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Rapidly rotating condensates in a bubble trap

Guilherme Tomishiyo Teixeira de Sousa

Published Dec 1, 2022• 0 citations
Publisher

Abstract

We study a rotating Bose-Einstein Condensate (BEC) trapped in a shifted harmonic oscillator and Mexican Hat trap, which approximates the potential of a bubble trap potential in some situations.We determined the vortices configurations that appears in this system by varying the interaction and angular momentum of the atomic cloud.The system phase diagram has the macrovortex configurations for small values of the interaction parameter.The charge of the central vortex increases with increasing rotation.Higher values of the atomic interaction turns the macrovortex unstable.It decays into multiple single-charged vortices that arrange themselves in a lattice.Since the vortices are not always visible in the absorption images, we look for alternative methods to characterize the vortex configuration.More specifically, we search for experimental signatures to determine the transitions in the phase diagram.For that, we study how the BEC's velocity field affects the collective modes of the condensate.The splitting of the modes degenerescence and the increase in the mode frequency with angular velocity, which can be traced to a reduction in the gas compressibility, can be seen as an indirect signature of the presence of the vortices in the trapped BEC.

DOI
10.11606/t.76.2022.tde-14022023-101707

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We study a rotating Bose-Einstein Condensate (BEC) trapped in a shifted harmonic oscillator and Mexican Hat trap, which approximates the potential of a bubble trap potential in some situations.We determined the vortices configurations that appears in this system by varying the interaction and angular momentum of the atomic cloud.The system phase diagram has the macrovortex configurations for small values of the interaction parameter.The charge of the central vortex increases with increasing rotation.Higher values of the atomic interaction turns the macrovortex unstable.It decays into multiple single-charged vortices that arrange themselves in a lattice.Since the vortices are not always visible in the absorption images, we look for alternative methods to characterize the vortex configuration.More specifically, we search for experimental signatures to determine the transitions in the phase diagram.For that, we study how the BEC's velocity field affects the collective modes of the condensate.The splitting of the modes degenerescence and the increase in the mode frequency with angular velocity, which can be traced to a reduction in the gas compressibility, can be seen as an indirect signature of the presence of the vortices in the trapped BEC.
We study a rotating Bose-Einstein Condensate (BEC) trapped in a shifted harmonic oscillator and Mexican Hat trap, which approximates the potential of a bubble trap potential in some situations. We determined the vortices configurations that appears in this system by varying the interaction and angular momentum of the atomic cloud. The system phase diagram has the macrovortex configurations for small values of the interaction parameter. The charge of the central vortex increases with increasing rotation. Higher values of the atomic interaction turns the macrovortex unstable. It decays into multiple single-charged vortices that arrange themselves in a lattice. Since the vortices are not always visible in the absorption images, we look for alternative methods to characterize the vortex configuration. More specifically, we search for experimental signatures to determine the transitions in the phase diagram. For that, we study how the BECs velocity field affects the collective modes of the condensate. The splitting of the modes degenerescence and the increase in the mode frequency with angular velocity, which can be traced to a reduction in the gas compressibility, can be seen as an indirect signature of the presence of the vortices in the trapped BEC.
We studied a rotating Bose–Einstein condensate confined in ring trap configurations that can be produced starting with a bubble trap confinement, approximated by a Mexican hat and shift harmonic oscillator potentials. Using a variational technique and perturbation theory, we determined the vortex configurations in this system by varying the interparticle interaction and the angular velocity of the atomic cloud. We found that the phase diagram of the system has macrovortex structures for small positive values of the interaction parameter, and the charge of the central vortex increases with rotation. Strengthening the atomic interaction makes the macrovortex unstable, and it decays into multiple singly charged vortices that arrange themselves in a lattice configuration. We also look for experimentally realizable methods to determine the vortex configuration without relying upon absorption imaging since the structures are not always visible in the latter. More specifically, we study how the vortex distribution affects the collective modes of the condensate by solving the Gross–Pitaevskii equation numerically and by analytical predictions using the sum-rule approach for the frequencies of the modes. These results reveal important signatures to characterize the macrovortices and vortex lattice transitions in the experiments.
Abstract In a harmonically-trapped rotating Bose–Einstein condensate (BEC), a vortex of large angular momentum decays to multiple vortices of unit angular momentum from an energetic consideration. We demonstrate the formation of a robust and dynamically stable giant vortex of large angular momentum in a harmonically trapped rotating BEC with a potential hill at the center, thus forming a Mexican hat like trapping potential. For a small inter-atomic interaction strength, a highly controllable stable giant vortex appears, whose angular momentum slowly increases as the angular frequency of rotation is increased. As the inter-atomic interaction strength is increased beyond a critical value, only vortices of unit angular momentum are formed, unless the strength of the potential hill at the center is also increased: for a stronger potential hill at the center a giant vortex is again formed. The dynamical stability of the giant vortex is demonstrated by real-time propagation numerically. These giant vortices of large angular momentum can be observed and studied experimentally in a highly controlled fashion.
We consider a Bose-Einstein condensate confined in a ``Mexican hat'' or sombrero potential, with a quartic minus quadratic radial dependence. We find conditions under which the ground state is annular in shape, with a hole in the center of the condensate. Rotation leads to the appearance of stable multiply quantized vortices, giving rise to a superfluid flow around the ring. The collective modes of the system are explored both numerically and analytically using the Gross-Pitaevskii and hydrodynamic equations. Potential experimental schemes to detect vorticity are proposed and evaluated, which include measuring the splitting of collective-mode frequencies, observing expansion following release from the trap, and probing the momentum distribution of the condensate.
After reviewing the ideal Bose-Einstein gas in a box and in a harmonic trap, I discuss the effect of interactions on the formation of a Bose-Einstein condensate (BEC), along with the dynamics of small-amplitude perturbations (the Bogoliubov equations). When the condensate rotates with angular velocity Omega, one or several vortices nucleate, with many observable consequences. With more rapid rotation, the vortices form a dense triangular array, and the collective behavior of these vortices has additional experimental implications. For Omega near the radial trap frequency omega_perp, the lowest-Landau-level approximation becomes applicable, providing a simple picture of such rapidly rotating condensates. Eventually, as Omega approaches omega_perp, the rotating dilute gas is expected to undergo a quantum phase transition from a superfluid to various highly correlated (nonsuperfluid) states analogous to those familiar from the fractional quantum Hall effect for electrons in a strong perpendicular magnetic field.
We study the formation, stability, and decay of macrovortices in a rotating Bose gas confined by a Mexican-hat potential with a multiconfigurational ansatz. By systematically including correlations beyond the mean-field level, we map the equilibrium phase diagram and identify regimes of coexistence between vortex lattices and multiply charge central vortices. Quench dynamics reveals that macrovortices are robust under changes in rotation or interaction strength, sustaining clean monopole oscillations with well-separated, vorticity-dependent breathing frequencies. In contrast, trap quenches trigger a universal decay process mediated by vortex-phonon coupling, in which rotational energy is progressively transferred to compressible modes until the macrovortex splits into singly quantized vortices. Our results demonstrate that macrovortex lifetimes and decay pathways can be tuned by trap confinement, providing experimentally accessible signatures of vortex-phonon interactions and collective energy transfer in correlated quantum fluids.