Understanding the interface dynamics in non-equilibrium quantum systems remains a challenge. We study the interface dynamics of strongly coupled immiscible binary superfluids by using holographic duality. The full nonlinear evolution of the binary superfluids with a relative velocity shows rich nonlinear patterns toward quantum turbulence, which is reminiscent of the quantum Kelvin-Helmholtz instability. The wave number of the fast growing modes $k_0$ extracted from the interface pattern yields a non-monotonic dependence of the relative velocity, independent of the temperature and interaction. The value of $k_0$ first increases with the velocity difference and then decreases, which stands in sharp contrast to the results of mean-field theory described by the Gross-Pitaevskii equation and is confirmed by using the linear analyses on top of the stationary configuration. We uncover that the critical velocity associated with the maximum correspond to the case when the mean separation of vortices generated by interface instabilities becomes comparable to the vortex size, which could be a universal physical mechanism at strongly interacting superfluids and is directly testable in laboratory experiments.
We present a mathematically rigorous analysis of the superfluid properties of a Bose-Einstein condensate in the many-body ground state of a one-dimensional model of interacting bosons in a random potential.
Transport in strongly interacting Fermi gases provides a window into the non-equilibrium behavior of strongly correlated fermions. In particular, the interface between a strongly polarized normal gas and a weakly polarized superfluid at finite temperature presents a model for understanding transport at normal-superfluid and normal-superconductor interfaces. An excess of polarization in the normal phase or a deficit of polarization in the superfluid brings the system out of equilibrium, leading to transport currents across the interface. We implement a phenomenological mean-field model of the u…
We report on the observation of a quenched moment of inertia as resulting from superfluidity in a strongly interacting Fermi gas. Our method is based on setting the hydrodynamic gas in slow rotation and determining its angular momentum by detecting the precession of a radial quadrupole excitation. The measurements distinguish between the superfluid or collisional origin of hydrodynamic behavior, and show the phase transition.
We theoretically investigate dynamic structure factors of a strongly interacting Fermi superfluid near an orbital Feshbach resonance with random phase approximation, and find their dynamical characters during the phase transition between a balanced conventional Bardeen-Cooper-Schrieffer superfluid and a polarized Sarma superfluid by continuously varying the chemical potential difference of two spin components. In a BEC-like regime of the BCS superfluid, dynamic structure factors can do help to distinguish the in-phase ground state from the out-of-phase metastable state by the relative location…
Recent experiments on ultracold atoms in optical lattices have synthesized a variety of tunable bands with degenerate double-well structures in momentum space. Such degeneracies in the single particle spectrum strongly enhance quantum fluctuations, and may lead to exotic many-body ground states. Here we consider weakly interacting spinor Bose gases in such bands, and discover a universal quantum "order by disorder" phenomenon which selects a novel chiral spin superfluid with remarkable properties such as spontaneous anomalous spin Hall effect and momentum space antiferromagnetism. For bosons i…
The induced interaction among the majority spin species, due to the presence of the minority species, is computed for the case of a population-imbalanced resonantly-interacting Fermi gas. It is shown that this interaction leads to an instability, at low temperatures, of the recently observed polaron Fermi liquid phase of strongly imbalanced Fermi gases to a p-wave superfluid state. We find that the associated transition temperature, while quite small in the weakly interacting BCS regime, is experimentally accessible in the strongly interacting unitary regime.
We investigate the superfluid state of repulsively interacting three-component (color) fermionic atoms in optical lattices. When the anisotropy of the three repulsive interactions is strong, atoms of two of the three colors form Cooper pairs and atoms of the third color remain a Fermi liquid. An effective attractive interaction is induced by density fluctuations of the third-color atoms. This superfluid state is stable against changes in filling close to half filling. We determine the phase diagrams in terms of temperature, filling, and the anisotropy of the repulsive interactions.
We investigate the nature of superfluid pairing in a strongly interacting Fermi gas near orbital Feshbach resonances with spin-population imbalance in three dimensions, which can be well described by a two-band or two-channel model. We show that a Sarma superfluid with gapless single-particle excitations is favored in the closed channel at large imbalance. It is thermodynamically stable against the formation of an inhomogeneous Fulde\textendash Ferrell\textendash Larkin\textendash Ovchinnikov superfluid and features a well-defined Goldstone-Anderson-Bogoliubov phonon mode and a massive Leggett…
Motivated by recent advance in orbitally tuned Feshbach resonance experiments, we analyze the ground-state phase diagram and related low-energy excitation spectra of a d-wave interacting Bose gas. A two-channel model with d-wave symmetric interactions and background s-wave interactions is adopted to characterize the gas. The ground state is found to show three interesting phases: atomic, molecular, and atomic-molecular superfluidity. Remarkably differently from what was previously known in the p-wave case, the atomic superfluid is found to be momentum-independent in the present d-wave case. Bo…
We study the localization of collective pair excitations in weakly-interacting Bose superfluids in one-dimensional quasiperiodic lattices. The localization diagram is first determined numerically. For intermediate interaction and quasiperiodic amplitude we find a sharp localization transition, with extended low-energy states and localized high-energy states. We then develop an analytical treatment, which allows us to quantitatively map the localization transition into that of an effective multiharmonic quasiperiodic system.
We use a path integral approach to calculate the superfluid density of a Bose lattice gas in the limit where the number of atoms per site is large. Our analytical expressions agree with numerical results on small systems for low temperatures and relatively weak interactions. We also calculate the superfluid density and drag for two-component lattice bosons. To attain the correct results we develop tools for calculating discrete time path integrals. These tools should be broadly applicable to a range of systems which are naturally described within an overcomplete basis.
We propose a new theoretical formalism which describes the Bose Einstein condensation of weakly interacting bosons with finite life time interacting with a thermal bath. We show that if a quasi-thermal distribution function of particles is achieved, the elementary excitations of the condensate show a linear spectrum characteristic of a superfluid, with a renormalized sound velocity with respect to the equilibrium case.
We discuss quantum fluctuations of the interface between a superfluid and a Mott-insulating state of ultracold atoms in a trap. The fluctuations of the boundary are due to a new type of surface modes, whose spectrum is similar (but not identical) to classical capillary waves. The corresponding quantum capillary length sets the scale for the penetration of the superfluid into the Mott-insulating regime by the proximity effect and may be on the order of several lattice spacings. It determines the typical magnitude of the interface width due to quantum fluctuations, which may be inferred from sin…
We report the observation of many-body interaction effects for a homonuclear bosonic mixture in a three-dimensional optical lattice with variable state dependence along one axis. Near the superfluid-to-Mott insulator transition for one component, we find that the presence of a second component can reduce the apparent superfluid coherence, most significantly when it either experiences a strongly localizing lattice potential or none at all. We examine this effect by varying the relative populations and lattice depths, and discuss the observed behavior in view of recent proposals for scattering f…
Theoretical predictions for the dynamic structure factor of a harmonically trapped Fermi superfluid near the BEC-BCS crossover are compared with recent Bragg spectroscopy measurements at large transferred momenta. The calculations are based on a random-phase (or time-dependent Hartree-Fock-Gorkov) approximation generalized to the strongly interacting regime. Excellent agreement with experimental spectra at low temperatures is obtained, with no free parameters. Theoretical predictions for zero-temperature static structure factor are also found to agree well with the experimental results and ind…
We theoretically investigate the critical behavior of second sound mode in a harmonically trapped ultracold atomic Fermi gas with resonant interactions. Near the superfluid phase transition with critical temperature $T_{c}$, the frequency or the sound velocity of second sound mode depends crucially on the critical exponent $β$ of superfluid fraction. In an isotropic harmonic trap, we predict that the mode frequency diverges like $(1-T/T_{c})^{β-1/2}$ when $β<1/2$. In a highly elongated trap, the speed of second sound reduces by a factor $1/\sqrt{2β+1}$ from that in a homogeneous three-dimensio…
Using the Gaussian pair fluctuation theory, we investigate quantum fluctuations of a strongly interacting two-dimensional chiral \textit{p}-wave Fermi superfluid at the transition from a Bose-Einstein condensate (BEC) to a topologically non-trivial Bardeen-Cooper-Schrieffer (BCS) superfluid. Near the topological phase transition at zero chemical potential, $μ=0$, we observe that quantum fluctuations strongly renormalize the zero-temperature equations of state, sound velocity, pair-breaking velocity, and Berezinskii-Kosterlitz-Thouless (BKT) critical temperature of the Fermi superfluid, all of …
Two-dimensional superfluidity and quantum turbulence are directly connected to the microscopic dynamics of quantized vortices. However, surface effects have prevented direct observations of coherent vortex dynamics in strongly-interacting two-dimensional systems. Here, we overcome this challenge by confining a two-dimensional droplet of superfluid helium at microscale on the atomically-smooth surface of a silicon chip. An on-chip optical microcavity allows laser-initiation of vortex clusters and nondestructive observation of their decay in a single shot. Coherent dynamics dominate, with therma…
It is of central importance to probe the \emph{local} spectral function $A(\mathbf{k},ω)$ of a strongly interacting Fermi gas in a trap. Momentum resolved rf spectroscopy has been demonstrated to be able to probe the trap averaged $A(\mathbf{k},ω)$. However, the usefulness of this technique was limited by the trap inhomogeneity. Independent of a specific theory, here we propose that by studying the momentum resolved rf spectra of the minority fermions of a phase separated, population imbalanced Fermi gas at low temperature, one can effectively extract $A(\mathbf{k},ω)$ of a homogeneous superfl…
We have observed the superfluid phase transition in a strongly interacting Fermi gas via high-precision measurements of the local compressibility, density and pressure down to near-zero entropy. Our data completely determine the universal thermodynamics of strongly interacting fermions without any fit or external thermometer. The onset of superfluidity is observed in the compressibility, the chemical potential, the entropy, and the heat capacity. In particular, the heat capacity displays a characteristic lambda-like feature at the critical temperature of $T_c/T_F = 0.167(13)$. This is the firs…
Superfluidity is a macroscopic quantum phenomenon, which shows up below a critical temperature and leads to a peculiar behavior of matter, with frictionless flow, the formation of quantized vortices, and the quenching of the moment of inertia being intriguing examples. A remarkable explanation for many phenomena exhibited by a superfluid at finite temperature can be given in terms of a two-fluid mixture comprised of a normal component that behaves like a usual fluid and a superfluid component with zero viscosity and zero entropy. Important examples of superfluid systems are liquid helium and n…
By studying the 2-dimensional Su-Schrieffer-Heeger-Bose-Hubbard model, we show the existence of topological Higgs amplitude modes in the strongly interacting superfluid phase. Using the slave boson approach, we find that, in the large filling limit, the Higgs excitations and the Goldstone excitations above the ground state are well decoupled, and both of them exhibit nontrivial topology inherited from the underlying noninteracting bands. At finite fillings, they become coupled at high energies; nevertheless, the topology of these modes are unchanged. Moreover, based on an effective action anal…
An iterative scheme based on the kernel polynomial method is devised for the efficient computation of the one-body density matrix of weakly interacting Bose gases within Bogoliubov theory. This scheme is used to analyze the coherence properties of disordered bosons in one and two dimensions. In the one-dimensional geometry, we examine the quantum phase transition between superfluid and Bose glass at weak interactions, and we recover the scaling of the phase boundary that was characterized using a direct spectral approach by Fontanesi et al. [Phys. Rev. A 81, 053603 (2010)]. The kernel polynomi…
We study the dynamics of a vortex in a quasi two-dimensional Bose gas consisting of light matter coupled atoms forming two-component pseudo spins. The gas is subject to a density dependent gauge potential, hence governed by an interacting gauge theory, which stems from a collisionally induced detuning between the incident laser frequency and the atomic energy levels. This provides a back-action between the synthetic gauge potential and the matter field. A Lagrangian approach is used to derive an expression for the force acting on a vortex in such a gas. We discuss the similarities between this…
We uncover current-bias characteristics of superfluid-normal state junctions with weakly-interacting Bose gases. It is shown that in the presence of a chemical potential bias the characteristics can strongly be asymmetric for origin. The salient feature that is absent in the fermionic counterpart arises from a tunneling process associated with a condensate and a bosonic Andreev reflection process. It turns out that such processes are intrinsically nonlinear and therefore do not obey Ohm's law even at a low bias. In addition, the remaining processes are found to obey Ohm's law and become domina…
We review our theoretical analysis of repulsively interacting three-component fermionic atoms in optical lattices. We discuss quantum phase transitions at around half filling with a balanced population by focusing on Mott transitions, staggered ordering, and superfluidity. At half filling (with 3/2 atoms per site), characteristic Mott transitions are induced by the anisotropic interactions, where two-particle repulsions between any two of the three colors have different strengths. At half filling, two types of staggered ordered states appear at low temperatures depending on the anisotropy of t…
We investigate the zero-temperature quasiparticle properties of a mobile impurity immersed in a strongly interacting Fermi superfluid at the crossover from a Bose-Einstein condensate (BEC) to a Bardeen--Cooper--Schrieffer (BCS) superfluid, by using a many-body $T$-matrix approach that excludes Efimov trimer bound states. Termed BEC-BCS crossover polaron, or crossover polaron in short, this quasiparticle couples to elementary excitations of a many-body background and therefore could provide a useful probe of the underlying strongly interacting Fermi superfluid. Due to the existence of a signifi…
We study a model of interacting bosons that occupy the first excited p-band states of a two-dimensional optical lattice. In contrast to the much studied single band Bose-Hubbard Hamiltonian, this more complex model allows for non-trivial superfluid phases associated with condensation at non-zero momentum and staggered order of the orbital angular momentum in addition to the superfluid-Mott insulator transition. More specifically, we observe staggered orbital angular momentum order in the Mott phase at commensurate filling and superfluidity at all densities. We also observe a transition between…
The presence of attractive interaction between fermions can lead to pairing and superfluidity in an optical lattice. The temperature needed to observe superfluidity is about a tenth of the tunneling energy in the optical lattice, and currently beyond experimental reach. However, at strong coupling the precursors to global superfluidity should be visible at achievable temperatures, in terms of fluctuating domains with strong pairing correlations. We explore this regime of the attractive two dimensional fermion Hubbard model, in the presence of a confining potential, using a new Monte Carlo tech…
Chiral $p$-wave superfluids are fascinating topological quantum states of matter that have been found in the liquid $^3$He-A phase and arguably in the electronic Sr$_2$RuO$_4$ superconductor. They are shown fundamentally related to the fractional $5/2$ quantum Hall state which supports fractional exotic excitations. A common understanding is that such states require spin-triplet pairing of fermions due to $p$-wave interaction. Here we report by controlled theoretical approximation that a center-of-mass Wannier $p$-wave chiral superfluid state can arise from spin-singlet pairing for an $s$-wave…
Near a continuous phase transition, systems with different microscopic origins display universal dynamics if their underlying symmetries are compatible. In a thermally quenched system, the Kibble-Zurek mechanism for the creation of topological defects unveils this universality through a characteristic power-law exponent, which captures the dependence of the defect density on the quench rate. Here, we report the observation of the Kibble-Zurek universality in a strongly interacting Fermi superfluid. As the system's microscopic description is tuned from bosonic to fermionic, the quench formation…
We study the one-dimensional Bose gas in spatially correlated disorder at zero temperature, using an extended density-phase Bogoliubov method. We analyze in particular the decay of the one-body density matrix and the behaviour of the Bogoliubov excitations across the phase boundary. We observe that the transition to the Bose glass phase is marked by a power-law divergence of the density of states at low energy. A measure of the localization length displays a power-law energy dependence in both regions, with the exponent equal to -1 at the boundary. We draw the phase diagram of the superfluid-i…
We report on the observation of Faraday waves in a cigar-shaped Fermi superfluid of $^6$Li parametrically excited by modulating the radial trap frequency. We characterize the phenomenon as a function of the interaction parameter by means of a Feshbach resonance. Starting from the BEC side of the resonance we observe a drop on the visibility of the Faraday pattern as we approach to unitarity, possibly due to the increased incompressibility of the system. We probe the superfluid excitation spectrum by extracting an effective 1D speed of sound for different values of the interaction parameter, in…
We map the infrared dynamics of a relativistic single component ($N=1$) interacting scalar field theory to that of nonrelativistic complex scalar fields. The Gross-Pitaevskii (GP) equation, describing the real time dynamics of single component ultracold Bose gases, is obtained at first nontrivial order in an expansion proportional to the powers of $λϕ^2/m^2$ where $λ$, $ϕ$ and $m$ are the coupling constant, the scalar field and the particle mass respectively. Our analytical studies are corroborated by numerical simulations of the spatial and momentum structure of overoccupied scalar fields in …
We examine the superfluid properties of a 1D Bose gas in a ring trap based on the model of Lieb and Liniger. While the 1D Bose gas has nonclassical rotational inertia and exhibits quantization of velocities, the metastability of currents depends sensitively on the strength of interactions in the gas: the stronger the interactions, the faster the current decays. It is shown that the Landau critical velocity is zero in the thermodynamic limit due to the first supercurrent state, which has zero energy and finite probability of excitation. We calculate the energy dissipation rate of ring currents …
Using perturbed Bogoliubov equations, we study the linear response to a weak orbital magnetic field of the heat conductivity of the normal-superfluid interface of a polarized Fermi gas at sufficiently low temperature. We consider the various scattering regions of the BCS regime and analytically obtain the transmission coefficients and the heat conductivity across the interface in an arbitrary weak orbital field. For a definite choice of the field, we consider various values of the scattering length in the BCS range and numerically obtain the allowed values of the average and species-imbalance …
Non-Hermitian quantum many-body systems are a fascinating subject to be explored. Using the generalized density matrix renormalisation group method and complementary exact diagonalization, we elucidate the many-body ground states and dynamics of a 1D interacting non-Hermitian Aubry-Andre-Harper model for bosons. We find stable ground states in the superfluid and Mott insulating regimes under wide range of conditions in this model. We reveal a skin superfluid state induced by the non-Hermiticity from the nonreciprocal hopping. We investigate the topology of the Mott insulating phase and find it…
A perturbative way to investigate superfluid properties of various systems under nonuniform potential is presented. We derive the perturbation expansion of the superfluid fraction, which indicates how liquid exhibits nonclassical rotational inertia, in terms of the strength of nonuniform potential and find that the coefficient of the leading term reflects the density fluctuation of the system. Our formulation does not assume anything about Bose-Einstein condensation and thus is applicable to wide variety of systems. Superfluid properties of some examples including (non-)interacting Bose system…
We present a series of theoretical studies of the boundary between a superfluid and normal region in a partially polarized gas of strongly interacting fermions. We present mean-field estimates of the surface energy in this boundary as a function of temperature and scattering length. We discuss the structure of the domain wall, and use a previously introduced phenomonological model to study its influence on experimental observables. Our microscopic mean-field calculations are not consistent with the magnitude of the surface tension found from our phenomonological modelling of data from the Rice…
Motivated by the recent experiment [Takafumi Tomita \emph{et al.}, Sci. Adv. {\bf 3}, (2017)], we study the dynamics of interacting bosons in a two-dimensional optical lattice with local dissipation. Together with the Gutzwiller mean-field theory for density matrices and Lindblad master equation, we show how the onsite interaction between bosons affects the particle loss for various strengths of dissipation. For moderate dissipation, the trend in particle loss differs significantly near the superfluid-Mott boundary than the deep superfluid regime. While the loss is suppressed for stronger diss…
We study the critical vortex shedding in a strongly interacting fermionic superfluid of $^{6}$Li across the BEC-BCS crossover. By moving an optical obstacle in the sample and directly imaging the vortices after time of flight, the critical velocity $v_{\rm c}$ for vortex shedding is measured as a function of the obstacle travel distance $L$. The observed $v_{\rm c}$ increases with decreasing $L$, where the rate of increase is the highest in the unitary regime. In the deep BEC regime, an empirical dissipation model well captures the dependence of $v_{\rm c}$ on $L$, characterized by a constant …
We study the quantum fluctuations in the condensates of a mixture of bosonic atoms and molecules with interspecies p-wave interaction. Our analysis shows that the quantum phase of coexisting atomic and molecular condensates is unstable at the mean-field level. Unlike the mixture of s-wave interaction, the Lee-Huang-Yang correction of p-wave interaction is unexpectedly found here to exhibit an opposite sign with respect to its mean-field term above a critical particle density. This quantum correction to the mean-field energy provides a remarkable mechanism to self-stabilize the phase. The order…
The flow of a uniform Bose gas at speeds greater than the Landau critical velocity, v_c, does not necessarily destroy superfluidity, but rather need only lead to a decrease of the superfluid mass density, ρ_s. Analyzing a weakly interacting Bose gas with a finite range interparticle interaction that leads to a Landau critical velocity at non-zero quasiparticle momentum, we explicitly construct the (non-uniform) condensate for fluid flow faster than v_c and calculate the accompanying decrease in ρ_s. We briefly comment on the relation of the physics to other problems in superfluids, e.g., solit…
We theoretically study the ground-state phase diagram of strongly interacting bosons on a generalized zig-zag ladder model, the rail-road trestle (RRT) model. By means of analytical arguments in the limits of decoupled chains and the case of vanishing fillings as well as extensive DMRG calculations we examine the rich interplay between frustration and interaction for various parameter regimes. We distinguish three different cases, the fully frustrated RRT model where the dispersion relation becomes doubly degenerate and an extensive chiral superfluid regime is found, the anti-symmetric RRT wit…
Recent advanced experimental implementations of optical lattices with highly tunable geometry open up new regimes for quantum many-body states of matter that previously had not been accessible. Here we introduce a symmetry-based method of utilizing the geometry of optical lattice to systematically control topologically non-trivial orbital hybridization. Such an orbital mixing leads to an unexpected and yet robust topological semimetal at single-particle level for a gas of fermionic atoms. When considering s-wave attractive interaction between atoms as for instance tuned by Feshbach resonance, …
We theoretically investigate the effects of pairing fluctuations in an ultracold Fermi gas near a Feshbach resonance with a negative effective range. By employing a many-body T-matrix theory with a coupled boson-fermion model, we show that the single-particle density of states exhibits the so-called pseudogap phenomenon which is a precursor of superfluidity induced by strong pairing fluctuations. We clarify the region where strong pairing fluctuations play a crucial role in single-particle properties, from the broad-resonance region to the narrow-resonance limit at the divergent two-body scatt…
Motivated by experimental advances in the synthesis of gauge potentials for ultracold atoms, we consider the superfluid phase of interacting bosons on a square lattice in the presence of a magnetic field. We show that superfluid order implies spatial symmetry breaking, and predict clear signatures of many-body effects in time-of-flight measurements. By developing a Bogoliubov expansion based on the exact Hofstadter spectrum, we find the dispersion of the quasiparticle modes within the superfluid phase, and describe the consequences for Bragg spectroscopy measurements. The theory also provides …
We theoretically investigate sound modes in a weakly-interacting collisional Bose gas in $D$ dimensions. Using the Landau's two-fluid hydrodynamics and working within the Bogoliubov theory, we observe the hybridization of the first and second sound modes for $D\ge 2$. To model the recent measurements of the sound velocities in 2D, obtained in the weakly-interacting regime and around the Berezinskii-Kosterlitz-Thouless transition temperature, we derive a refined calculation of the superfluid density, finding a fair agreement with the experiment. In the 1D case, for which experimental results ar…
We study the instability of a mixture of two interacting counter-flowing superfluids. For a homogeneous system, we show that superfluid hydrodynamics leads to the existence of a dynamical instability at a critical value of the relative velocity $v_{cr}$. When the interspecies coupling is small the critical value approaches the value $v_{cr}=c_1+c_2$, given by the sum of the sound velocities of the two uncoupled superfluids, in agreement with the recent prediction of [1] based on Landau's argument. The crucial dependence of the critical velocity on the interspecies coupling is explicitly discus…
