Superfluid Bose Gas Research Articles

A modified point-vortex model for the vortex dynamics in a two-dimensional superfluid Bose gas

In this paper, we investigate the dynamics of the vortices in the homogeneous two-dimensional Bose–Einstein condensate by considering the condensate density variation. It is shown that the condensate density variation plays an important role when two vortices are close together. By the time-dependent Lagrangian functional method and the numerical simulation, we study how the interaction strength of the vortices varies with the distance between two vortices with the same or different topological charges, and generalize the results for the vortex pairs to the multi-vortex case. The numerical simulations demonstrate the validity of our theory.

Sound modes in collisional superfluid Bose gases

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 ⩾ 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 are currently unavailable, we find no hybridization, triggering the necessity of future investigations. Our analysis provides a systematic understanding of sound propagation in a collisional weakly-interacting Bose gas in D dimensions.

On the long-term stability of space-time crystals

We investigate a space-time crystal in a superfluid Bose gas. Using a well-controlled periodic drive we excite only one crystalline mode in the system, which can be accurately modeled in the rotating frame of the drive. Using holographic imaging we observe the stability of the crystal over an extended period of time and show the robustness of its structure in both space and time. By introducing a fourth-order term in the Hamiltonian we show that the crystal stabilizes at a fixed number of quanta. The results of the model are compared to the experimental data and show good agreement, with a small number of free parameters. The results yield insights in the long-term stability of the crystal, which can only be obtained by the combination of the extended control in the experiment and the nearly ab initio character of the model. From the model we derive a phase diagram of the system, which can be exploited in the future to study the phase transitions for this new state of matter in even more detail.

Perfect transmission of Higgs modes via antibound states

We study tunneling properties of Higgs modes in superfluid Bose gases in optical lattices in the presence of a potential barrier introduced by local modulation of hopping amplitude. Solving the time-dependent Ginzburg-Landau equation, Higgs modes are found to exhibit perfect transmission through a potential barrier if the barrier strength is weak. There exists, on the other hand, localized Higgs bound states in the presence of a strong potential barrier. We find that the perfect transmission disappears at the critical barrier strength above which one of the odd antibound state turns into a true bound state. We demonstrate that the perfect transmission of Higgs modes is mediated by resonance with the antibound states of Higgs modes.

Dynamics of a space-time crystal in an atomic Bose-Einstein condensate

A space-time crystal has recently been observed in a superfluid Bose gas. Here we construct a variational model that allows us to describe from first principles the coupling between the radial breathing mode and the higher-order axial modes that underlies the observation of the space-time crystal. By comparing with numerical simulations we verify the validity of our variational Ansatz. From the model we determine the requirements for the observation of the space-time crystal and the Ising-like nature of the symmetry breaking involved. Also, we find the onset and growth rate of the space-time crystal, which can be compared to experiments.

Response of the Higgs amplitude mode of superfluid Bose gases in a three-dimensional optical lattice

We study the Higgs mode of superfluid Bose gases in a three dimensional optical lattice, which emerges near the quantum phase transition to the Mott insulator at commensurate fillings. Specifically, we consider responses of the Higgs mode to temporal modulations of the onsite interaction and the hopping energy. In order to calculate the response functions including the effects of quantum and thermal fluctuations, we map the Bose-Hubbard model onto an effective pseudospin-one model and use a perturbative expansion based on the imaginary-time Green's function theory. We also include the effects of an inhomogeneous trapping potential by means of a local density approximation. We find that the response function for the hopping modulation is equal to that for the interaction modulation within our approximation. At the unit filling rate and in the absence of a trapping potential, we show that the Higgs mode can exist as a sharp resonance peak in the dynamical susceptibilities at typical temperatures. However, the resonance peak is significantly broadened due to the trapping potential when the modulations are applied globally to the entire system. We suggest that the Higgs mode can be detected as a sharp resonance peak by partial modulations around the trap center.

Vortex mass in a superfluid

We consider the inertial mass of a vortex in a superfluid. We obtain a vortex mass that is well defined and is determined microscopically and self-consistently by the elementary excitation energy of the kelvon quasiparticle localised within the vortex core. The obtained result for the vortex mass is found to be consistent with experimental observations on superfluid quantum gases and vortex rings in water. We propose a method to measure the inertial rest mass and Berry phase of a vortex in superfluid Bose and Fermi gases.

Bogoliubov Theory for a Superfluid Bose Gas Flowing in a Random Potential: Stability and Critical Velocity

We investigate the stability and critical velocity of a weakly interacting Bose gas flowing in a random potential. By applying the Bogoliubov theory to a disordered Bose system with a steady flow, the condensate density and the superfluid density are determined as functions of the disorder strength, flow velocity, and temperature. The critical velocity, at which the steady flow becomes unstable, is calculated from the spectrum of hydrodynamic excitation. We also show that in two dimensions the critical velocity strongly depends on the system size.

Localized Higgs modes of superfluid Bose gases in optical lattices: A Gutzwiller mean-field study

We study effects of a potential barrier on collective modes of superfluid Bose gases in optical lattices. We assume that the barrier is created by local suppression of the hopping amplitude. When the system is in a close vicinity of the Mott transition at commensurate fillings, where an approximate particle-hole symmetry emerges, there exist bound states of Higgs amplitude mode that are localized around the barrier. By applying the Gutzwiller mean-field approximation to the Bose-Hubbard model, we analyze properties of normal modes of the system with a special focus on the Higgs bound states. We show that when the system becomes away from the Mott transition point, the Higgs bound states turn into quasi-bound states due to inevitable breaking of the particle-hole symmetry. We use a stabilization method to compute the resonance energy and line width of the quasi-bound states. We compare the results obtained by the Gutzwiller approach with those by the Ginzburg-Landau theory. We find that the Higgs bound states survive even in a parameter region far from the Mott transition, where the Ginzburg-Landau theory fails.

Damping of the Higgs and Nambu–Goldstone modes of superfluid Bose gases at finite temperatures

We study collective modes of superfluid Bose gases in optical lattices at commensurate fillings. We focus on the vicinity of the quantum phase transition to the Mott insulator, where there exists the Higgs amplitude mode in addition to the Nambu-Goldstone phase mode associated with the spontaneous U(1) symmetry breaking. We analyze finite-temperature effects on the damping of the collective modes by using an effective spin-1 model and the field theoretical methods based on the finite-temperature Green's function. We calculate the damping rates up to 1-loop order and evaluate them analytically and numerically. We show that the damping rate of the Higgs mode increases with increasing the temperature but it remains underdamped up to a typical temperature achieved in experiments. Moreover, we find that the Nambu-Goldstone mode attenuates via a Landau damping process resulting from interactions with the Higgs mode and it can be overdamped at the typical temperature in a certain parameter region.

Formation of Vortex Lattices in Superfluid Bose Gases at Finite Temperatures

We study the dynamics of a rotating trapped Bose–Einstein condensate (BEC) at finite temperatures. Using the Zaremba–Nikuni–Griffin formalism, based on a generalized Gross–Pitaevskii equation for the condensate coupled to a semiclassical kinetic equation for a thermal cloud, we numerically simulate vortex lattice formation in the presence of a time-dependent rotating trap potential. At low rotation frequency, the thermal cloud undergoes rigid body rotation, while the condensate exhibits irrotational flow. Above a certain threshold rotation frequency, vortices penetrate into the condensate and form a vortex lattice. Our simulation result clearly indicates a crucial role for the thermal cloud, which triggers vortex lattice formation in the rotating BEC.

Critical Velocity of a Superfluid Bose Gas Flowing in a Random Potential

We investigate the critical velocity of a weakly interacting Bose gas flowing in a random potential. By applying the Bogoliubov theory to a disordered Bose system with a steady flow, we determine the critical velocity for weak and moderate disorder. We also calculate the superfluid density and the condensate density as a function of the disorder strength and the flow velocity, and their behaviors near the critical velocity are discussed.

Fano resonance through Higgs bound states in tunneling of Nambu-Goldstone modes

We study collective modes of superfluid Bose gases in optical lattices combined with potential barriers. We assume that the system is in the vicinity of the quantum phase transition to a Mott insulator at a commensurate filling, where emergent particle-hole symmetry gives rise to two types of collective mode, namely a gapless Nambu-Goldstone (NG) phase mode and a gapful Higgs amplitude mode. We consider two kinds of potential barrier: One does not break the particle-hole symmetry while the other does. In the presence of the former barrier, we find Higgs bound states that have binding energies lower than the bulk Higgs gap and are localized around the barrier. We analyze tunneling properties of the NG mode incident to both barriers to show that the latter barrier couples the Higgs bound states with the NG mode, leading to Fano resonance mediated by the bound states. Thanks to the universality of the underlying field theory, it is expected that Higgs bound states may be present also in other condensed matter systems with a particle-hole symmetry and spontaneous breaking of a continuous symmetry, such as quantum dimer antiferromagnets, superconductors, and charge-density-wave materials.

Hybridization of first and second sound in a weakly interacting Bose gas

Using Landau's theory of two-fluid hydrodynamics we investigate the sound modes propagating in a uniform weakly interacting superfluid Bose gas for values of temperature up to the critical point. In order to evaluate the relevant thermodynamic functions needed to solve the hydrodynamic equations, including the temperature dependence of the superfluid density, we use the Bogoliubov theory at low temperatures and the results of a perturbative approach based on the Beliaev diagrammatic technique at higher temperatures. Special focus is given on the hybridization phenomenon between first and second sound which occurs at low temperatures of the order of the interaction energy and we discuss explicitly the behavior of the two sound velocities near the hybridization point.

Emergence of order from turbulence in an isolated planar superfluid.

We study the relaxation dynamics of an isolated zero temperature quasi-two-dimensional superfluid Bose-Einstein condensate that is imprinted with a spatially random distribution of quantum vortices. Following a period of vortex annihilation the remaining vortices self-organize into two macroscopic coherent "Onsager vortex" clusters that are stable indefinitely--despite the absence of driving or external dissipation in the dynamics. We demonstrate that this occurs due to a novel physical mechanism--the evaporative heating of the vortices--that results in a negative-temperature phase transition in the vortex degrees of freedom. At the end of our simulations the system is trapped in a nonthermal state. Our computational results provide a pathway to observing Onsager vortex states in a superfluid Bose gas.

Shear Viscosity of a Superfluid Dipolar Gas at Low Temperatures

We compute the shear viscosity of superfluid Bose and Fermi gases on the base of Boltzmann equation and relaxation times. We show that, in the low temperature limit, the shear viscosities of Bose and Fermi gases are proportional to T-1evp0/T and T-4, respectively. For the superfluid Bose gas at low temperature limit, only splitting processes contribute to the shear viscosity.

Quantum Phase Slips of Trapped Superfluid Bose Gases in One Dimension

We discuss transport of trapped one-dimensional superfluids through a single impurity potential, in connection with quantum phase-slip nucleation rate Γ. We specifically consider damping of dipole oscillations induced by sudden displacement of the trapping potential, which has been investigated in previous experiments. Applying the time-evolving block decimation method to the 1D Bose-Hubbard model with an impurity potential in the hardcore limit, we calculate the dynamics of dipole oscillations and extract the damping rate from the oscillations. We show that there is a broad parameter region in which the damping rate G of the oscillation obeys the formula G∝Γ/v∝v2K−2 with the Tomonaga-Luttinger parameter K, regardless of whether the impurity potential is repulsive or attractive. We find that in that parameter region the damping rate is almost symmetric with respect to the change of the sign of the impurity strength.

Tuning universality far from equilibrium.

Possible universal dynamics of a many-body system far from thermal equilibrium are explored. A focus is set on meta-stable non-thermal states exhibiting critical properties such as self-similarity and independence of the details of how the respective state has been reached. It is proposed that universal dynamics far from equilibrium can be tuned to exhibit a dynamical transition where these critical properties change qualitatively. This is demonstrated for the case of a superfluid two-component Bose gas exhibiting different types of long-lived but non-thermal critical order. Scaling exponents controlled by the ratio of experimentally tuneable coupling parameters offer themselves as natural smoking guns. The results shed light on the wealth of universal phenomena expected to exist in the far-from-equilibrium realm.

Damping of phase fluctuations in superfluid Bose gases

Using Popov's hydrodynamic approach we derive an effective Euclidean action for the long-wavelength phase fluctuations of superfluid Bose gases in D dimensions. We then use this action to calculate the damping of phase fluctuations at zero temperature as a function of D. For D >1 and wavevectors | k | << 2 mc (where m is the mass of the bosons and c is the sound velocity) we find that the damping in units of the phonon energy E_k = c | k | is to leading order gamma_k / E_k = A_D (k_0^D / 2 pi rho) (| k | / k_0)^{2 D -2}, where rho is the boson density and k_0 =2 mc is the inverse healing length. For D -> 1 the numerical coefficient A_D vanishes and the damping is proportional to an additional power of |k | /k_0; a self-consistent calculation yields in this case gamma_k / E_k = 1.32 (k_0 / 2 pi rho)^{1/2} |k | / k_0. In one dimension, we also calculate the entire spectral function of phase fluctuations.

Pair Density Waves and Vortices in an Elongated Spin-1/2Fermi Gas

We study the vortex structures of a (pseudo)spin-1/2 Fermi gas experiencing a uniform effective magnetic field in an anisotropic trap that interpolates between quasi-one dimensional (1D) and quasi-two dimensional (2D). At a fixed chemical potential, reducing the anisotropy (or equivalently increasing the attractive interactions or increasing the magnetic field) leads to instabilities towards pair density waves and vortex lattices. Reducing the chemical potential stabilizes the system. We calculate the phase diagram and explore the density and pair density. The structures are similar to those predicted for superfluid Bose gases. We further calculate the paired fraction, showing how it depends on the chemical potential and anisotropy.