Figure - available from: Journal of Physics: Condensed Matter
This content is subject to copyright. Terms and conditions apply.
(a) Number of vortices and (b) energy per atom in the rotating frame for a rapidly rotating quasi-2D BEC confined in a circular box of radius R=8 with g = 5000 versus angular frequency of rotation Ω. The theoretical estimates for number and energy (17) and (19) with E0ci=13.3 due to Feynman and Fetter are also shown. The crosses are the actual points obtained numerically whereas the straight lines are shown to guide the eye.
Source publication
We study numerically the vortex-lattice formation in a rapidly rotating uniform quasi-two-dimensional Bose-Einstein condensate (BEC) in a box trap. We consider two types of boxes: square and circle. In a square-shaped 2D box trap, when the number of generated vortices is the square of an integer, the vortices are found to be arranged in a perfect s...
Similar publications
We describe a protocol to prepare solitons in a quasi-one-dimensional (quasi-1D) box-trapped Bose-Einstein condensate using a quench of the isotropic s-wave scattering length. A quench to exactly four times the initial 1D coupling strength creates one soliton at each boundary of the box, which then propagate in a uniform background density and coll...
We present numerical simulations to unravel the dynamics associated with the creation of a vortex in a Bose–Einstein condensate (BEC), from another nonrotating BEC using two-photon Raman transition with Gaussian (G) and Laguerre–Gaussian (LG) laser pulses. In particular, we consider BEC of Rb atoms at their hyperfine ground states confined in a qua...
We study the coupled atomic–molecular quantized ring vortices of ⁸⁷Rb Bose–Einstein condensates trapped in a rotating 3D anisotropic cylindrical trap using both time-independent and time-dependent Gross–Pitaevskii approaches. For atomic to molecular conversion and vice versa, a two-photon Raman photoassociation scheme has been used. Atomic and mole...
We examine the dynamics associated with the creation of a vortex in a Bose-Einstein condensate (BEC), from another nonrotating BEC using two-photon Raman transition with Gaussian (G) and Laguerre-Gaussian (LG) laser pulses. In particular, we consider BEC of Rb atoms at their hyperfine ground states confined in a quasi two dimensional harmonic trap....
Citations
... Recent advances in the shaping of optical potentials have opened many new possibilities to investigate the effect of the trap geometry on various quantum orders [2,14,49], such as modified stripe and odd-petal-number states on a toroidal trap [67,76], exotic vortices in a cylindrical or hollow spherical surface trap [3,11,59], static and dynamic properties of shell-shaped condensates [14,58]. One major development is the increasingly popular use of the optical box trap [1,[4][5][6]8,34,37,38,41,50,51]. Scientific breakthroughs in a wide range of areas have been allowed for a scalar BEC in uniform optical box traps [45], including short-wavelength excitations [27], dynamical excitation [5], the formation of a supersolid-like spatially-periodic crystallization [46,71]. ...
We demonstrate the dynamics of a spin-1 ferromagnetic Bose-Einstein condensate (BEC) with Rashba
spin-orbit (SO) coupling in a narrow square box trap when an obstacle potential is moving in it. The
ground-state energy would be enhanced with the box trap becomes narrower. From the Bogoliubov
analytical excitation spectrum lines, we obtain the dependence of critical excitation velocity and
momentum on the trap geometry under different SO coupling. Numerically, when the obstacle moves
along the direction of plane wave ground state, in addition to spin-density waves being excited
periodically, a long density belt accompanied by density island chain is found ahead of the obstacle. Such
density distribution is mainly determined by the narrow box trap. A series of density islands arranged
more closely are generated as the obstacle moves along opposite direction. There exists another velocity
threshold for different density excitation under a larger SO coupling.
... These solutions are calculated using a finite difference scheme, the details of which are provided in Appendix A. Understanding the possible vortex configurations in superfluid systems remains an ongoing interest, see for example refs. [76][77][78] for recent studies. ...
Motivated by recent experiments, we theoretically study a gas of atomic bosons confined in an elliptical harmonic trap; forming a quasi-two-dimensional atomic Bose-Einstein condensate subject to a density-dependent gauge potential which realises an effective density-angular-momentum coupling. We present exact Thomas-Fermi solutions which allows us to identify the stable regimes of the full parameter space of the model. Accompanying numerical simulations reveal the effect of the interplay of the rigid body and density-angular-momentum coupling for the elliptically confined condensate. By varying the strength of the gauge potential and trap anisotropy we explore how the superfluid state emerges in different experimentally accessible geometries, while for large rotation strengths dense vortex lattices and concentric vortex ring arrangements are obtained.
... Quantum mechanical gases manifest superfluidity by the nucleation of quantized vortices when the gas undergoes rotation. Typically, this leads to the formation of the Abrikosov lattice at equilibrium; however, recent work has revealed that homogeneous [21], multi-component [22,23], and densitydependent [24] gauge theories all exhibit novel vortex configurations. Since individual vortices are topologically protected, they represent an intriguing candidate for hosting impurities within the matter wave [25]. ...
We explore the effect of using two-dimensional matter-wave vortices to confine an ensemble of bosonic quantum impurities. This is modeled 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 that the shape of the vortices is deformed even at modest imbalances, leading to barrel-shaped vortices, which we quantify using a multicomponent variational approach. The energy of impurity carrying vortex pairs is computed, revealing a mass-dependent energy splitting. We then compute the excited states of the impurity, which we in turn use to construct “covalent bonds” for vortex pairs. Our work opens a route to simulating synthetic chemical reactions with superfluid systems.
... The Bose-Einstein condensation (BEC) is a purely quantum-statistical phase transition characterized by the appearance of macroscopic population in ground state below the critical temperature T c , and it plays an important role in condensed matter [1][2][3][4][5][6][7][8][9], optics [10,11], atomic and molecular physics [12][13][14][15], etc. It is emphasized that the transition actually occurs at the thermodynamic limit, or when the discrete level structure is approximated by a continuous density of states [14,[16][17][18][19][20][21]. ...
We investigate the statistical distribution for ideal Bose gases with constant particle density in the 3D box of volume V=L3. By changing linear size L and imposing different boundary conditions on the system, we present a numerical analysis on the characteristic temperature and condensate fraction and find that a smaller linear size is efficient to increase the characteristic temperature and condensate fraction. Moreover, there is a singularity under the antiperiodic boundary condition.
... Quantum mechanical gases manifest superfluidity by the nucleation of quantized vortices when the gas un-dergoes rotation. Typically this leads to the formation of the Abrikosov lattice at equilibrium, however recent work has revealed that homogeneous [21], multicomponent [22,23] and density-dependent [24] gauge theories all exhibit novel vortex configurations. Since individual vortices are topologically protected, they represent an intriguing candidate for hosting impurities within the matter-wave [25]. ...
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. 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-dependent energy splitting. We then compute the excited states of the impurity, which we in turn use to construct `covalent bonds' for vortex pairs, leading to the prediction of impurity mediated bound states. Our work opens a new route to simulating synthetic chemical reactions with superfluid systems.
... As intriguing as topological defects might be, crystals made out of them appear to be even more exotic, like the soliton lattice that forms in doped polyacetylene [1], for instance. Examples of topological defect lattices abound in Condensed Matter Physics where one might find lattices of parallel screw dislocations in solids [2], vortex lattices in rotating superfluids [3] and in Bose-Einstein condensates [4], as well as the much studied magnetic flux lattices in type II superconductors [5]. Liquid crystals contribute with lattices of disclinations in nematics [6], and with lattices of screw dislocations in cholesterics (known as twist grain boundaries) [7]. ...
Since the logarithm function is the solution of Poisson's equation in two dimensions, it appears as the Coulomb interaction in two dimensions, the interaction between Abrikosov flux lines in a type II superconductor, or between line defects in elastic media, and so on. Lattices of lines interacting logarithmically are, therefore, a subject of intense research due to their manifold applications. The solution of the Poisson equation for such lattices is known in the form of an infinite sum since the late 1990's. In this article we present an alternative analytical solution, in closed form, in terms of the Jacobi theta function.
... As intriguing as topological defects might be, crystals made out of them appear to be even more exotic, like the soliton lattice that forms in doped polyacetylene [1], for instance. Examples of topological defect lattices abound in Condensed Matter Physics where one might find lattices of parallel screw dislocations in solids [2], vortex lattices in rotating superfluids [3] and in Bose-Einstein condensates [4], as well as the much studied magnetic flux lattices in type II superconductors [5]. Liquid crystals contribute with lattices of disclinations in nematics [6], and with lattices of screw dislocations in cholesterics (known as twist grain boundaries) [7]. ...
Since the logarithm function is the solution of Poisson's equation in two dimensions, it appears as the Coulomb interaction in two dimensions, the interaction between Abrikosov flux lines in a type II superconductor, or between line defects in elastic media, and so on. Lattices of lines interacting logarithmically are therefore a subject of intense research due to their manifold applications. The solution of the Poisson equation for such lattices is known in the form of an infinite sum since the late 1990's. In this article we present an alternative analytical solution, in closed form, in terms of the Jacobi theta function.
... The unique quantum phenomena of Bose-Einstein condensation (BEC) have played an important role in condensed matter [1][2][3], optics [4][5][6], superconductivity [7] as well as in atomic and molecular physics [8,9]. However, it is the extremely low achievable temperature that is demanding on experimental technology equipments. ...
We investigate the statistical distribution that governs an ideal gases of N bosons confined in a limited cubic volume V . By adjusting the spatial sizes and imposing the boundary conditions that can be manipulated by the phase factors, we numerically calculate the critical temperature of Bose-Einstein condensation to analyse the statistical properties in these systems. We find that, the smaller spatial sizes can sufficiently increase the magnitude of the critical temperature. And the critical temperature exhibits a periodic variation of 2{\pi} with the phase, particularly, the counterperiodic boundary condition is more capable of increasing the critical temperature for Bose-Einstein condensation.
We consider a disk-shaped cold atom Bose-Einstein condensate with repulsive atom-atom interactions within a circular trap, described by a two-dimensional time-dependent Gross-Pitaevskii equation with cubic nonlinearity and a circular box potential. In this setup, we discuss the existence of a type of stationary nonlinear waves with propagation-invariant density profiles, consisting of vortices located at the vertices of a regular polygon with or without an antivortex at its center. These polygons rotate around the center of the system and we provide approximate expressions for their angular velocity. For any size of the trap, we find a unique regular polygon solution that is static and is seemingly stable for long evolutions. It consists of a triangle of vortices with unit charge placed around a singly charged antivortex, with the size of the triangle fixed by the cancellation of competing effects on its rotation. There exist other geometries with discrete rotational symmetry that yield static solutions, even if they turn out to be unstable. By numerically integrating in real time the Gross-Pitaevskii equation, we compute the evolution of the vortex structures and discuss their stability and the fate of the instabilities that can unravel the regular polygon configurations. Such instabilities can be driven by the instability of the vortices themselves, by vortex-antivortex annihilation or by the eventual breaking of the symmetry due to the motion of the vortices.
Motivated by recent experiments, we study theoretically a gas of atomic bosons confined in an elliptical harmonic trap, forming a quasi-two-dimensional atomic Bose-Einstein condensate subject to a density-dependent gauge potential which realizes an effective density-angular-momentum coupling. We present exact Thomas-Fermi solutions which allow us to identify the stable regimes of the full parameter space of the model. Accompanying numerical simulations reveal the effect of the interplay of the rigid body and density-angular-momentum coupling for the elliptically confined condensate. By varying the strength of the gauge potential and trap anisotropy, we explore how the superfluid state emerges in different experimentally accessible geometries, while for large rotation strengths dense vortex lattices and concentric vortex ring arrangements are obtained.
