Session X11: Fermions in Optical Lattices II

Non-Equilibrium Enhancement of Superfluidity in a Trapped Fermi Gas

In 1970, Eliashberg showed that superconductivity could be stimulated by pushing the quasiparticle spectrum out of equilibrium and to higher energies using a periodic perturbation with a frequency of the order of the superconducting gap (Eliashberg, JETP Lett. 11, 114 (1970)). This effect has been observed in thin films (TM Klapwijk et al. JLTP 26, 3-4 (1977)). The theory of this gap enhancement can be mapped onto a cold Fermi gas. We present here the theoretical framework for describing the stimulation of the BCS order parameter in an interacting Fermi gas by means of a periodic perturbation.   

Realizing the Strongly Correlated $d$-Wave Mott-Insulator State in a Fermionic Cold-Atom Optical Lattice

We show that a new state of matter, the $d$-wave Mott-insulator state ($d$-Mott state) (introduced recently by [H. Yao, W. F. Tsai, and S. A. Kivelson, Phys. Rev. B 76, 161104 (2007)]), which is characterized by a nonzero expectation value of a local plaquette operator embedded in an insulating state, can be engineered using ultracold atomic fermions in two-dimensional double-well optical lattices. We characterize and analyze the parameter regime where the $d$-Mott state is stable. We predict the testable signatures of the state in the time-of-flight measurements.   

Spectral function of spinless fermions on a one-dimensional lattice

We study the spectral function of spinless fermions for an integrable lattice model away from half-filling. The sharp features of the spectral function at arbitrary momentum are argued to be power law singularities analogous to the x-ray edge singularity. Besides the singularity at the energy of the single-particle excitation, we find that at low fillings the spectral function can exhibit a second divergence associated with the formation of a p-wave antibound state. The predictions from the effective field theory are compared with numerical results from the time-dependent density matrix renormalization group.   

Superfluidity at the BEC-BCS crossover in two-dimensional Fermi gases with population and mass imbalance

We explore the zero-temperature phase behavior of a two-dimensional two-component atomic Fermi gas with population and mass imbalance in the regime of the BEC-BCS crossover. Working in the mean-field approximation, we show that the normal and homogeneous balanced superfluid phases are separated by an inhomogeneous superfluid phase of Fulde-Ferrel-Larkin-Ovchinnikov (FFLO) type. We obtain an analytical expression for the line of continuous transitions separating the normal and inhomogeneous FFLO phases. We further show that the transition from the FFLO phase to the homogeneous balanced superfluid is discontinuous leading to phase separation. If the species have different masses, the superfluid phase is favored when the lighter species is in excess. We explore the implications of these findings for the properties of the two-component Fermi gas in the atomic trap geometry. Finally, we compare and contrast our findings with the predicted phase behavior of the electron-hole bilayer system. [1] Phys. Rev. A 77, 053617 (2008)   

Effective theory for weakly coupled one-dimensional imbalanced Fermi gas

We present a theory for a lattice array of weakly coupled one-dimensional ultracold attractive Fermi gases (1D ``tubes") with spin imbalance, which are currently under experimental investigation using ultra-cold $^6$Li atoms. We first construct an effective field theory for the 1D Fulde-Ferrel-Larkin-Ovchinnikov (FFLO) state based on the exact solution. Special attention is paid to the effect of spin-charge mixing. Then we analyze the instability of the 1D FFLO state against inter-tube tunneling by renormalization group analysis to obtain the phase diagram of the quasi-1D system and further determine the scaling of the superfluid transition temperature with intertube coupling.   

Cold Fermionic Atoms in Two Dimensional Traps--Pairing versus Hund's Rule

The microscopic properties of a finite many-body system of few interacting cold fermionic atoms confined in a two-dimensional (2D) harmonic trap are studied by numerical diagonalization. For repulsive interactions, a strong shell structure dominates with Hund's Rule acting in its extreme for mid-shell configurations. In the attractive case, odd/even oscillations due to pairing occur simultaneously with deformations in the internal structure of the ground states, as seen from pair correlation functions.   

Cold Fermion Pairing in Two-Dimensional Harmonic Traps

Trapped, ultra-cold atomic gasses have provided a rich testing ground for quantum theories. We apply a pairing model from nuclear physics to a 2D harmonically confined, two-component atomic gas containing 2-9 particles. Our Hamiltonian consists of the oscillator mean field and a contact pairing interaction. We calculate excitation spectra, yrast spectra, the BCS delta, and addition energies for various values of the pairing strength. As expected, when the interaction is weak, the oscillator mean field is dominant, and as the interaction strength is increased, pairing effects become quite clear. Results are compared with \textit{ab initio} calculations.   

Ultra-cold fermions with attractive interactions in optical lattices

We address how attractive Hubbard model can be simulated using ultra-cold fermions with attractive interactions loaded into optical lattices. Our study may be relevant to high-temperature superconductivity. For s-wave pairing, smooth crossover behavior similar to the BCS-Bose Einstein condensation crossover in homogeneous Fermi gases can only be observed at low fillings. Near half filling crossover in lattices is interrupted and the BCS wavefunction breaks down. By analyzing the attractive Hubbard model in the strongly attractive regime, we show that states with local pairs instead of Cooper pairs are better ground states. We also study d-wave pairing in optical lattices and find that interruption of crossover occurs at almost all fillings. Our phase diagram for d-wave pairing capture some features of experimental phase diagrams of high-temperature superconductors.   

General Hubbard Model for Fermions in an Optical Lattice

For two-component fermions in an optical lattice, an effective general Hubbard model (GHM) with tunable on-site attraction/repulsion and occupation-dependent hopping rates emerges from very general arguments [1]. This model is quite interesting, containing as special cases both the t-J and the XXZ models. However, the experimental range of applicability and the connection between the model parameters and the actual experimental parameters must be determined explicitly. To this end, we have used a stochastic variational approach with a correlated gaussian wavefunction to numerically find the eigenstates of two atoms interacting in a 3D few-well trap. By matching the few-site spectrum of the GHM to the variational spectrum obtained, the validity of the model and the relationship between experimental and model parameters are determined. [1] L.-M. Duan, Euro. Phys. Lett. 81, 20001 (2008).   

Probing Nagaoka ferromagnetism in optical superlattices

In 1966, Nagaoka predicted that interaction-induced ferromagnetism occurs~in lattices with specific geometry when there is one fewer electron than in the half-filled system. Here, we describe a controllable method for observing Nagaoka Ferromagnetism in isolated plaquettes (four lattice sites arranged in a square) created using~optical superlattices. We next discuss the weakly coupled plaquettes and suggest several approaches for creating systems exhibiting itinerant ferromagnetism.   

Competition between spin imbalance and mass imbalance in the 1D asymmetric Hubbard model

In this talk, I will discuss the spin imbalance in the 1D asymmetric Hubbard model in the negative U region by the Bosonization method. A ground-state phase diagram has been obtained. We find that, unlike the $N_\downarrow=N_\uparrow$ case, there is no other phase transition in the ground state (always Singlet Superconducting) before it enters into the phase separation region, and the pairing correlation function is founding to oscillate in real space (FFLO state). The maximum mode is only determined by difference of Fermi momenta, and the correlation exponent is determined by both the mass difference and spin polarization.   

Spin-coherent and -incoherent Luttinger liquids in trapped ultracold atomic Fermi gases

Recent success in manipulating ultracold atomic systems allows to probe different strongly correlated regimes in one dimension. Experimentally, 1D tubes are defined by turning on a 2D optical lattice. Regimes such as the spin-coherent Luttinger liquid and the spin-incoherent Luttinger liquid can be realized by tuning the inter-atomic interaction strength and trap parameters. Due to the trap potential the density decreases near the edges of the tubes and the spin-incoherent regime is inevitably realized. In general, the spin-coherent Luttinger liquid regime in the center of the tube crosses over to its spin-incoherent counterpart at the edges. We identify the noise correlations of density fluctuations as a robust observable (uniquely suited in the context of trapped atomic gases) to discriminate between these two regimes. Finally, we address the concrete prospects of realizing and probing these phenomena experimentally using optical lattices.