Strongly Interacting p-wave Fermi Gas in Two-Dimensions: Universal Relations and Breathing Mode

The contact is an important concept that characterizes the universal properties of a strongly interacting quantum gas. It appears in both thermodynamic (energy, pressure, etc.) and dynamic quantities (radio-frequency and Bragg spectroscopies, etc.) of the system. Very recently, the concept of contact has been extended to higher partial waves, in particular, the p-wave contacts have been experimentally probed in recent experiment. So far discussions on p-wave contacts have been limited to three-dimensions. In this paper, we generalize the p-wave contacts to two-dimensions and derive a series of universal relations, including the adiabatic relations, high momentum distribution, virial theorem and pressure relation. At high temperature and low density limit, we calculated the p-wave contacts explicitly using virial expansion. A formula which directly connects the shift of the breathing mode frequency and the p-wave contacts are given in a harmonically trapped system. Finally, we also derive the relationships between interaction parameters in three and two dimensional Fermi gas and discuss possible experimental realization of two dimensional Fermi gas with p-wave interactions.Comment: 12 pages,4 figur

Quantum Phases and Collective Excitations in Bose-Hubbard Models with Staggered Magnetic Flux

We study the quantum phases of a Bose-Hubbard model with staggered magnetic flux in two dimensions, as has been realized recently [Aidelsburger {\it et al.}, PRL, {\bf 107}, 255301 (2011)]. Within mean field theory, we show how the structure of the condensates evolves from weak to strong coupling limit, exhibiting a tricritical point at the Mott-superfluid transition. Non-trivial topological structures (Dirac points) in the quasi-particle (hole) excitations in the Mott state are found within random phase approximation and we discuss how interaction modifies their structures. Excitation gap in the Mott state closes at different ${\bf k}$ points when approaching the superfluid states, which is consistent with the findings of mean field theory.Comment: 5 pages, 3 figure

Effective theory and universal relations for Fermi gases near a dd-wave interaction resonance

In this work, we present an effective field theory to describe a two-component Fermi gas near a $d$-wave interaction resonance. The effective field theory is renormalizable by matching with the low energy $d$-wave scattering phase shift. Based on the effective field theory, we derive universal properties of the Fermi gas by the operator product expansion method. We find that beyond the contacts defined by adiabatic theorems, the asymptotic expressions of the momentum distribution and the Raman spectroscopy involve two extra contacts which provide additional information of correlations of the system. Our formalism sets the stage for further explorations of many-body effects in a $d$-wave resonant Fermi gas. Finally we generalise our effective field theory for interaction resonances of arbitrary higher partial waves.Comment: revised versio

Evidence for correlated states in a cluster of bosons with Rashba spin-orbit coupling

We study the ground state properties of spin-half bosons subjected to the Rashba spin-orbit coupling in two dimensions. Due to the enhancement of the low energy density of states, it is expected that the effect of interaction becomes more important. After reviewing several possible ideal condensed states, we carry out an exact diagonalization calculation for a cluster of the bosons in the presence of strong spin-orbit coupling on a two-dimensional disk and reveal strong correlations in its ground state. We derive a low-energy effective Hamiltonian to understand how states with strong correlations become energetically more favorable than the ideal condensed states.Comment: 23 pages, 6 figure

Mott-Superfluid Transition for Spin-Orbit Coupled Bosons in One-Dimensional Optical Lattices

We study the effects of spin-orbit coupling on the Mott-superfluid transition of bosons in a one-dimensional optical lattice. We determine the strong coupling magnetic phase diagram by a combination of exact analytic and numerical means. Smooth evolution of the magnetic structure into the superfluid phases are investigated with the density matrix renormalization group technique. Novel magnetic phases are uncovered and phase transitions between them within the superfluid regime are discussed. Possible experimental detection are discussed.Comment: 5 pages, 4 figure

Fluctuation Effects on the Transport Properties of Unitary Fermi Gases

In this letter, we investigate the fluctuation effects on the transport properties of unitary Fermi gases in the vicinity of the superfluid transition temperature $T_c$. Based on the time-dependent Ginzburg-Landau formalism of the BEC-BCS crossover, we investigate both the residual resistivity below $T_c$ induced by phase slips and the paraconductivity above $T_c$ due to pair fluctuations. These two effects have been well studied in the weak coupling BCS superconductor, and here we generalize them to the unitary regime of ultracold Fermi gases. We find that while the residual resistivity below $T_c$ increases as one approaches the unitary limit, consistent with recent experiments, the paraconductivity exhibits non-monotonic behavior. Our results can be verified with the recently developed transport apparatus using mesoscopic channels.Comment: 8 pages and 4 figures including supplementary material

Evolution of Higgs mode in a Fermion Superfluid with Tunable Interactions

In this letter we present a coherent picture for the evolution of Higgs mode in both neutral and charged $s$-wave fermion superfluids, as the strength of attractive interaction between fermions increases from the BCS to the BEC regime. In the case of neutral fermionic superfluid, such as ultracold fermions, the Higgs mode is pushed to higher energy while at the same time, gradually loses its spectral weight as interaction strength increases toward the BEC regime, because the system is further tuned away from Lorentz invariance. On the other hand, when damping is taken into account, Higgs mode is significantly broadened due to coupling to phase mode in the whole BEC-BCS crossover. In the charged case of electron superconductor, the Anderson-Higgs mechanism gaps out the phase mode and suppresses the coupling between the Higgs and the phase modes, and consequently, stabilizes the Higgs mode.Comment: 5 figures, 9 pages, including supplementary materia