Session H32: Quantum Fermi Gases

Superfluid-Insulator Transition of Fermions in Optical Lattices across a Feshbach Resonance

We study superfluid-insulator (SI) transition of fermions in an optical lattice as a function of scattering length and fermion density. For systems with two fermions (hence one boson) per site, SI transition is the usual Mott transition between bosonic molecules on the BEC side of resonance. On the BCS side, the insulating phase is the band insulator. SI transition is caused by the energy gain in promoting two fermions in valance band to various valance bands to form Cooper pairs. This phenomena become even more intriguing at higher fermion densities. In this talk, we shall present the phase diagram for SI transition across a Feshbach resonance for different densities. Our results directly related to the recent MIT experiment on SI transition of lattice fermions with two fermion per site.   

p-wave Feshbach Molecules.

We present evidence for the production and detection of molecules using a p-wave Feshbach resonance between 40K atoms. We have measured the binding energies and lifetimes for these molecules. We find that the binding energies scale linearly with magnetic field near the resonance. At magnetic fields above the resonance we detect quasi-bound molecules with lifetimes set by the tunneling rate through the centrifugal barrier. We discuss the possibility of using a p-wave Feshbach resonance to study BEC-BCS crossover physics with finite angular momentum pairing.   

Quantum Phase Transitions of Ultra Cold Gases in the Fermi-Bose Hubbard Hamiltonian

The experimental realization of ultracold fermions has stimulated work on theoretical models of zero-temperature quantum phase transitions and the BCS-BEC crossover. Ultracold gases confined in optical lattices can demonstrate a wide range of different phases by varying controllable system parameters, such as optical lattice intensity, particle number, spin composition and atomic interactions. We perform numerical studies of a Fermi-Bose-Hubbard Hamiltonian with the Vidal algorithm (Time Evolving Block Decimation). Our Hamiltonian treats a one dimensional system of fermions coupled to a bosonic molecular state, as occurs in Feshbach resonances, and encompasses a very large parameter space. We present the quantum phase diagram, focusing on small systems and the most experimentally relevant parameters.   

Destruction of $p$-wave weakly bound molecules in a gas of spin-polarized fermions

We have studied collisional aspects which might affect the lifetime of $p$-wave molecules created in ultracold spin-polarized fermi gases near a Feshbach resonance [1]. Atom-molecule inelastic collisions might be the main process in which the collision products can be released from typical traps. Our study allows us describe the dependence of the collision rates on the $p$-wave scattering length, which is crucial for understanding the stability of such molecules in the strongly interacting regime. [1] H. Suno, B. D. Esry, and C. H. Greene, Phys. Rev. Lett. 90, 053202 (2003). This work was supported in part by the National Science Foundation.   

The potential energy of a $^{40}$K Fermi gas in the BCS-BEC crossover

We present a measurement of the potential energy of an ultracold trapped gas of $^{40}$K atoms in the BCS-BEC crossover and investigate the temperature dependence of this energy at a wide Feshbach resonance, where the gas is in the unitarity limit. In particular, we study the ratio of the potential energy in the region of the unitarity limit to that of a non-interacting gas, and in the $T=0$ limit we extract the universal many-body parameter $\beta$. We find $\beta = -0.54^{+0.05}_{-0.12}$; this value is consistent with previous measurements using $^{6}$Li atoms and also with recent theory and Monte Carlo calculations. This result demonstrates the universality of ultracold Fermi gases in the strongly interacting regime.   

Phase separation in a mixture of two species of fermionic atoms in one-dimensional optical lattice

In this work, we study the ground-state phase diagram of a mixture of two species of fermionic atoms in one-dimensional optical lattice, as described by an asymmetric Hubbard model. We investigate the quantum phase transition from density wave to phase separation by studying both the corresponding charge order parameter and quantum entanglement, and present phase diagram as function of band-filling. A rigorous prove, that even for the case of a single hole doping, the density wave is unstable to the phase separation in the infinite U limit, will be presented. We also discuss experimental feasibility of observing such a phase separation.   

Natural orbits of atomic Cooper pairs in a nonuniform Fermi gas

We present the natural orbits of atomic Cooper pairs in an inhomogeneous Fermi gas. These orbits provide the pairing mode functions of constructing BCS states in finite systems. We further exploit such orbits to study Cooper pair wave functions in various trapping situations. In particular, we quantify and characterize the quantum entanglement between atoms in a Cooper pair associated with the spatial degrees of freedom. \newline (Reference : Y.H. Pong, C.K. Law, Phy. Rev. A \textbf{74}, 013618 (2006))   

Spontaneous Magnetization of Harmonically Trapped Ultracold Fermions in an Optical Lattice

We use a single-band Fermi Hubbard Hamiltonian to study the ground states of a system of ultracold fermions in a one dimensional optical lattice with an external harmonic trap. We perform simulations using exact diagonalization for small systems with one to five wells and we employ Vidal's algorithm (Time Evolving Block Decimation) for larger systems with up to a hundred wells. As the trapping frequency increases we observe spontaneous transverse magnetization at the edges of the trap. We present a theoretical interpretation of this intriguing result, and discuss how it can be observed in experiments.   

Spin Drag and Spin-Charge Separation in Cold Fermi Gases

Low-energy spin and charge excitations of one-dimensional interacting fermions are completely decoupled and propagate with different velocities. These modes however do not live forever and can decay due to several possible mechanisms, even in the complete absence of impurities. In the spin channel the main mechanism of decay at finite temperature is related to a distinctive mechanism of friction that dominates spin transport: the spin drag. In this work we show how two component cold Fermi gases confined inside a tight atomic waveguide offer the unique opportunity to measure directly the spin-drag relaxation time that controls the broadening of a spin packet.   

Dynamics of particle density and noise correlators of a cold Fermi system expanding from a harmonic trap

We have studied dynamics of an atomic Fermi system with a finite number of particles $N$ after it is released from a harmonic trapping potential. We consider two different initial states: the Fermi sea state and the projected BCS (PBCS) state described by the projection of the grand-canonical BCS wave function onto the subspace with a fixed number of particles. In the former case, we derive exact and simple analytic expressions for the particle density $n({\bf r},t)$ and density-density correlation functions $\left\langle n({\bf r},t) n({\bf r}',t)\right\rangle$ taking into account the level quantization and possible anisotropy of the trap. In the latter case of the PBCS state, we obtain analytic expressions for the density and its correlators in the leading order with respect to the ratio of the trap frequency and the superconducting gap (the ratio assumed small). We discuss several interesting dynamic features, which may be used to distinguish between the Fermi sea and BCS states.   

Pairing with multiple flavors of fermions in ultracold atoms

We use Ginburg-Landau formalism to discuss s-wave pairing in ultracold Fermi gases with N flavors and with SU(N) symmetric interactions. We show that when the number of flavors is greater than two, the uniform superfluid state is unstable since the magnetization or flavor imbalance couples directly to the superfluid order parameter. We study the case of three flavors in detail to analyze the competition between phase separation and non-uniform FFLO-like superfluid states. Implications of our results for experiments will be discussed.   

Two-species fermion mixtures with mass and population imbalance

We analyze the phase diagram of uniform superfluidity for two-species fermion mixtures from the Bardeen-Cooper-Schrieffer (BCS) to Bose-Einstein condensation (BEC) limit as a function of the scattering parameter and population imbalance. We find at zero temperature that the phase diagram of population imbalance versus scattering parameter is asymmetric for unequal masses, having a larger stability region for uniform superfluidity when the lighter fermions are in excess. In addition, we find topological quantum phase transitions associated with the disappearance or appearance of momentum space regions of zero quasiparticle energies. Lastly, near the critical temperature, we derive the Ginzburg- Landau equation, and show that it describes a dilute mixture of composite bosons and unpaired fermions in the BEC limit.