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arXiv:1805.02417 · International Journal of Modern Physics B

Bose–Einstein condensation in nonuniform rotation

Saswata Sahu

Published May 22, 2026• 0 citations
arXivHTMLPDF

Abstract

In this work, we study Bose–Einstein condensation in a system, where the rotation frequency decreases radially from the center. The system is described by a modified Gross–Pitaevskii equation that includes a nonuniform rotation term controlled by a parameter [Formula: see text], with the length scale of the rotation variation fixed relative to the healing length. The results show behavior distinctly different from the uniformly rotating condensate. In the uniform case, a triangular vortex lattice forms, whereas here we observe that above a critical value [Formula: see text] the vortices arrange themselves into a circular ring-shaped pattern near the boundary. Below [Formula: see text], the vortex configuration is disordered, lacking both triangular symmetry and a clear ring structure. The energy and chemical potential exhibit a sharp change at [Formula: see text], signaling a structural phase transition. A phase diagram is presented for the transition from the disordered to the ring-shaped vortex arrangement. The findings are discussed in the context of current experiments on synthetic gauge fields and structured rotation.

DOI
10.1142/s0217979226501821

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In this work, we study Bose–Einstein condensation in a system, where the rotation frequency decreases radially from the center. The system is described by a modified Gross–Pitaevskii equation that includes a nonuniform rotation term controlled by a parameter [Formula: see text], with the length scale of the rotation variation fixed relative to the healing length. The results show behavior distinctly different from the uniformly rotating condensate. In the uniform case, a triangular vortex lattice forms, whereas here we observe that above a critical value [Formula: see text] the vortices arrange themselves into a circular ring-shaped pattern near the boundary. Below [Formula: see text], the vortex configuration is disordered, lacking both triangular symmetry and a clear ring structure. The energy and chemical potential exhibit a sharp change at [Formula: see text], signaling a structural phase transition. A phase diagram is presented for the transition from the disordered to the ring-shaped vortex arrangement. The findings are discussed in the context of current experiments on synthetic gauge fields and structured rotation.
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We investigate the vortex lattices of harmonically confined quasi-two-dimensional tilted rotational dipolar Bose-Einstein condensates. By employing an extended Gross-Pitaevskii equation for a rotating condensate, we reveal the structural transformation of vortices from square to triangular lattices as the tilt of dipolar bosons relative to the polarization axis approaches a critical angle. When the tilt of the magnetic dipoles surpasses the magic angle, the condensate elongates diagonally and becomes devoid of vortices. Moreover, we include the Lee-Huang-Yang correction, which enables the formation of vortices in the elongated condensate. Additionally, when dipoles are oriented perpendicular to the polarization axis, the Lee-Huang-Yang correction results in the fragmentation of condensates under strong rotation. The quench dynamics of the rotational frequency demonstrate the development of vortex lattices; however, with a strong rotational quench, the condensate remains free of vortices. Our numerical analysis highlights the beyond mean-field effects of the rotational properties of anisotropic dipolar bosons, which can be observed in current dipolar quantum gas experiments.
In this paper, we study the static and dynamic properties of vortices formation in a rotating Bose–Einstein condensate in synthetic magnetic field. The condensate is confined in a harmonic potential and an optical lattice potential. We numerically solve the time-dependent Gross–Pitaevskii equation in two dimensions and compare the vortices formation process with rotating frame method. We derive the two expressions about vortex number N[Formula: see text] and chemical potential [Formula: see text] as a function of rotational frequency [Formula: see text], which show that the number of vortices N[Formula: see text] increases linearly with [Formula: see text], while the chemical potential [Formula: see text] remains nearly unchanged with increasing [Formula: see text]. The analytical results are in qualitative agreement with the numerical ones. Moreover, we also investigate the vortex dynamics. Numerical results indicate that the time spent for the formation of steady state vortices is reduced drastically if the optical lattice is considered. Nevertheless, the synthetic magnetic field approach is still low efficient to generate more vortices.
We study the vortex pinning effect on the vortex lattice structure of the rotating two-component Bose-Einstein condensates (BECs) in the presence of impurities or disorder by numerically solving the time-dependent coupled Gross-Pitaevskii equations. We investigate the transition of the vortex lattice structures by changing conditions such as angular frequency, the strength of the inter-component interaction and pinning potential, and the lattice constant of the periodic pinning potential. We show that even a single impurity pinning potential can change the unpinned vortex lattice structure from triangular to square or from triangular to a structure which is the overlap of triangular and square. In the presence of a periodic pinning potential or optical lattice, we observe the structural transition from the unpinned vortex lattice to the pinned vortex lattice structure of the optical lattice. In the presence of a random pinning potential or disorder, the vortex lattice melts following a two-step process by creation of lattice defects, dislocations, and disclinations, with the increase of rotational frequency, similar to that observed for single-component Bose-Einstein condensates. However, for the binary BECs, we show that the two-step vortex lattice melting also occurs with increasing strength of the intercomponent interaction.
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 square lattice, although deviations near the center are found when the number of generated vortices is arbitrary. In case of a circular box trap, the generated vortices in the rapidly rotating BEC lie on concentric closed orbits. Near the center, these orbits have the shape of polygons, whereas near the periphery the orbits are circles. The circular box trap is equivalent to the rotating cylindrical bucket used in early experiment(s) with liquid He II. The number of generated vortices in both cases is in qualitative agreement with Feynman's universal estimate. The numerical simulation for this study is performed by a solution of the underlying mean-field Gross-Pitaevskii (GP) equation in the rotating frame, where the wave function for the generated vortex lattice is a stationary state. Consequently, the imaginary-time propagation method can be used for a solution of the GP equation, known to lead to an accurate numerical solution. We also demonstrated the dynamical stability of the vortex lattices in real-time propagation upon a small change of the angular frequency of rotation, using the converged imaginary-time wave function as the initial state.
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