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arXiv:2210.10525 · Physical Review A

Equatorial waves in rotating bubble-trapped superfluids

Guangyao Li, Dmitry K. Efimkin

Published Feb 23, 2023• 17 citations
arXivHTMLPDF

Abstract

As the Earth rotates, the Coriolis force causes various oceanic and atmospheric waves to be trapped along the equator, including Kelvin, Yanai, Rossby, and Poincar\'e modes. It has been demonstrated that the mathematical origin of these waves is related to the nontrivial topology of the underlying hydrodynamic equations. Inspired by recent observations of Bose-Einstein condensation (BEC) in bubble-shaped traps in microgravity ultracold quantum gas experiments, we demonstrate that equatorial modes are supported by a rapidly rotating condensate in a spherical geometry. Using a zero-temperature coarse-grained hydrodynamic framework, we reformulate the coupled oscillations of the superfluid and the Abrikosov vortex lattice resulting from rotation as a Schr\"odinger-like eigenvalue problem. The resulting non-Hermitian Hamiltonian is topologically nontrivial. We also solve the hydrodynamic equations for a spherical geometry and find that the rotating superfluid hosts Kelvin, Yanai, and Poincar\'e equatorial modes, but not the Rossby mode. Our predictions can be tested with state-of-the-art bubble-shaped trapped BEC experiments.

DOI
10.1103/physreva.107.023319

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As the Earth rotates, the Coriolis force causes various oceanic and atmospheric waves to be trapped along the equator, including Kelvin, Yanai, Rossby, and Poincar'e modes. It has been demonstrated that the mathematical origin of these waves is related to the nontrivial topology of the underlying hydrodynamic equations. Inspired by recent observations of Bose-Einstein condensation (BEC) in bubble-shaped traps in microgravity ultracold quantum gas experiments, we demonstrate that equatorial modes are supported by a rapidly rotating condensate in a spherical geometry. Using a zero-temperature coarse-grained hydrodynamic framework, we reformulate the coupled oscillations of the superfluid and the Abrikosov vortex lattice resulting from rotation as a Schr"odinger-like eigenvalue problem. The resulting non-Hermitian Hamiltonian is topologically nontrivial. We also solve the hydrodynamic equations for a spherical geometry and find that the rotating superfluid hosts Kelvin, Yanai, and Poincar'e equatorial modes, but not the Rossby mode. Our predictions can be tested with state-of-the-art bubble-shaped trapped BEC experiments.
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.
We predict and describe a new collective mode in rotating Bose–Einstein condensates, which is very similar to 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 zero-point pressure and inhomogeneity of the gas. 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 them to those resulting from the Thomas–Fermi approximation.
The irrotational nature of superfluids leads to spectacular rotational properties. For the fluid to rotate, its density must locally vanish at a singular point called a quantum vortex. The annular geometry is of great interest for studying superfluidity as the gas can rotate in this geometry around a central hole without requiring any singularity, allowing the existence of persistent currents along the ring with a quantized circulation. In out experiment, we confine cold atoms dressed by a radiofrequency field in an adiabatic potential based on a quadrupolar magnetic trap. The resulting bubble-shaped potential, both very smooth and easily tunable, allows us to produce two types of ring-shaped Bose-Einstein condensates. A first strategy consists in adding a far-detuned light sheet to confine the atoms at the intersection between the bubble and the horizontal plane imposed by the light field – i.e. a ring. We present the implementation and optimization of this trap and demonstrate the possibility to prepare and observe superfluid currents in the ring. A second path exploits the centrifugal force and the anharmonicity of the adiabatic potential to create an effective Mexican hat potential by rotating the trapped atoms at the bottom of the bubble faster than the trap frequency. After having realized such a system, we probe its quadrupolar modes to characterize the rotation. The study of vortex distribution in the rotating gas also shows a thermal melting effect of the finite temperature vortex lattice.
Motivated by the recent realization of space-borne Bose-Einstein Condensates (BECs) under microgravity conditions, we extend the understanding of ultracold dipolar bosonic gases by exploring their behavior in a novel trapping configuration known as the ``bubble trap'' topology. Utilizing the three-dimensional numerical simulations within the extended Gross-Pitaevskii framework, we unveil diverse ground-state phases in this static curved topology. Subsequently, we investigate the influence of rotation on a dipolar BEC confined to the surface of a spherical bubble. Our findings reveal that the rotation of a bubble trap at certain rotation frequencies can modify the effective local dipole-dipole interaction strength, leading to the induction of supersolidity and the formation of quantum droplets. In addition, we demonstrate that a bubble trap can sustain high circulation, with the flow persisting for a longer time. Significantly, adjusting the rf detuning parameter allows the condensate to achieve hypersonic velocity. Finally, we also explore the impact of drastic change in the topological nature of the trap on the rotating dipolar BEC, transitioning from a filled shell trap to a bubble trap and vice versa. Based on the results of the topological transition, we propose a dynamic protocol to drive the interacting atomic gas into the quantum Hall regime.
The tensor-virial method is applied for a study of oscillation modes of uniformly rotating Bose-Einstein condensed gases, whose rigid-body rotation is supported by an vortex array. The second-order virial equations are derived in the hydrodynamic regime for an arbitrary external harmonic trapping potential assuming that the condensate is a superfluid at zero temperature. The axisymmetric equilibrium shape of the condensate is determined as a function of the deformation of the trap; its domain of stability is bounded by the constraint \ensuremath{\Omega}1 on the rotation rate (measured in units of the trap frequency ${\ensuremath{\omega}}_{0}).$ The oscillations of the axisymmetric condensate are stable with respect to the transverse-shear and toroidal modes of oscillations, corresponding to the l=2,∣m∣=1,2l=2,|m|=1,2l=2,∣m∣=1,2 surface deformations. The eigenfrequencies of the modes are real and represent undamped oscillations. The condensate is also stable against quasiradial pulsation modes (l=2,m=0),(l=2,m=0),(l=2,m=0), and its oscillations are undamped, if the superflow is assumed incompressible. In the compressible case we find that for a polytropic equation of state, the quasiradial oscillations are unstable when $\ensuremath{\gamma}(3\ensuremath{-}{\ensuremath{\Omega}}^{2})1\ensuremath{-}3{\ensuremath{\Omega}}^{2},$ and are stable otherwise. Thus, a dilute Bose gas, whose equation of state is polytropic with \ensuremath{\gamma}=2 to leading order in the diluteness parameter, is stable irrespective of the rotation rate. In nonaxisymmetric traps, the equilibrium constrains the (dimensionless) deformation in the plane orthogonal to the rotation to the domain ${A}_{2}{\ensuremath{\Omega}}^{2}$ with \ensuremath{\Omega}1. The second-harmonic-oscillation modes in nonaxisymmetric traps separate into two classes that have even or odd parity with respect to the direction of the rotation axis. Numerical solutions show that these modes are stable in the parameter domain where equilibrium figures exist.
Ultracold quantum gases are highly controllable and thus capable of simulating difficult quantum many-body problems ranging from condensed matter physics to astrophysics. Although experimental realizations have so far been restricted to flat geometries, recently also curved quantum systems, with the prospect of exploring tunable geometries, have been produced in microgravity facilities as ground-based experiments are technically limited. Here, we analyze bubble-trapped condensates, in which the atoms are confined on the surface of a thin spherically symmetric shell by means of external magnetic fields. A thermally induced proliferation of vorticity yields a vanishing of superfluidity. We describe the occurrence of this topological transition by conceptually extending the theory of Berezinskii, Kosterlitz, and Thouless for infinite uniform systems to such finite-size systems. Unexpectedly, we find universal scaling relations for the mean critical temperature and the finite width of the superfluid transition. Furthermore, we elucidate how they could be experimentally observed in finite-temperature hydrodynamic excitations.