Ultracold quantum gases are highly controllable and, thus, capable of simulating difficult quantum many-body problems ranging from condensed matter physics to astrophysics. Although experimental realizations have so far been restricted to flat geometries, recently also curved quantum systems, with the prospect of exploring tunable geometries, are produced in microgravity facilities as ground-based experiments are technically limited. Here we analyze bubble-trapped condensates, in which the atoms are confined on the surface of a thin spherically-symmetric shell by means of external magnetic fields. A thermally-induced proliferation of vorticity yields a vanishing of superfluidity. We describe the occurrence of this topological transition by conceptually extending the theory of Berezinskii, Kosterlitz and Thouless for infinite uniform systems to such finite-size systems. Unexpectedly, we find universal scaling relations for the mean critical temperature and the finite width of the superfluid transition. Furthermore, we elucidate how they could be experimentally observed in finite-temperature hydrodynamic excitations.
Based on a unified theoretical treatment of the 1D Bogoliubov-de Genes equations, the superfluidity phenomenon of the Bose-Einstein condensates (BEC) loaded into trapped optical lattice is studied. Within the perturbation regime, an all-analytical framework is presented enabling a straightforward phenomenological mapping of the collective excitation and oscillation character of a trapped BEC where the available experimental configurations also fit.
As the Earth rotates, the Coriolis force causes several oceanic and atmospheric waves to be trapped along the equator, including Kelvin, Yanai, Rossby, and Poincaré modes. It has been demonstrated that the mathematical origin of these waves is related to the nontrivial topology of the underlying hydrodynamic equations. Inspired by recent observations of Bose-Einstein condensation (BEC) in bubble-shaped traps in microgravity ultracold quantum gas experiments, we show that equatorial modes are supported by a rapidly rotating condensate in a spherical geometry. Based on a zero-temperature coarse-…
This paper reports the model free determination of the two-fluid dynamics in a trapped two-dimensional Bose gas, relying on a local principal component analysis of the dynamics after a sudden excitation.
We theoretically investigate the pair-superfluid phase of two-component ultracold gases with negative inter-species interactions in an optical lattice. We establish the phase diagram for filling $n=1$ at zero and finite temperature, by applying Bosonic Dynamical Mean-Field Theory, and confirm the stability of pair-superfluidity for asymmetric hopping of the two species. While the pair superfluid is found to be robust in the presence of a harmonic trap, we observe that it is destroyed already by a small population imbalance of the two species.
Superfluidity is a fascinating phenomenon that, at the macroscopic scale, leads to dissipationless flow and the emergence of vortices. While these macroscopic manifestations of superfluidity are well described by theories that have their origin in Landau's two-fluid model, our microscopic understanding of superfluidity is far from complete. Using analytical and numerical \textit{ab initio} approaches, this paper determines the superfluid fraction and local superfluid density of small harmonically trapped two-component Fermi gases as a function of the interaction strength and temperature. At lo…
We study soliton oscillations in a trapped superfluid Fermi gas across the Bose-Einstein condensate to Bardeen-Cooper-Schrieffer (BEC-BCS) crossover. We derive an exact equation relating the phase jump across the soliton to its energy, and hence obtain an expression for the soliton period. Our analytic approach is supported by simulations of the time-dependent Bogoliubov-de Gennes equations, which show that the period dramatically increases as the soliton becomes shallower on the BCS side of the resonance. Finally, we propose an experimental protocol to test our predictions.
I study vortex ring oscillations in a superfluid, trapped in an elongated trap, under the conditions of the Local Density Approximation. On the basis of the Hamiltonian formalism I develop a hydrodynamic theory, which is valid for an arbitrary superfluid and depends only on the equation of state. The problem is reduced to an ordinary differential equation for the ring radius. The cases of the dilute BEC and the Fermi gas at unitarity are investigated in detail. Simple analytical equations for the periods of small oscillations are obtained and the equations of non-linear dynamics are solved in …
We develop the Hartree-Fock-Bogoliubov theory at finite temperature for Bose gas trapped in the two dimensional optical lattices. The on-site energy is considered low enough that the gas presents superfluid properties. We obtain the condensate density as function of the temperature neglecting the anomalous density in the thermodynamics equations. The condensate fraction provide two critical temperature. Below the temperature $T_{C1}$ there is one condensate fraction. Above two possible fractions merger up to the critical temperature $T_{C2}$. Then the gas provides an first order transition at …
We investigate equilibration processes shortly after sudden perturbations are applied to ultracold trapped superfluids. We show the similarity of phase imprinting and localized density depletion perturbations, both of which initially are found to produce "phase walls". These planar defects are associated with a sharp gradient in the phase. Importantly they relax following a quite general sequence. Our studies, based on simulations of the complex time-dependent Ginzburg-Landau equation, address the challenge posed by these experiments: how a superfluid eventually eliminates a spatially extended…
We numerically model experiments on the superfluid critical velocity of an elongated, harmonically trapped Bose-Einstein condensate as reported by [P. Engels and C. Atherton, Phys. Rev. Lett. 99, 160405 (2007)]. These experiments swept an obstacle formed by an optical dipole potential through the long axis of the condensate at constant velocity. Their results found an increase in the resulting density fluctuations of the condensate above an obstacle velocity of $v\approx 0.3$ mm/s, suggestive of a superfluid critical velocity substantially less than the average speed of sound. However, our ana…
We study the stability region of the topological superfluid phase in a trapped two-dimensional polarized Fermi gas with spin-orbit coupling and across a BCS-BEC crossover. Due to the competition between polarization, pairing interaction and spin-orbit coupling, the Fermi gas typically phase separates in the trap. Employing a mean field approach that guarantees the ground state solution, we systematically study the structure of the phase separation and investigate in detail the optimal parameter region for the preparation of the topologically non-trivial superfluid phase. We then calculate the …
The stability conditions for the singular vortex which accompanies Majorana zero modes at the core are investigated for p-wave resonant superfluids of atomic Fermi gases. Within the Ginzburg-Landau framework we determine the stable conditions in the parameter space for the external rotation frequency and the harmonic trap frequency. There exists the narrow stable region in this parameter space for quasi-two-dimensional condensates. We also describe the detailed characterizations of the spatial structure of the order parameter in the chiral p-wave superfluids under rotation.
We have studied the exotic superfluid phases of degenerated Fermi gases with spin-orbit coupling in a mixed dimensional system, where the motion of atoms are free in the x-direction and the tunneling between nearest tubes in the y-direction is permitted. Using the mean-field method, we obtain the phase diagrams of the system during the dimensional crossover between quasi one dimension to quasi two dimension. We find the existence of the topological state and Majorana edge mode in the weak tunneling case, and a rich phase diagram including two kinds of nodal superfluid phase and gapped superflu…
We investigate pseudogap phenomena in the unitarity limit of a trapped superfluid Fermi gas. Including effect of strong pairing fluctuations within a $T$-matrix approximation, as well as effects of a harmonic trap within the local density approximation (LDA), we calculate the local superfluid density of states below the superfluid phase transition temperature $T_{\rm c}$. We show that the spatial region where single-particle excitations are dominated by the pseudogap may still exist even below $T_{\rm c}$, due to inhomogeneous pairing fluctuations caused by the trap potential. From the tempera…
We investigate strong pairing fluctuations and effects of a harmonic trap in the superfluid phase of an ultracold Fermi gas. Including amplitude and phase fluctuations of the inhomogeneous superfluid order parameter $Δ(r)$ in a trap within a combined $T$-matrix theory with the local density approximation, we examine local properties of single-particle excitations and a thermodynamic quantity in the BCS-BEC crossover region. Below the superfluid phase transition temperature $T_{\rm c}$, we show that inhomogeneous pairing fluctuations lead to a shell structure of the gas cloud in which the spati…
We investigate the superfluid properties of a dipolar Bose-Einstein condensate (BEC) in a fully three-dimensional trap. Specifically, we calculate a superfluid critical velocity for this system by applying the Landau criterion to its discrete quasiparticle spectrum. We test this critical velocity by direct numerical simulation of condensate depletion as a blue-detuned laser moves through the condensate. In both cases, the presence of the roton in the spectrum serves to lower the critical velocity beyond a critical particle number. Since the shape of the dispersion, and hence the roton minimum,…
We study ultra-cold dipolar excitons confined in a 10$μ$m trap of a double GaAs quantum well. Based on the local density approximation, we unveil for the first time the equation of state of excitons at pure thermodynamic equilibrium. In this regime we show that, below a critical temperature of about $1$ Kelvin, a superfluid forms in the inner region of the trap at a local exciton density $n \sim 2-3 \, 10^{10} \text{cm}^{-2}$, encircled by a more dilute and normal component in the outer rim of the trap. Remarkably, this spatial arrangement correlates directly with the concentration of defects …
We describe the emergence of superfluid phases of ultracold dipolar fermions in optical lattices for two-dimensional systems. Considering the many-body screening of dipolar interactions at intermediate and larger filling factors, we show that several superfluid phases with distinct pairing symmetries naturally arise in the singlet channel: local s-wave $(sl)$, extended s-wave $(se)$, d-wave $(d)$ or time-reversal-symmetry breaking $(sl + se \pm id)$-wave. We obtain the temperature versus filling factor phase diagram and show that d-wave pairing is favored near half-filling, that $(sl + se)$-wa…
We study a system of periodic Bose condensed atoms coupled to cavity photons using the input-output formalism. We show that the cavity will either act as a through pass Lorentzian filter when the superfluid fraction of the condensate is minimum or completely reflect the input field when the superfluid fraction is maximum. We show that by monitoring the ratio between the transmitted field and the reflected field, one can estimate the superfluid fraction.
A Rossby-Haurwitz (RH) wave is an excitation mode of a fluid on a rotating spherical surface, which propagates westward in the rotating frame of reference. Motivated by the recent realization of the shell-shaped Bose-Einstein condensate in microgravity, we investigate the RH wave in a superfluid rotating on a spherical-surface geometry. We employ the point-vortex model and the three-dimensional Gross-Pitaevskii equation, and numerically demonstrate that RH waves can be observed in the system of a superfluid with quantized vortices.
We study thermal properties of a trapped Bose-Bose mixture in a dilute regime using quantum Monte Carlo methods. Our main aim is to investigate the dependence of the superfluid density and the condensate fraction on temperature, for the mixed and separated phases. To this end, we use the diffusion Monte Carlo method, in the zero-temperature limit, and the path-integral Monte Carlo method for finite temperatures. The results obtained are compared with solutions of the coupled Gross-Pitaevskii equations for the mixture at zero temperature. We notice the existence of an anisotropic superfluid den…
We apply a recently developed effective string theory for vortex lines to the case of two-dimensional trapped superfluids. We do not assume a perturbative microscopic description for the superfluid, but only a gradient expansion for the long-distance hydrodynamical description and for the trapping potential. For any regular trapping potential, we compute the spatial dependence of the superfluid density and the orbital frequency and trajectory of an off-center vortex. Our results are fully relativistic, and in the non-relativistic limit reduce to known results based on the Gross-Pitaevskii mode…
We consider the problem of spin-triplet p-wave superfluid pairing with total spin projection $m_s=0$ in atomic Fermi gas across the Feshbach resonance. We allow for imbalanced populations and take into account the effects due to presence of a parabolic trapping potential. Within the mean-field approximation for the one- and two-channel pairing models we show that depending on the distance from the center of a trap at least two superfluid states will have the lowest energy. Superfluid shells which emerge in a trap may have two out of three angular components of the p-wave superfluid order param…
We present phase diagrams for population imbalanced, trapped Fermi superfluids near unitarity. In addition to providing quantitative values for the superfluid transition temperature, the pairing onset temperature and the transition line (separating the Sarma and phase separation regimes), we study experimental signatures of these transitions based on density profiles and density differences at the center. Predictions on the BCS side of resonance show unexpected behavior, which should be searched for experimentally.
We extend our recent work [Y. Endo et. al., Phys. Rev. 92, 023610 (2015)] for a parity-mixing effect in a model two-dimensional lattice fermions to a realistic three-dimensional ultracold Fermi gas. Including effects of broken local spatial inversion symmetry by a trap potential within the framework of the real-space Bogoliubov-de Gennes theory at $T=0$, we point out that an odd-parity $p$-wave Cooper-pair amplitude is expected to have already been realized in previous experiments on an (even-parity) $s$-wave superfluid Fermi gas with spin imbalance. This indicates that, when one suddenly chan…
The vortex nucleation and the emergence of quantum turbulence induced by oscillating magnetic fields, introduced by Henn E A L, et al. 2009 (Phys. Rev. A 79, 043619) and Henn E A L, et al. 2009 (Phys. Rev. Lett. 103, 045301), left a few open questions concerning the basic mechanisms causing those interesting phenomena. Here, we report the experimental observation of the slosh dynamics of a magnetically trapped $^{87}$Rb Bose-Einstein condensate (BEC) under the influence of a time-varying magnetic field. We observed a clear relative displacement in between the condensed and the thermal fraction…
We consider quantized vortices in two-component Bose-Einstein condensates and three-component Fermi gases with attractive interactions. In these systems, the vortex core can be either empty (normal in the fermion case) or filled with another superfluid. We determine critical values of the parameters -- chemical potentials, scattering lengths and, for Fermi gases, temperature -- at which a phase transition between the two types of vortices occurs. Population imbalance can lead to superfluid core (coreless) vorticity in multicomponent superfluids which otherwise support only usual vortices. For …
We propose and analyze a variational wave function for a population-imbalanced one-dimensional Fermi gas that allows for Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) type pairing correlations among the two fermion species, while also accounting for the harmonic confining potential. In the strongly interacting regime, we find large spatial oscillations of the order parameter, indicative of an FFLO state. The obtained density profiles versus imbalance are consistent with recent experimental results as well as with theoretical calculations based on combining Bethe ansatz with the local density approxi…
We present a theory of a two-component atomic Fermi gas with tunable attractive contact interactions on a spherical shell going through the Bardeen-Cooper-Schrieffer (BCS) - Bose Einstein condensation (BEC) crossover, inspired by the realizations of spherical bubble traps for ultracold atoms in microgravity. The derivation follows the BCS-Leggett theory to obtain the gap and number equations. The BCS-BEC crossover can be induced by tuning the interaction, and the properly normalized gap and chemical potential exhibit universal behavior regardless of the planar or spherical geometry. Neverthele…
We present an investigation of generation, dynamics and stability of dark solitons in anisotropic Fermi gases for a range of particle numbers and trap aspect ratios within the framework of the order-parameter equation. We calculate the periods of dark solitons oscillating in a trap, and find a good agreement with the results based on the Bogoliubov-de Gennes equations. By studying the stability of initially off-center dark solitons under various tight transverse confinements in the unitarity limit, we not only give the criterion of dynamical stability, but also find that the soliton and a hybr…
From an extensive calculation of static properties of a trapped Fermi superfluid at zero temperature using a density-functional formulation, we demonstrate a universal behavior of its observables, such as energy, chemical potential, radius etc., over the crossover from the BCS limit to unitarity leading to scaling over many orders of magnitude in fermion number. This scaling allows to predict the static properties of the system, with a large number ($\sim 10^5$) of fermions, over the crossover with an error of 1-2%, from the knowledge of those for a small number ($\sim 10$) of fermions.
Using quantum Monte Carlo simulations, we investigate the finite-temperature phase diagram of hard-core bosons (XY model) in two- and three-dimensional lattices. To determine the phase boundaries, we perform a finite-size-scaling analysis of the condensate fraction and/or the superfluid stiffness. We then discuss how these phase diagrams can be measured in experiments with trapped ultracold gases, where the systems are inhomogeneous. For that, we introduce a method based on the measurement of the zero-momentum occupation, which is adequate for experiments dealing with both homogeneous and trap…
Zero-point energy of a trapped ultracold Fermi gas at unitarity: squeezing the Heisenberg uncertainty principle and suppressing the Pauli principle to produce a superfluid state
Specific topological excitations of energetically stable "core-and-mantle" configurations of trapped two-component immiscible Bose-Einstein condensates are studied numerically within the coupled Gross-Pitaevskii equations. Non-stationary long-lived coherent structures, that consist of several quantum vortex filaments penetrating the "mantle" from outside to inside and vice-versa and demonstrate quite nontrivial dynamics, are observed in simulations for the first time. The ends of filaments can remain attached to the interface between the "mantle" and the "core" if the latter is large enough wh…
We find a new physical regime in the trapped Bose-Hubbard Hamiltonian using time-evolving block decimation. Between Mott-insulating and superfluid phases, the latter induced by trap compression, a spatially self-organized state appears in which non-local entropy signals entanglement between spatially distant superfluid shells. We suggest a linear rather than harmonic potential as an ideal way to observe such a self-organized system. We also explore both quantum information and thermal entropies in the superfluid regime, finding that while the former follows the density closely the latter can b…
We investigate the possibility that the broken spatial inversion symmetry by a trap potential induces a spin-triplet Cooper-pair amplitude in an $s$-wave superfluid Fermi gas. Being based on symmetry considerations, we clarify that this phenomenon may occur, when a spin rotation symmetry of the system is also broken. We also numerically confirm that a triplet pair amplitude is really induced under this condition, using a simple model. Our results imply that this phenomenon is already present in a trapped $s$-wave superfluid Fermi gas with spin imbalance. As an interesting application of this p…
We show that the Bose-Hubbard Model exhibits an increase in density with temperature at fixed pressure in the regular fluid regime and in the superfluid phase. The anomaly at the Bose-Einstein condensate is the first density anomaly observed in a quantum state. We propose that the mechanism underlying both the normal phase and the superfluid phase anomalies is related to zero point entropies and ground state phase transitions. A connection with the typical experimental scales and setups is also addressed. This key finding opens a new pathway for theoretical and experimental studies of water-li…
We investigate a procedure to generate turbulence in a trapped Bose-Einstein condensate which takes advantage of the decay of multicharged vortices. We show that the resulting singly-charged vortices twist around each other, intertwined in the shape of helical Kelvin waves, which collide and undergo vortex reconnections, creating a disordered vortex state. By examining the velocity statistics, the energy spectrum, the correlation functions and the temporal decay, and comparing these properties with the properties of ordinary turbulence and observations in superfluid helium, we conclude that th…
Trapped ultra-cold atom experiments provide a unique opportunity to understand Bose-Fermi superfluid mixtures occurring in contrasting areas of physics. At present there are several atom-trap experiments that could potentially explore this superfluid-mixture regime, thus warranting a detailed understanding of the occurrence and stability of various possible thermodynamic phases in the mixture. In the present work, we therefore construct the finite temperature phase diagram of an interacting atomic mixture of Bose and Fermi superfluids. Our study reveals a unique region of phase space, where th…
Trapped ultracold Fermi gases provide a system that can be tuned between the BCS and BEC regimes by means of a magnetic-field Feshbach resonance. Condensation of fermionic atom pairs in a $^{40}$K gas was demonstrated experimentally by a sweep technique that pairwise projects fermionic atoms onto molecules. In this paper we examine previous data obtained with this technique that probed the phase boundary in the temperature-magnetic field plane. Comparison of the $^{40}$K data to a theoretically computed phase diagram demonstrates good agreement between the two.
In order to help detecting superfluidity, we theoretically investigate p-wave pairing superfluids in neutral Fermion atom gases confined by a three dimensimentional (3D) harmonic potential. The Ginzburg-Landau framework, which is generic for p-wave superfluids, is used to describe the order parameter spatial structure, or texture characterized by the l-vector both at rest and under rotation. The l-vector configuration is strongly contrained by the boundary condition due to a trap. It is found that the ground state textures exhibit spontaneous supercurrent at rest both cigar and pancake shape t…
Systems with long-range interactions show a variety of intriguing properties: they typically accommodate many meta-stable states, they can give rise to spontaneous formation of supersolids, and they can lead to counterintuitive thermodynamic behavior. However, the increased complexity that comes with long-range interactions strongly hinders theoretical studies. This makes a quantum simulator for long-range models highly desirable. Here, we show that a chain of trapped ions can be used to quantum simulate a one-dimensional model of hard-core bosons with dipolar off-site interaction and tunnelin…
We use the Bogoliubov-de Gennes formalism to analyze harmonically trapped Fermi gases with Rashba-type spin-orbit coupling in two dimensions. We consider both population-balanced and -imbalanced Fermi gases throughout the BCS-BEC evolution, and study the effects of spin-orbit coupling on the spontaneously induced countercirculating mass currents and the associated intrinsic angular momentum. In particular, we find that even a small spin-orbit coupling destabilizes Fulde-Ferrel-Larkin-Ovchinnikov (FFLO)-type spatially modulated superfluid phases as well as the phase-separated states against the…
We investigate a dilute Bose gas confined in a tight one-dimensional (1D) optical lattice plus a superimposed random potential at zero temperature. Accordingly, the ground state energy, quantum depletion and superfluid density are calculated. The presence of the lattice introduces a crossover to the quasi-2D regime, where we analyze asymptotically the 2D behavior of the system, particularly the effects of disorder. We thereby offer an analytical expression for the ground state energy of a purely 2D Bose gas in a random potential. The obtained disorder-induced normal fluid density $n_n$ and qua…
We study quantum vortex states consisting of a ring of vortices with alternating sign, in a homogeneous superfluid confined to a circular domain. We find an exact stationary solution of the point vortex model for the neutral vortex necklace. We investigate the stability of the necklace state within both the point-vortex model and the Gross-Pitaevskii equation describing a trapped atomic Bose-Einstein condensate at low temperature. The point-vortex stationary states are found to also be stationary states of the Gross-Pitaevskii equation provided the finite thickness of the outer fluid boundary …
Two species superfluid Fermi gas is investigated on the BCS side up to the Feshbach resonance. Using the Greens's function technique gradient corrections are calculated to the generalized Thomas-Fermi theory including Cooper pairing. Their relative magnitude is found to be measured by the small parameter $(d/R_{TF})^4$, where $d$ is the oscillator length of the trap potential and $R_{TF}$ is the radial extension of the density $n$ in the Thomas-Fermi approximation. In particular at the Feshbach resonance the universal %constant $A_{TF}$ has the %correction in the center $A=A_{TF}+A_2(d/R_{TF})…
Superfluids can transport heat via simultaneous opposite flows of their spatially interpenetrating condensate and thermal components. While this internal convection is usually described within Landau's phenomenological two fluid hydrodynamics, we apply quantum kinetic theory to a dilute Bose gas held beween thermal reservoirs at different temperatures, and show that the phenomenon also appears in collisionless kinetic regimes, and should be directly observable in currently feasible experiments on trapped ultracold vapors.
The c-field simulation technique is used to study a trapped quasi-two dimensional Bose gas. We calculate the central curvature of the system density and fluctuations of the condensate mode in the degenerate regime. These results provide new understanding of the system behavior in the region of the superfluid transition.
We explore the effect of using two-dimensional matter-wave vortices to confine an ensemble of bosonic quantum impurities. This is modelled theoretically using a mass-imbalanced homogeneous two component Gross-Pitaevskii equation where each component has independent atom numbers and equal atomic masses. By changing the mass imbalance of our system we find the shape of the vortices are deformed even at modest imbalances, leading to barrel shaped vortices; which we quantify using a multi-component variational approach. The energy of impurity carrying vortex pairs are computed, revealing a mass-de…
