loh and N. Trivedi, Phys. Rev. Lett. 104, 165302 (2010). M. Swanson et al., arXiv:1106.3908   

A single impurity atom in a two-dimensional Fermi gas

We consider a single impurity atom immersed in a Fermi gas in two dimensions and interacting via an attractive, short-range potential. Using variational wave functions for polarons, molecules, trimers, and quadrumers, we arrive at the ground state phase diagram as a function of mass ratio and interaction strength. We show that the phase diagram includes a Fulde-Ferrell-Larkin-Ovchinnikov phase for experimentally relevant mass ratios.   

Realization of a Resonant Fermi Gas with a Large Effective Range

We have measured the interaction energy and three-body recombination rate for a two-component Fermi gas near a narrow Feshbach resonance and found both to be strongly energy dependent. Even for deBroglie wavelengths greatly exceeding the van der Waals length scale, the behavior of the interaction energy as a function of temperature cannot be described by atoms interacting via a contact potential. Rather, energy-dependent corrections beyond the scattering length approximation are required, indicating a resonance with an anomalously large effective range. For fields where the molecular state is above threshold, the rate of three-body recombination is enhanced by a sharp, two-body resonance arising from the closed-channel molecular state which can be magnetically tuned through the continuum. This narrow resonance can be used to study strongly correlated Fermi gases that simultaneously have a sizeable effective range and a large scattering length.   

Anomalous Dimers in Quantum Mixtures near Broad Resonances:Pauli Blocking, Fermi Surface Dynamics and Implications

We study the energetics and dispersion of anomalous dimers that are induced by the Pauli blocking effect in a quantum Fermi gas of majority atoms near interspecies resonances. Unlike in vacuum, we find that both the sign and magnitude of the dimer masses are tunable via Feshbach resonances. We also investigate the effects of particle-hole fluctuations on the dispersion of dimers and demonstrate that the particle-hole fluctuations near a Fermi surface (with Fermi momentum $\hbar k_F$) generally reduce the effective two-body interactions and the binding energy of dimers. Furthermore, in the limit of light minority atoms the particle-hole fluctuations disfavor the formation of dimers with a total momentum $\hbar k_F$, because near $\hbar k_F$ the modes where the dominating particle-hole fluctuations appear are the softest. Our calculation suggests that near broad interspecies resonances when the minority-majority mass ratio $m_B/m_F$ is smaller than a critical value (estimated to be 0.136), dimers in a finite-momentum channel are energetically favored over dimers in the zero-momentum channel. We apply our theory to quantum gases of $^{6}$Li$^{40}$K, $^{6}$Li$^{87}$Rb, $^{40}$K$^{87}$Rb and $^{6}$Li$^{23}$Na near broad interspecies resonances, and discuss the implications.   

Unpolarized Fermi gas in squeezed anisotropic harmonic trap by Quantum Monte Carlo methods

Using diffusion Monte Carlo (DMC) method, we calculate the ground state properties of unpolarized Fermi gas at unitarity regime in both isotropic and anisotropic harmonic potentials. We study the effects of anisotropy by increasing the frequency in z direction $\omega_z$ of the harmonic potential while keeping the frequency in x and y direction unchanged. The true unitarity regime is obtained by extrapolating the interaction range to zero and the calculations are done using the fixed-node diffusion Monte Carlo method. The trial function is of the BCS form with the pairing function expanded in appropriate linear combinations of the anisotropic oscillator eigenstates. We evaluate the binding energies for varying particle numbers and we estimate its behavior in the limit of large number of atoms. We estimate dependence of projected density profile and momentum distribution on the X-Y plane with respect to $\omega_z$. Our results can be readily used as a benchmark for the cold atom experiment with similar experimental set-up. Supported by ARO and NSF.   

A Theory for Normal Fermi Gases at Unitarity

In this study, we will develop a simple, yet accurate, mean-field-like theory for the normal phase of a unitarity Fermi gas. First, we derive a self-consistent equation for the self-energy using a momentum-dependent coupling constant. Using zero temperature Monte Carlo results as a starting point, we then derive an analytical expression for the momentum-dependent self-energy within one-step iteration. Lastly, we determine the validity of our analytical self-energy by comparing it to fully numerical calculations. Our theory shows excellent agreement with pressure measurements made by Nascimbene, \textit{et al.} in a recent experiment performed by the ENS group.