Abstract We consider a two-dimensional weakly interacting ultracold Bose gas whose constituents are two-level atoms. We study the effects of a synthetic density-dependent gauge field that arises from laser–matter coupling in the adiabatic limit with a laser configuration such that the single-particle zeroth-order vector potential corresponds to a constant synthetic magnetic field. We find a new exotic type of current nonlinearity in the Gross–Pitaevskii equation which affects the dynamics of the order parameter of the condensate. We investigate the rotational properties of this system in the Thomas–Fermi limit, focusing in particular on the physical conditions that make the existence of a quantized vortex in the system energetically favourable with respect to the non-rotating solution. We point out that two different physical interpretations can be given to this new nonlinearity: firstly it can be seen as a local modification of the mean field coupling constant, whose value depends on the angular momentum of the condensate. Secondly, it can be interpreted as a density modulated angular velocity given to the cloud. Looking at the problem from both of these viewpoints, we show that the effect of the new nonlinearity is to induce a rotation to the condensate, where the transition from non-rotating to rotating states depends on the density of the cloud.
Abstract We consider a two-dimensional weakly interacting ultracold Bose gas whose constituents are two-level atoms. We study the effects of a synthetic density-dependent gauge field that arises from laser–matter coupling in the adiabatic limit with a laser configuration such that the single-particle zeroth-order vector potential corresponds to a constant synthetic magnetic field. We find a new exotic type of current nonlinearity in the Gross–Pitaevskii equation which affects the dynamics of the order parameter of the condensate. We investigate the rotational properties of this system in the Thomas–Fermi limit, focusing in particular on the physical conditions that make the existence of a quantized vortex in the system energetically favourable with respect to the non-rotating solution. We point out that two different physical interpretations can be given to this new nonlinearity: firstly it can be seen as a local modification of the mean field coupling constant, whose value depends on the angular momentum of the condensate. Secondly, it can be interpreted as a density modulated angular velocity given to the cloud. Looking at the problem from both of these viewpoints, we show that the effect of the new nonlinearity is to induce a rotation to the condensate, where the transition from non-rotating to rotating states depends on the density of the cloud.
Abstract Ultracold atoms endowed with tunable spin-orbital-angular-momentum coupling (SOAMC) represent a promising avenue for delving into exotic quantum phenomena. Building on recent experimental advancements, we propose the generation of synthetic gauge fields, and by including exotic vortex phases within spinor Bose–Einstein condensates, employing a combination of a running wave and Laguerre–Gaussian laser fields. We investigate the ground-state characteristics of the SOAMC condensate, revealing the emergence of exotic vortex states with controllable orbital angular momenta. It is shown that the interplay of the SOAMC and conventional spin-linear-momentum coupling induced by the running wave beam leads to the formation of a vortex state exhibiting a phase stripe hosting single multiply quantized singularity. The phase of the ground state will undergo the phase transition corresponding to the breaking of rotational symmetry while preserving the mirror symmetry. Importantly, the observed density distribution of the ground-state wavefunction, exhibiting broken rotational symmetry, can be well characterized by the synthetic magnetic field generated through light interaction with the dressed spin state. Our findings pave the way for further exploration into the rotational properties of stable exotic vortices with higher orbital angular momenta against splitting in the presence of synthetic gauge fields in ultracold quantum gases.
One of the key issues related to superfluidity is the existence of quantized vortices. Following recent experiments on Bose–Einstein condensates exhibiting vortices, we investigate the behavior of the wave function which solves the Gross–Pitaevskii equation. For a rotating Bose–Einstein condensate in a harmonic trap, we give a simplified expression of the Gross–Pitaevskii energy in the Thomas–Fermi regime, which only depends on the number and shape of the vortex lines. This allows us to study in detail the structure of the line of a single quantized vortex, which has a U or S shape. S type vortices exist for all values of the angular velocity Ω but are not minimizers of the energy while U vortices are minimizers and exist only for Ω sufficiently large. Finally, we study the drag created by the movement of a detuned laser beam in a condensate and the nucleation of vortices in the low density region close to the boundary layer of the cloud.
Gauge fields are ubiquitous in modern quantum physics. In superfluids, quantized vortices can be induced by gauge fields. Here we demonstrate the first experimental observation of vortex nucleations in light-dressed spinor Bose-Einstein condensates under radially localized synthetic magnetic fields. The light-induced spin-orbital-angular-momentum coupling creates azimuthal gauge potentials A[over →] for the lowest-energy spinor branch dressed eigenstate. The observation of the atomic wave function in the lowest-energy dressed eigenstate reveals that vortices nucleate from the cloud center of a vortex-free state with canonical momentum p[over →]=0. This is because a large circulating azimuthal velocity field ∝p[over →]-A[over →] at the condensate center results in a dynamically unstable localized excitation that initiates vortex nucleations. Furthermore, the long-time dynamics to reach the ground state stops in a metastable state when |A[over →]| is not sufficiently large. Our observation has reasonable agreement with the time-dependent Gross-Pitaevskii simulations.
In this thesis, I explore the behavior of rotating ultra-cold Bose gases, by diagonalizing the Hamiltonian. This method has the advantage of being exact in the limit of weak interactions, and thus is a useful complement to the more commonly used Gross-Pitaevskii (GP) equation, which relies on a mean-field approximation. It is generally known that an ultra-cold Bose gas shows some remarkable properties under rotation, such as quantized vortices and persistent currents, and these are one main reason why we choose to study rotation. Abstract A repulsively interacting Bose-Einstein condensate (BEC) in a harmonic trapping potential will form singly quantized vortices when rotated. Papers I-V are examples of different kinds of generalizations to this basic system, each showing its particular non-trivial new features. Abstract In Paper I we make the trapping potential weakly anharmonic, and confirm the existence of multiply quantized vortices in both repulsively and attractively interacting condensates, which were previously predicted in Gross-Pitaevskii calculations. Abstract In Papers II and III, we generalize to a two-component system in a harmonic trap. The vortices that form under rotation will in general be coreless, i.e. one component will form a vortex and rotate around the other component. In Paper II we give some analytical expressions for the dispersion relation and occupation numbers at low angular momenta, and in Paper III we show how multiply quantized vortices can be stable in these systems. Abstract Finally we investigate bosons in potentials which can support persistent currents, i.e. rotating states that do not decay in a finite amount of time. These are possible if there is an energy barrier separating the rotating state from the non-rotating ground state. In Paper IV, we have a two-component condensate in a one-dimensional potential and we calculate among other things the minimum interaction strength where persistent currents can occur. In Paper V, we study an experimentally relevant two-dimensional annulus. Again we find that persistent currents are possible above a certain interaction strength, and we find this strength as a function of the width of the annulus, as well as how it depends on the relative population of the two species.
We demonstrate that a spin-orbit-coupled Bose-Einstein condensate can be effectively rotated by adding a real magnetic field to inputting gauge angular momentum, which is distinctly different from the traditional ways of rotation by stirring or Raman laser dressing to inputting canonical angular momentum. The gauge angular momentum is accompanied by the spontaneous generation of equal and opposite canonical angular momentum in the ground states, and it leads to the nucleation of quantized vortices. We explain this by indicating that the effective rotation with the vortex nucleation results from the effective magnetic flux induced by the gauge potential, which is essentially different from the previous scheme of creating vortices by synthetic magnetic fields. In the weakly interacting regime, symmetrically placed domains separated by vortex lines as well as half-integer giant vortices are discovered. With relatively strong interatomic interaction, we predict a structure of coaxially arranged annular vortex arrays, which is in stark contrast to the familiar Abrikosov vortex lattice. The developed way of rotation may be extended to a more general gauge system.
The dynamics of interacting quantized vortex filaments in a rotating Bose–Einstein condensate existing in the Thomas–Fermi regime at zero temperature and obeying the Gross–Pitaevskii equation has been considered in the hydrodynamic “nonelastic” approximation. A noncanonical Hamilton equation of motion for the macroscopically averaged vorticity has been derived for a smoothly inhomogeneous array of filaments (vortex lattice) taking into account spatial nonuniformity of the equilibrium density of the condensate, which is determined by the trap potential. The minimum of the corresponding Hamiltonian describes the static configuration of the deformed vortex lattice against the preset density background. The condition of minimum can be reduced to a nonlinear second-order partial differential vector equation for which some exact and approximate solutions are obtained. It has been shown that if the condensate density has an anisotropic Gaussian profile, the equation of motion for the averaged vorticity has solutions in the form of a vector exhibiting a nontrivial time dependence, but homogeneous in space. An integral representation has also been obtained for the matrix Green function that determines the nonlocal Hamiltonian of a system of several quantized vortices of an arbitrary shape in a Bose–Einstein condensate with the Gaussian density. In particular, if all filaments are straight and oriented along one of the principal axes of the ellipsoid, we have a finitedimensional reduction that can describe the dynamics of the system of pointlike vortices against an inhomogeneous background. A simple approximate expression is proposed for the 2D Green function with an arbitrary density profile and is compared numerically with the exact result in the Gaussian case. The corresponding approximate equations of motion, describing the long-wavelength dynamics of interacting vortex filaments in condensates with a density depending only on transverse coordinates, have been derived.