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arXiv:2403.17403 · Physical Review Letters

Vortex Nucleations in Spinor Bose Condensates under Localized Synthetic Magnetic Fields

L.-R. Liu, Shun‐Chi Wu, T.-W. Liu, Hei-Chen Hsu, T. -K. Shen, Sungkit Yip, Yuki Kawaguchi, Y.-J. Lin

Published Jul 28, 2025• 1 citation
arXivHTMLPDF

Abstract

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.

DOI
10.1103/zj34-15bk

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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.
We observed a new mechanism for vortex nucleation in Bose–Einstein condensates (BECs) subject to synthetic magnetic fields. We made use of a strong synthetic magnetic field initially localized between a pair of merging BECs to rapidly create vortices in the bulk of the merged condensate. Unlike previous implementations and in agreement with our Gross–Pitaevskii equation simulations, our dynamical process rapidly injects vortices into our system's bulk, and with initial number in excess of the system's equilibrium vortex number.
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.
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.
Quantum mechanically, static or applied gauge fields manifest themselves by directly coupling to a system's phase. Artificial gauge field techniques manipulate the phase of a Bose-Einstein condensate's order parameter, yielding effects present in condensed matter systems subject to magnetic fields, electric fields, or spin-orbit coupling. In this chapter, we explore the impact of these artificial gauge fields on Bose- Einstein condensates and explain the consequences. Several analogues to traditional condensed matter systems are enabled by these techniques, including the Hall effect, superfluid vortex nucleation in systems with artificial magnetic fields, and magnetic-like phase transitions in systems with spin-orbit coupling. Introduction Since the first experiments with Bose-Einstein condensates (BECs), researchers have exploited the universality of physical laws to draw analogies between the behavior of ultracold quantum gases and systems ranging from material to astrophysical. These analogous situations are deliberately engineered, giving cold-atom “quantum simulators” [1] that exhibit behavior either observed or predicted in analogous quantum systems. Superfluidity was one of the first many-body quantum phenomena demonstrated in BECs. For example, several experiments showed superfluid behavior by rapidly rotating the condensates and observing the formation of vortices [2, 3, 4, 5] – quantized point-defects in the BEC's order parameter. In the rotating frame of these experiments, this nucleation of vortices could be understood as the consequence of an artificial magnetic field [6] that arises via the formal equivalence of the rotating-frame Coriolis force and the Lorentz force, which we describe in Section 15.4.1. Together with other measurements, these results proved to be in excellent agreement with the predictions of the Gross-Pitaevskii equation (GPE) [7], a decades-old idealization of superfluid helium. Buoyed by the prospect for studying magnetic field–driven strongly correlated systems using these nearly ideal quantum gases, proposals for alternate techniques to simulate gauge fields were developed. These methods primarily employ an internal state–selective atom–light coupling, where the photon momentum provides the forces necessary to mimic a Lorentz force [8, 9, 10, 11, 12, 13, 14, 15, 16]. The first demonstration of this type of technique used a spatially dependent Ramantransition scheme to effect a magnetic field [17], and experiments demonstrating artificial electric fields [18] and spin-orbit coupling [19, 20, 21, 22, 23, 24] soon followed.
We demonstrate synthetic azimuthal gauge potentials for Bose-Einstein condensates from engineering atom-light couplings. The gauge potential is created by adiabatically loading the condensate into the lowest energy Raman-dressed state, achieving a coreless vortex state. The azimuthal gauge potentials act as effective rotations and are tunable by the Raman coupling and detuning. We characterize the spin textures of the dressed states, in agreements with the theory. The lowest energy dressed state is stable with a 4.5-s half-atom-number-fraction lifetime. In addition, we exploit the azimuthal gauge potential to demonstrate the Hess-Fairbank effect, the analogue of Meissner effect in superconductors. The atoms in the absolute ground state has a zero quasiangular momentum and transits into a polar-core vortex when the synthetic magnetic flux is tuned to exceed a critical value. Our demonstration serves as a paradigm to create topological excitations by tailoring atom-light interactions where both types of SO(3) vortices in the |⟨F[over →]⟩|=1 manifold, coreless vortices and polar-core vortices, are created in our experiment. The gauge field in the stationary Hamiltonian opens a path to investigating rotation properties of atomic superfluids under thermal equilibrium.
Realistic methods to create vortices in spin-orbit-coupled Bose-Einstein condensates are discussed. It is shown that, contrary to common intuition, rotation of the trap containing a spin-orbit condensate does not lead to an equilibrium state with static vortex structures but gives rise instead to nonequilibrium behavior described by an intrinsically time-dependent Hamiltonian. We propose here the following alternative methods to induce thermodynamically stable static vortex configurations: (i) to rotate both the lasers and the anisotropic trap and (ii) to impose a synthetic Abelian field on top of synthetic spin-orbit interactions. Effective Hamiltonians for spin-orbit condensates under such perturbations are derived for most currently known realistic laser schemes that induce synthetic spin-orbit couplings. The Gross-Pitaevskii equation is solved for several experimentally relevant regimes. The new interesting effects include spatial separation of left- and right-moving spin-orbit condensates, the appearance of unusual vortex arrangements, and parity effects in vortex nucleation where the topological excitations are predicted to appear in pairs. All these phenomena are shown to be highly nonuniversal and depend strongly on a specific laser scheme and system parameters.