We investigate strong-coupling effects on normal state properties of an ultracold Fermi gas. Within the framework $T$-matrix approximation in terms pairing fluctuations, we calculate single-particle density states (DOS), as well spectral weight, over entire BCS-BEC crossover region above superfluid phase transition temperature $T_{\rm c}$. Starting from weak-coupling BCS regime, show that so-called pseudogap develops DOS c}$, which becomes remarkable region. The structure continuously...

We study the superfluid-Mott-insulator transition of antiferromagnetic spin-1 bosons in an optical lattice described by a Bose-Hubbard model. Our variational with Gutzwiller wave function determines that is first-order one at part phase boundary curve, contrary to spinless case.

We study the superfluid--Mott insulator (SF-MI) transition of spin-1 bosons interacting antiferromagnetically in an optical lattice. Starting from a Bose-Hubbard tight-binding model for bosons, we obtain zero-temperature phase diagram by mean-field approximation. find that MI with even number atoms per site is spin singlet state, while odd has 1 at each limit $t=0$, where $t$ hopping matrix element. also show superfluid polar state as case Bose condensate harmonic trap. It found strongly...

We investigate single-particle excitations and strong-coupling effects in the BCS-BEC crossover regime of a superfluid Fermi gas. Including phase amplitude fluctuations order parameter within $T$-matrix theory, we calculate density states (DOS), as well spectral weight, over entire region below transition temperature ${T}_{\mathrm{c}}$. clarify how pseudogap normal state evolves into gap, one passes through While DOS continuously gap weak-coupling BCS regime, is shown to appear after...

We investigate the photoemission-type spectrum in a cold Fermi gas which was recently measured by JILA group [Stewart et al., Nature (London) 454, 744 (2008)]. This quantity gives us very useful information about single-particle properties BCS-BEC crossover. In this paper, including pairing fluctuations within $T$-matrix theory, as well effects of harmonic trap local density approximation, we show that spatially inhomogeneous due to potential are an important key understanding observed...

The excitations of a two-dimensional (2D) Bose-Einstein condensate in the presence soliton are studied by solving Kadomtsev-Petviashvili equation which is valid when velocity approaches speed sound. excitation spectrum found to contain states localized near and have dispersion law similar one stable branch transverse oscillations 1D gray 2D condensate. By using stabilization method we show that these behave as resonant coupled continuum free

We theoretically investigate excitation properties in the pseudogap regime of a trapped Fermi gas. Using combined $T$-matrix theory with local density approximation, we calculate strong-coupling corrections to single-particle states (LDOS), as well spectral weight (LSW). Starting from superfluid phase transition temperature ${T}_{\mathrm{c}}$, clarify how structures these quantities disappear increasing temperature. As case uniform gas, LDOS and LSW give different temperatures ${T}^{*}$...

We investigate strong-coupling properties of a trapped two-dimensional normal Fermi gas. Within the framework combined $T$-matrix theory with local density approximation, we calculate states, as well photoemission spectrum, to see how pairing fluctuations affect these single-particle quantities. In BCS (Bardeen-Cooper-Schrieffer)--BEC (Bose-Einstein condensation) crossover region, show that states exhibits dip structure in trap center, which is more remarkable than three-dimensional case....

We study the stability of Bose-Einstein condensates with superfluid currents in a one-dimensional periodic potential. By using Kronig-Penney model, condensate and Bogoliubov bands are analytically calculated potential is discussed. The Landau dynamical instabilities occur when quasimomentum exceeds certain critical values as sinusoidal It found that onsets coincide point where perfect transmission low energy excitations through each barrier forbidden. instability caused by small $q$...

We study spin imbalance effects on the Larkin-Ovchinnikov-Fulde-Ferrel (LOFF) state relevant for superconductors under a strong magnetic field and polarized ultracold Fermi gas. obtain exact solution condensates with arbitrary fermion spectrum perturbatively in presence of small imbalance. also zero mode exactly without perturbation theory.

We study the Higgs amplitude mode in $s$-wave superfluid state on honeycomb lattice inspired by recent cold atom experiments. consider attractive Hubbard model and focus vicinity of a quantum phase transition between semimetal phases. On either side transition, we find collective excitations that are stable against decay into quasiparticle pairs. In phase, modes have ``Cooperon'' exciton character. These smoothly evolve across become Anderson-Bogoliubov phase. The accommodated within window...

We find the angular Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) states (or twisted kink crystals) in which a phase and an amplitude of pair potential modulate simultaneously quasi-one-dimensional superconducting ring with static Zeeman magnetic field applied on Aharonov-Bohm flux penetrating ring. The produces persistent current, whereas split Fermi energy results spatial modulation potential. show that these two fields stabilize FFLO large parameter region fields. further draw diagram kinds...

Extending recent work to finite temperatures, we calculate the Landau damping of a Bogoliubov excitation in an optical lattice, due coupling thermal cloud such excitations. For simplicity, consider 1D Bose-Hubbard model and restrict ourselves first energy band. conservation be satisfied, excitations collision processes must exhibit ``anomalous dispersion'', analogous phonons superfluid $^4\rm{He}$. This leads disappearance all when $U n^{\rm c 0}\ge 6t$, where $U$ is on-site interaction, $t$...

Motivated by recent developments in the experimental study of superconducting graphene and transition metal dichalcogenides, we investigate superconductivity Kane-Mele (KM) model with short-range attractive interactions on two-dimensional honeycomb lattice. We show that intra-valley spin-triplet pairing arises from nearest-neighbor (NN) interaction intrinsic spin-orbit coupling. demonstrate this two independent approaches: instability driven condensation Cooperons, which are in-gap bound...

We study the Landau damping of Bogoliubov excitations in two- and three-dimensional optical lattices at finite temperatures, extending our recent work on one-dimensional (1D) lattices. use a Bose-Hubbard tight-binding model Popov approximation to calculate temperature dependence number condensate atoms ${n}^{\mathrm{c}0}(T)$ each lattice well. As with 1D lattices, only occurs if exhibit anomalous dispersion (i.e., excitation energy bends upward low momentum), analogous case phonons...

We study the stability of superfluid Fermi gases in deep optical lattices BCS--Bose-Einstein condensation (BEC) crossover at zero temperature. Within tight-binding attractive Hubbard model, we calculate spectrum low-energy Anderson-Bogoliubov (AB) mode as well single-particle excitations presence flow order to determine critical velocities. To obtain AB mode, density response function generalized random-phase approximation applying Green's formalism developed by C\^ot\'e and Griffin model....

We investigate strong pairing fluctuations and effects of a harmonic trap in the superfluid phase an ultracold Fermi gas. Including amplitude inhomogeneous order parameter $\ensuremath{\Delta}(r)$ within combined $T$-matrix theory with local density approximation, we examine properties single-particle excitations thermodynamic quantity BCS-BEC crossover region. Below transition temperature ${T}_{\mathrm{c}}$, show that lead to shell structure gas cloud which spatial region where ordinary...

A massive Goldstone (MG) mode, often referred to as a Higgs amplitude is collective excitation that arises in system involving spontaneous breaking of continuous symmetry, along with gapless Nambu-Goldstone mode. It has been known the previous studies pure MG mode emerges superconductors if dispersion fermions exhibits particle-hole (p-h) symmetry. However, clear understanding relation between symmetry Hamiltonian and modes not reached. Here we reveal fundamental connection discrete...

We study collective modes of superfluid Bose gases in optical lattices combined with potential barriers. assume that the system is vicinity quantum phase transition to a Mott insulator at commensurate filling, where emergent particle-hole symmetry gives rise two types mode, namely gapless Nambu-Goldstone (NG) mode and gapful Higgs amplitude mode. consider kinds barrier: One does not break while other does. In presence former barrier, we find bound states have binding energies lower than bulk...

We investigate tunneling properties of Bogoliubov phonons in a Bose-Einstein condensate. find the anomalous enhancement quasiparticle current ${J}_{\mathrm{q}}$ carried by near potential barrier, due to supply excess from This effect leads increase transmission probability low energy region found Kovrizhin et al. also show that twists phase condensate wave function across leading finite Josephson supercurrent ${J}_{\mathrm{s}}$ through barrier. induced flows opposite direction so as cancel...

We investigate tunneling properties of Bogoliubov mode in a Bose-Einstein condensate. Using an exactly solvable model with $\ensuremath{\delta}$-functional barrier, we show that each component the two-component wave function $(u,v)$ low-energy phonon has same form as condensate supercurrent state. As result, currents ${J}_{u}$ and ${J}_{v}$ associated $u$ $v$, respectively, have those carried by Thus, described these two shows perfect transmission. also behaviors still exist presence...

With use of the Kronig-Penney model, we study excitation spectrum a Bose-Einstein condensate in one-dimensional periodic potential. We solve Bogoliubov equations analytically and obtain band structure for arbitrary values lattice depth. find that is gapless linear at low energies, it due to anomalous tunneling low-energy excitations, predicted by Kagan et al.

We study the tunneling of Bogoliubov excitations through a barrier in Bose-Einstein condensate. extend our previous work [S. Tsuchiya and Y. Ohashi, Phys. Rev. A 78, 013628 (2008)] to case when condensate densities are different between left right potential. In framework mean-field theory, we calculate transmission probability phase shift, as well energy flux quasiparticle current carried by excitations. find that phonons twist due back-reaction effect, which induces Josephson supercurrent....