We show that in a rotating two-component Bose mixture, the spin drag between the two different spin species shows a Hall effect. This spin drag Hall effect can be observed experimentally by studying the out-of-phase dipole mode of the mixture. We determine the damping of this mode due to spin drag as a function of temperature. We find that due to Bose stimulation there is a strong enhancement of the damping for temperatures close to the critical temperature for Bose-Einstein condensation.
We show how time-dependent magnetic fields lead to spin motive forces and spin drag in a spinor Bose gas. We propose to observe these effects in a toroidal trap and analyze this particular proposal in some detail. In the linear-response regime we define a transport coefficient that is analogous to the usual drag resistivity in electron bilayer systems. Due to Bose enhancement of atom-atom scattering, this coefficient strongly increases as temperature is lowered. We also investigate the effects of heating.
We study the effect of thermal and quantum fluctuations on the dynamical response of a one-dimensional strongly-interacting Bose gas in a tight atomic waveguide. We combine the Luttinger liquid theory at arbitrary interactions and the exact Bose-Fermi mapping in the Tonks-Girardeau-impenetrable-boson limit to obtain the dynamic structure factor of the strongly-interacting fluid at finite temperature. Then, we determine the drag force felt by a potential barrier moving along the fluid in the experimentally realistic situation of finite barrier width and temperature.
Microscopic Theory of Drag in a Bose Condensate Interacting with a Moving Reservoir
Joint Quantum Institute, University of Maryland（马里兰大学联合量子研究所）；Department of Physics, University of Pittsburgh（匹兹堡大学物理系）；Dodd-Walls Centre for Photonic and Quantum Technologies, Department of Physics, University of Otago（奥塔哥大学光子与量子技术多德-沃尔斯中心物理系）
We use kinetic theory to model the dynamics of a small Bose condensed cloud of heavy particles moving through a larger degenerate Fermi gas of light particles. Varying the Bose-Fermi interaction, we find a crossover between bulk and surface dominated regimes -- where scattering occurs throughout the Bose cloud, or solely on the surface. We calculate the damping and frequency shift of the dipole mode in a harmonic trap as a function of the magnetic field controlling an inter-species Feshbach resonance. We find excellent agreement between our stochastic model and the experimental studies of Cs-L…
In multicomponent superfluids and superconductors, co- and counter-flows of components have in general different properties. It was discussed in 1975 by Andreev and Bashkin, in the context of He$^3$/He$^4$ superfluid mixtures, that inter-particle interactions produce a dissipationless drag. The drag can be understood as a superflow of one component induced by phase gradients of the other component. Importantly the drag can be both positive (entrainment) and negative (counter-flow). The effect is known to be of crucial importance for many properties of diverse physical systems ranging from the …
We theoretically investigate the elusive Andreev-Bashkin collisionless drag for a two-component onedimensional Bose-Hubbard model on a ring. By means of tensor network algorithms, we calculate the superfluid stiffness matrix as a function of intra- and interspecies interactions and of the lattice filling. We then focus on the most promising region close to the so-called pair-superfluid phase, where we observe that the drag can become comparable with the total superfluid density. We elucidate the importance of the drag in determining the long-range behavior of the correlation functions and the …
We investigate the drag force on a moving impurity in a spin-orbit coupled Bose-Einstein condensate. We prove rigorously that the superfluid critical velocity is zero when the impurity moves in all but one directions, in contrast to the case of liquid helium and superconductor where it is finite in all directions. We also find that when the impurity moves in all directions except two special ones, the drag force has nonzero transverse component at small velocity. When the velocity becomes large and the states of the upper band are also excited, the transverse force becomes very small due to op…
The superfluid drag-coefficient of a weakly interacting three-component Bose-Einstein condensate is computed deep into the superfluid phase, starting from a Bose-Hubbard model with component-conserving, on-site interactions and nearest-neighbor hopping. Rayleigh-Schrödinger perturbation theory is employed to provide an analytic expression for the drag density. In addition, the Hamiltonian is diagonalized numerically to compute the drag within mean-field theory at both zero and finite temperatures to all orders in inter-component interactions. Moreover, path integral Monte Carlo simulations hav…
It is well known that the charge current in a conductor is proportional to the applied electric field. This famous relation, known as Ohm's law, is the result of relaxation of the current due to charge carriers undergoing collisions, predominantly with impurities and lattice vibrations in the material. The field of spintronics, where the spin of the electron is manipulated rather than its charge, has recently also led to interest in spin currents. Contrary to charge currents, these spin currents can be subject to strong relaxation due to collisions between different spin species, a phenomenon …
The phase diagram of a spin-orbit-coupled two-component Bose gas includes a supersolid stripe phase, which is featuring density modulations along the direction of the spin-orbit coupling. This phase has been recently found experimentally [J.~Li \textit{et al.}, Nature (London) \textbf{543}, 91 (2017)]. In the present work we characterize the superfluid behavior of the stripe phase by calculating the drag force acting on a moving impurity. Because of the gapless band structure of the excitation spectrum, the Landau critical velocity vanishes if the motion is not strictly parallel to the stripes…
We study two-species Bose-Einstein condensates in quasi two-dimensional optical lattices of varying geometry and potential depth. Based on the numerically exact Bloch and Wannier functions obtained using the plane-wave expansion method, we quantify the drag (entrainment coupling) between the condensate components. This drag originates from the (short range) inter-species interaction and increases with the kinetic energy. As a result of the interplay between interaction and kinetic energy effects, the superfluid-drag coefficient shows a non-monotonic dependence on the lattice depth. To make con…
The existence of frictionless flow below a critical velocity for obstacles moving in a superfluid is well established in the context of the mean-field Gross-Pitaevskii theory. We calculate the next order correction due to quantum and thermal fluctuations and find a non-zero force acting on a delta-function impurity moving through a quasi-one-dimensional Bose-Einstein condensate at all subcritical velocities and at all temperatures. The force occurs due to an imbalance in the Doppler shifts of reflected quantum fluctuations from either side of the impurity. Our calculation is based on a consist…
We consider the motion of a point-like impurity through a three-dimensional two-component Bose-Einstein condensate subject to Weyl spin-orbit coupling. Using linear-response theory, we calculate the drag force felt by the impurity and the associated anisotropic critical velocity from the spectrum of elementary excitations. The drag force is shown to be generally not collinear with the velocity of the impurity. This unusual behavior is a consequence of condensation into a finite-momentum state due to the spin-orbit coupling.
An important component of the structure of the atom, the effects of spin-orbit coupling are present in many sub-fields of physics. Most of these effects are present continuously. We present a detailed study of the dynamics of changing the spin-orbit coupling in an ultra-cold Bose gas, coupling the motion of the atoms to their spin. We find that the spin-orbit coupling greatly increases the damping towards equilibrium. We interpret this damping as spin drag, which is enhanced by spin-orbit coupling rate, scaled by a remarkable factor of $8.9(6)$~s. We also find that spin-orbit coupling lowers t…
Ultracold atomic gases can be spined up either by confining them in rotating frame, or by introducing ``synthetic" magnetic field. In this paper, thermodynamics of rotating ideal Bose gases are investigated within truncated-summation approach which keeps to take into account the discrete nature of energy levels, rather than to approximate the summation over single-particle energy levels by an integral as does in semi-classical approximation. Our results show that Bose gases in rotating frame exhibit much stronger dependence on rotation frequency than those in ``synthetic" magnetic field. Conse…
We consider spin transport in a two-component atomic Bose gas in three dimensions, at temperatures just above the critical temperature for Bose-Einstein condensation. In these systems the spin conductivity is determined by spin drag, i.e., frictional drag between the two spin components due to interactions. We find that in the critical region the temperature dependence of the spin conductivity deviates qualitatively from the Boltzmann result and is fully determined by the critical exponents of the phase transition. We discuss the size of the critical region where these results may be observed …
We consider rotating finite size vortex arrays in Bose-Einstein condensates that are confined by cylindrically symmetric external potentials. We show that such systems possess two exact Nambu-Goldstone zero modes associated with two spontaneously broken continuous symmetries of the system. We verify our analytical result via direct numerical diagonalizations of the Bogoliubov-de Gennes equations. We conclude by comparing rotating vortex lattices in superfluids to supersolids and discrete time crystals.
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.
In this work we are concerned with the understanding of the collisionless drag or entrainment between two superfluids, also called Andreev-Bashkin effect, in terms of current response functions. The drag density is shown to be proportional to the cross transverse current-current response function, playing the role of a normal component for the single species superfluid density. We can in this way link the existence of finite entrainment with the exhaustion of the energy-weighted sum rule in the spin channel. The formalism is then used to reproduce some known results for a weakly interacting Bo…
We investigate the structure and dynamics of a rotating superfluid Bose-Fermi mixture (SBFM) made of superfluid bosons and two-component (spin up and down) superfluid fermions. A ground-state phase diagram for the nonrotating case of a SBFM with specific parameters is given, where the ground-state configuration of a nonrotating SBFM is mainly determined by the boson-fermion interaction. For the rotating case of a SBFM with a sufficiently large rotation frequency, we show that the system supports a mixed phase and three typical layer separated phases. In particular, the visible vortex formation…
We reveal that Hopf solitons can be stabilized in rotating atomic Bose-Einstein condensate. The Hopfion is a matter-wave vortex complex which carries two independent winding numbers. Such a topological solitonic structure results from a superfluid flow of atoms simultaneously quantized in poloidal and toroidal directions. In the framework of a dissipative mean-field model we observe different unstable evolution scenarios of the Hopfions. We demonstrate energetic and dynamical stability of the Hopf solitons under experimentally feasible conditions.
We study the influence of dipole-dipole interaction on the formation of vortices in a rotating dipolar Bose-Einstein condensate (BEC) of $^{52}$Cr and $^{164}$Dy atoms in quasi two-dimensional geometry. By numerically solving the corresponding time-dependent mean-field Gross-Pitaevskii equation, we show that the dipolar interaction enhances the number of vortices while a repulsive contact interaction increases the stability of the vortices. Further, an ordered vortex lattice of relatively large number of vortices is found in a strongly dipolar BEC.
We investigate the dynamics of rotating pseudo-spin-1/2 Bose-Einstein condensates (BECs) with Rashba spin-orbit coupling (SOC) in a quasicrystalline optical lattice (QOL). For given parameters, the system evolves from an initial heliciform-stripe phase into a final visible vortex necklace with a giant vortex and a hidden vortex necklace. Simultaneously, the corresponding spin texture undergoes a transition from a meron-antimeron pair to a half-antiskyrmion necklace. During the dynamic evolution process, the angular momentum increases gradually, and then approaches to a convergent value. Furthe…
We found an analytical solution for the vortex structure in a rapidly rotating trapped Bose-Einstein condensate in the lowest Landau level approximation. This solution is exact in the limit of a large number of vortices and is obtained for the case of anisotropic harmonic potential. For the case of symmetric harmonic trap when the rotation frequency is equal to the trapping frequency, the solution coincides with the Abrikosov triangle vortex lattice in type-II superconductors. In a general case the coarse grained density is found to be close to the Thomas-Fermi profile, except the vicinity of …
We study the dynamics of vortex nucleation and lattice formation in a Bose--Einstein condensate in a rotating square optical lattice by numerical simulations of the Gross--Pitaevskii equation. Different dynamical regimes of vortex nucleation are found, depending on the depth and period of the optical lattice. We make an extensive comparison with the experiments by Williams {\it et al.} [Phys. Rev. Lett. {\bf 104}, 050404 (2010)], especially focusing on the issues of the critical rotation frequency for the first vortex nucleation and the vortex number as a function of rotation frequency.
Andreev-Bashkin drag plays a very important role in multiple areas like superfluid mixtures, superconductors and dense nuclear matter. Here, we point out that the drag phenomenon can be also important in physics of solitons, ubiquitous objects arising in a wide array of fields ranging from tsunami waves and fiber-optic communication to biological systems. So far, fruitful studies were conducted in ultracold atomic systems where nontrivial soliton dynamics occurred due to inter-component density-density interaction. In this work we show that current-current coupling between components (Andreev-…
We consider a rotating Bose-Einstein condensate in a square optical lattice in the regime in which the Hamiltonian of the system can be mapped onto a Josephson junction array. In an approximate scheme where the couplings are assumed uniform, the ground state energy is formulated in terms of the vortex configuration. The results are compared with experimental results and also previously reported results for frustrated XY model. We also show that vortex configuration is robust with respect to change of couplings and therefore the results remain valid when we consider more realistic model with no…
We investigate a model of a two-component Bose-Einstein condensate residing on an optical lattice. Within a Bogolioubov-approach at the mean-field level, we derive exact analytical expressions for the excitation spectrum of the two-component condensate when taking into account hopping and interactions between arbitrary sites. Our results thus constitute a basis for works that seek to clarify the effects of higher-order interactions in the system. We investigate the excitation spectrum and the two branches of superfluid velocity in more detail for two limiting cases of particular relevance. Mor…
Equilibrium vortex formation in rotating binary Bose gases with a rotating frequency higher than the harmonic trapping frequency is investigated theoretically. We consider the system being evaporatively cooled to form condensates and a combined numerical scheme is applied to ensure the binary system being in an authentic equilibrium state. To keep the system stable against the large centrifugal force of ultrafast rotation, a quartic trapping potential is added to the existing harmonic part. Using the Thomas-Fermi approximation, a critical rotating frequency Ω_c is derived, which characterizes …
Counter-rotating vortices in miscible two-component Bose-Einstein condensates, in which superflows counter-rotate between the two components around the overlapped vortex cores, are studied theoretically in a pancake-shaped potential. In a linear stability analysis with the Bogoliubov-de Gennes model, we show that counter-rotating vortices are dynamically unstable against splitting into multiple vortices. The instability shows characteristic behaviors as a result of countersuperflow instability, which causes relaxation of relative flows between the two components in binary condensates. The char…
We report on the manipulation of the center-of-mass motion (`sloshing') of a Bose Einstein condensate in a time-averaged orbiting potential (TOP) trap. We start with a condensate at rest in the center of a static trapping potential. When suddenly replacing the static trap with a TOP trap centered about the same position, the condensate starts to slosh with an amplitude much larger than the TOP micromotion. We show, both theoretically and experimentally, that the direction of sloshing is related to the initial phase of the rotating magnetic field of the TOP. We show further that the sloshing ca…
We present theoretical analysis and numerical studies of the quantized vortices in a rotating Bose-Einstein condensate with spatiotemporally modulated interaction in harmonic and anharmonic potentials, respectively. The exact quantized vortex and giant vortex solutions are constructed explicitly by similarity transformation. Their stability behavior has been examined by numerical simulation, which shows that a new series of stable vortex states (defined by radial and angular quantum numbers) can be supported by the spatiotemporally modulated interaction in this system. We find that there exist…
The production of quantized vortices having diverse structures is a remarkable effect of rotating Bose-Einstein condensates. Vortex formation described by the mean-field theory is valid only in the regime of weak interactions. The exploration of the rich and diverse physics of strongly interacting BEC requires a more general approach. This study explores the vortex formation of strongly interacting and rapidly rotating BEC from a general ab initio many-body perspective. We demonstrate that the quantized vortices form various structures that emerge from an intricate interplay between the angula…
The one-dimensional Bose gas is an unusual superfluid. In contrast to higher spatial dimensions, the existence of non-classical rotational inertia is not directly linked to the dissipationless motion of infinitesimal impurities. Recently, experimental tests with ultracold atoms have begun and quantitative predictions for the drag force experienced by moving obstacles have become available. This topical review discusses the drag force obtained from linear response theory in relation to Landau's criterion of superfluidity. Based upon improved analytical and numerical understanding of the dynamic…
Novel ground state properties of rotating Bose gases have been intensively studied in the context of neutral cold atoms. We investigate the rotating Bose gas in a trap from a thermodynamic perspective, taking the charged ideal Bose gas in magnetic field (which is equivalent to a neutral gas in a synthetic magnetic field) as an example. It is indicated that the Bose-Einstein condensation temperature is irrelevant to the magnetic field, conflicting with established intuition that the critical temperature decreases with the field increasing. The specific heat and Landau diamagnetization also exhi…
We study the hydrodynamic forces acting on a small impurity moving in a two-dimensional Bose-Einstein condensate at non-zero temperature. The condensate is modelled by the damped-Gross Pitaevskii (dGPE) equation and the impurity by a Gaussian repulsive potential coupled to the condensate. For weak coupling, we obtain analytical expressions for the forces acting on the impurity, and compare them with those computed through direct numerical simulations of the dGPE and with the corresponding expressions for classical forces. For non-steady flows, there is a time-dependent force dominated by inert…
We have calculated low-lying quasiparticle excitation spectra of rotating three-dimensional Bose-Einstein condensates. As opposed to the prediction of hydrodynamic continuum theories, we find a minimum in the Tkachenko mode spectrum at intermediate rotation frequencies of the harmonic trap. Such a minimum can harbour a Tkachenko quasiparticle with zero excitation energy. We discuss the experimental signatures of such a zero mode.
We have computed phase diagrams for rotating spin-1 Bose-Einstein condensates with long-range magnetic dipole-dipole interactions. Spin textures including vortex sheets, staggered half-quantum- and skyrmion vortex lattices and higher order topological defects have been found. These systems exhibit both superfluidity and magnetic crystalline ordering and they could be realized experimentally by imparting angular momentum in the condensate.
We study vortex formation in a Bose-Einstein condensate in a rotating double-well potential. Besides the ordinary quantized vortices and elusive ghost vortices, "hidden" vortices are found distributing along the central barrier. These hidden vortices are invisible like ghost vortex but carry angular momentum. Moreover, their core size is not given by the healing length, but is strongly influenced by the external potential. We find that the Feynman's rule can be well satisfied only after including the hidden vortices. There is no critical rotating frequency for the formation of hidden vortex wh…
We present a theoretical analysis of dilute gas Bose-Einstein condensates with dipolar atomic interactions under rotation in elliptical traps. Working in the Thomas-Fermi limit, we employ the classical hydrodynamic equations to first derive the rotating condensate solutions and then consider their response to perturbations. We thereby map out the regimes of stability and instability for rotating dipolar Bose-Einstein condensates and in the latter case, discuss the possibility of vortex lattice formation. We employ our results to propose several novel routes to induce vortex lattice formation i…
Quantum droplets may form out of a gaseous Bose-Einstein condensate, stabilized by quantum fluctuations beyond mean field. We show that multiple singly-quantized vortices may form in these droplets at moderate angular momenta in two dimensions. Droplets carrying these precursors of an Abrikosov lattice remain self-bound for certain timescales after switching off an initial harmonic confinement. Furthermore, we examine how these vortex-carrying droplets can be formed in a more pertubation-resistant setting, by starting from a rotating binary Bose-Einstein condensate and inducing a metastable pe…
In this paper, we investigate the thermodynamic behavior of a rotating Bose-Einstein condensation with non-zero interatomic interactions theoretically. The analysis relies on a semiclassical Hartree-Fock approximation where an integral is performed over the phase space and function of the grand canonical ensemble is derived. Subsequently, we use this result to derive several thermodynamic quantities including the condensate fraction, critical temperature, entropy and heat capacity. Thereby, we investigate the effect of the rotation rate and interactions parameter on the thermodynamic behavior.…
We study formation of rotating three-dimensional high-order solitons (azimuthons) in Bose Einstein condensate with attractive nonlocal nonlinear interaction. In particular, we demonstrate formation of toroidal rotating solitons and investigate their stability. We show that variational methods allow a very good approximation of such solutions and predict accurately the soliton rotation frequency. We also find that these rotating localized structures are very robust and persist even if the initial condensate conditions are rather far from the exact soliton solutions. Furthermore, the presence of…
The behaviors of a rapid rotating Bose-Einstein condensate under extreme elongation in a 2D anisotropic harmonic plus quartic trap are investigated. Due to the quartic trap, the system remains stable at high rotating velocity, $Ω\geq ω_\perp$ ($ω_\perp$ is the radial harmonic trap frequency), and vortex lattices form even in the absence of the repulsive s-wave interaction ($g$). When $g$ is present, the interplay between $g$ and the quartic trap potential can lead to rich vortex lattice transition states as a function of $Ω$, to which vortex lattices vanish eventually at some higher $Ω$.
We investigate the 2D weakly interacting Bose-Einstein condensate in a rotating trap by the tools of quantum information theory. The critical exponents of the ground state fidelity susceptibility and the correlation length of the system are obtained for the quantum phase transition when the frst vortex is formed. We also find the single-particle entanglement can be an indicator of the angular momentums for some real ground states. The single-particle entanglement of fractional quantum Hall states such as Laughlin state and Pfaffian state is also studied.
PT-symmetric quantum mechanics allows finding stationary states in mean-field systems with balanced gain and loss of particles. In this work we apply this method to rotating Bose-Einstein condensates with contact interaction which are known to support ground states with vortices. Due to the particle exchange with the environment transport phenomena through ultracold gases with vortices can be studied. We find that even strongly interacting rotating systems support stable PT-symmetric ground states, sustaining a current parallel and perpendicular to the vortex cores. The vortices move through t…
We use entanglement to investigate the transition from vortex liquid phase to vortex lattice phase in weakly interacting rotating Bose-Einstein condensate (BEC). Ground state entanglement spectrum is analyzed to distinguish these two different phases. For the torus geometry, the low-lying part of ground state entanglement spectrum, as well as the behavior of its lowest level change clearly when the transition occurs. For the sphere geometry, the disappearance of entanglement gap in the conformal limit (CL) can indicate this transition. We also show that the decrease of entanglement between par…
We predict and describe a new collective mode in rotating Bose-Einstein condensates, which is very similar to the Rossby waves in geophysics. In the regime of fast rotation, the Coriolis force dominates the dynamics and acts as a restoring force for acoustic-drift waves along the condensate. We derive a nonlinear equation that includes the effects of both the zero-point pressure and the anharmonicity of the trap. It is shown that such waves have negative phase speed, propagating in the opposite sense of the rotation. We discuss different equilibrium configurations and compare with those result…
We consider the quasi-2D two-component Bose-Einstein condensates with Rashba spin-orbit (SO) coupling in a rotating trap. An external Zeeman term favoring spin polarization along the radial direction is also considered, which has the same form as the non-canonical part of the mechanical angular momentum. The rotating condensate exhibits rich structures as varying the strengths of trapping potential and interaction. With a strong trapping potential, the condensate exhibits a half-quantum vortex-lattice configuration. Such a configuration is driven to the normal one by introducing the external r…
We derive analytically the phase diagram of a two-component Bose gas confined in an anharmonic potential, which becomes exact and universal in the limit of weak interactions and small anharmonicity of the trapping potential. The transitions between the different phases, which consist of vortex states of single and multiple quantization, are all continuous because of the addition of the second component.
We study the long time behavior of solutions to a nonlinear partial differential equation arising in the description of trapped rotating Bose-Einstein condensates. The equation can be seen as a hybrid between the well-known nonlinear Schrödinger/Gross-Pitaevskii equation and the Ginzburg-Landau equation. We prove existence and uniqueness of global in-time solutions in the physical energy space and establish the existence of a global attractor within the associated dynamics. We also obtain basic structural properties of the attractor and an estimate on its Hausdorff and fractal dimensions.
We present OpenMP version of a Fortran program for solving the Gross-Pitaevskii equation for a harmonically trapped three-component rotating spin-1 spinor Bose-Einstein condensate (BEC) in two spatial dimensions with or without spin-orbit (SO) and Rabi couplings. The program uses either Rashba or Dresselhaus SO coupling. We use the split-step Crank-Nicolson discretization scheme for imaginary- and real-time propagation to calculate stationary states and BEC dynamics, respectively.
