W. Vincent Liu

Interior gap superfluidity.

We propose a new state of matter in which the pairing interactions carve out a gap within the interior of a large Fermi ball, while the exterior surface remains gapless. This defines a system which contains both a superfluid and a normal Fermi liquid simultaneously, with both gapped and gapless quasiparticle excitations. The universality class of this state can be realized at weak coupling. We predict that a cold mixture of two species of fermionic atoms with different mass will exhibit this state. For electrons in appropriate solids, it would define a material that is simultaneously superconducting and metallic.

Topological semimetal in a fermionic optical lattice

Experimental progress has made it possible to load fermionic atoms into higher orbital bands. Such systems provide a platform for studying quantum states of matter that have no prior analogues in solid-state materials. This theoretical study predicts a semimetallic topological state in these systems, which can be turned into a topological insulating phase. Optical lattices have an important role in advancing our understandingof correlated quantum matter. The recent implementation of orbital degrees of freedom in chequerboard1,2 and hexagonal3 optical lattices opens up a new avenue towards discovering novel quantum states of matter that have no prior analogues in solid-state electronic materials. Here, we predict that an exotic topological semimetal emerges as a parity-protected gapless state in the orbital bands of a two-dimensional fermionic optical lattice. This new quantum state is characterized by a parabolic band-degeneracy point with Berry flux 2π, in sharp contrast to the π flux of Dirac points as in graphene. We show that the appearance of this topological liquid is universal for all lattices with D4 point-group symmetry, as long as orbitals with opposite parities hybridize strongly with each other and the band degeneracy is protected by odd parity. Turning on inter-particle repulsive interactions, the system undergoes a phase transition to a topological insulator whose experimental signature includes chiral gapless domain-wall modes, reminiscent of quantum Hall edge states.

Spin dependent Hubbard model and a quantum phase transition in cold atoms

We describe an experimental protocol for introducing spin-dependent lattice structure in a cold atomic Fermi gas using lasers. It can be used to realize Hubbard models whose hopping parameters depend on spin and whose interaction strength can be controlled with an external magnetic field. We suggest that exotic superfluidities will arise in this framework. An especially interesting possibility is a class of states that support coexisting superfluid and normal components, even at zero temperature. The quantity of normal component varies with external parameters. We discuss some aspects of the quantum phase transition that arises at the point where it vanishes.

Topological states in a ladder-like optical lattice containing ultracold atoms in higher orbital bands

Synthetic quantum orbital materials, such as the recent double-well optical lattices loaded with s and p orbital atoms [1, 2], open an avenue to exploit symmetries beyond natural crystals. Exotic superfluid states were reported for bosons. Here, we unveil a topological phase of interacting fermions on a two-leg ladder of unequal parity orbitals, derived from the experimentally realized double-well lattices by dimension reduction. Z2 topological invariant originates simply from the staggered phases of sp-orbital quantum tunneling, requiring none of the previously known mechanisms such as spin-orbit coupling or artificial gauge field. Another unique feature is that upon crossing over to two dimensions with coupled ladders, the edge modes from each ladder form a parity-protected flat band at zero energy, opening the route to strongly correlated states controlled by interactions. Experimental signatures are found in density correlations and phase transitions to trivial band and Mott insulators. The uneven double-well potential formed by laser light has been developed into a powerful tool for quantum gases by numerous groups [1–6]. For instance, controls of atoms on the sand p-orbitals of the checkerboard [1] and hexagonal [6] optical lattices have been demonstrated, and correlation between these orbitals tends to give exotic quantum states [6, 7]. Motivated by these developments, we consider a lattice of uneven double-wells where fermionic atoms are loaded up to the sand porbital levels of the shallow and deep wells respectively, as shown in Fig. 1. The spatial symmetry of the orbital wave function dictates the complex hopping amplitudes between nearby sites. Under certain circumstances, as for the uneven double wells, the orbital hopping pattern is sufficient for producing topologically nontrivial band structures [8]. We will first focus on a one-dimensional ladder system illustrated in Fig. 1b and 1c. This corresponds to the quasi-one dimensional limit of a standard double-well optical lattice, with the optical potential given byTopological insulators are classified according to their symmetries. Discovery of them in electronic solids is thus restricted by orbital and crystalline symmetries available in nature. Synthetic quantum matter, such as the recent double-well optical lattices loaded with s and p orbital ultracold atoms, can exploit symmetries and interaction beyond natural conditions. Here we unveil a topological phase of interacting fermionic atoms on a two-leg ladder derived from the above experimental optical lattice by dimension reduction. The topological band structure originates from the staggered phases of sp orbital tunnelling, requiring neither spin-orbit coupling nor other known mechanisms like p-wave pairing, artificial gauge field or rotation. Upon crossing over to two-dimensional coupled ladders, the edge modes from individual ladder form a parity-protected flat band at zero energy. Experimental signatures are found in density correlations and phase transitions to trivial band and Mott insulators.

Theory of quasi-one-dimensional imbalanced Fermi gases

We present a theory for a lattice array of weakly coupled one-dimensional ultracold attractive Fermi gases (1D tubes) with spin imbalance, where strong intratube quantum fluctuations invalidate mean-field theory. We first construct an effective field theory, which treats spin-charge mixing exactly, based on the Bethe ansatz solution of the 1D single tube problem. We show that the 1D Fulde-Ferrel-Larkin-Ovchinnikov (FFLO) state is a two-component Luttinger liquid, and its elementary excitations are fractional states carrying both charge and spin. We analyze the instability of the 1D FFLO state against intertube tunneling by renormalization group analysis, and find that it flows into either a polarized Fermi liquid or a FFLO superfluid, depending on the magnitude of interaction strength and spin imbalance. We obtain the phase diagram of the quasi-1D system and further determine the scaling of the superfluid transition temperature with intertube coupling.

Spirals and Skyrmions in Two Dimensional Oxide Heterostructures

We construct the general free energy governing long-wavelength magnetism in two dimensional oxide heterostructures, which applies irrespective of the microscopic mechanism for magnetism. This leads, in the relevant regime of weak but non-negligible spin-orbit coupling, to a rich phase diagram containing in-plane ferromagnetic, spiral, cone, and Skyrmion lattice phases, as well as a nematic state stabilized by thermal fluctuations.

Theoretical Study of the Damping of Collective Excitations in a Bose-Einstein Condensate

We study the damping of low-lying collective excitations of condensates in a weakly interacting Bose gas model within the framework of an imaginary time path integral. A general expression of the damping rate has been obtained for both the very low temperature regime and the higher temperature regime. For the latter, the result is new and applicable to recent experiments. Theoretical predictions for the damping rate are compared with the experimental values. {copyright} {ital 1997} {ital The American Physical Society}

Orbital order in Mott insulators of spinless p-band fermions.

A gas of strongly interacting single-species (spinless) p-orbital fermionic atoms in 2D optical lattices is proposed and studied. Several interesting new features are found. In the Mott limit on a square lattice, the gas is found to be described effectively by an orbital exchange Hamiltonian equivalent to a pseudospin-1/2 XXZ model. For a triangular, honeycomb, or kagome lattice, the orbital exchange is geometrically frustrated and described by a new quantum 120 degrees model. We determine the orbital ordering on the kagome lattice, and show how orbital wave fluctuations select ground states via the order by disorder mechanism for the honeycomb lattice. We discuss experimental signatures of various orbital ordering.

Quantum Stripe Ordering in Optical Lattices

We predict the robust existence of a novel quantum orbital stripe order in the p-band Bose-Hubbard model of two-dimensional triangular optical lattices with cold bosonic atoms. An orbital angular momentum moment is formed on each site exhibiting a stripe order both in the superfluid and Mott-insulating phases. The stripe order spontaneously breaks time-reversal, lattice translation, and rotation symmetries. In addition, it induces staggered plaquette bond currents in the superfluid phase. Possible signatures of this stripe order in the time of flight experiment are discussed.

Physics of higher orbital bands in optical lattices: a review.

The orbital degree of freedom plays a fundamental role in understanding the unconventional properties in solid state materials. Experimental progress in quantum atomic gases has demonstrated that high orbitals in optical lattices can be used to construct quantum emulators of exotic models beyond natural crystals, where novel many-body states such as complex Bose-Einstein condensates and topological semimetals emerge. A brief introduction of orbital degrees of freedom in optical lattices is given and a summary of exotic orbital models and resulting many-body phases is provided. Experimental consequences of the novel phases are also discussed.