ECAMP 15

Bose–Einstein condensates (BECs) provide a unique platform for studying quantum fluid dynamics, where macroscopic quantum phenomena such as superfluidity and quantised vortices emerge. Vortices in BECs are characterised by phase singularities in the condensate wave function, and they reveal insights into angular momentum quantisation and topological defects in quantum systems [1]. The study of vortices in degenerate bosonic and fermionic gases has broad implications, ranging from quantum turbulence [2] to connections with superconductivity and the structure of neutron stars [3].

A key challenge in the study of BEC vortices is their controlled creation and manipulation. Typically, the vortices are produced using optical means: through phase imprinting [4], stirring with a laser beam [5], or using beams carrying orbital angular momentum, such as Laguerre–Gaussian (LG) beams [6]. Relatedly, an interesting playground for optical experiments is provided by the so-called $\Lambda$-type coupling configuration and the presence of a dark state. This optical coupling scheme has been used to, among others, realise atom control at subwavelength resolution [7], make narrow structures in the BEC [8], and to create vortices in BEC using Raman-type schemes [9].

In this work, we study the vortex states that emerge as a result of continuous interaction of a trapped two-component BEC mixture with the light fields in a $\Lambda$-type configuration. Specifically, we consider the case where one of the two beams is an LG beam, and investigate the resulting stationary states. The angular momentum of $\ell\hbar$ per photon carried by the LG beam leads to either one or both components being in a vortex state, with their vorticities differing by $\ell$ units. Depending on the ratio of magnitudes of the two beams, the ground state may have an unconventional structure, whereby the component having a vortex is surrounded by the second one which is vortex-free. The density profile of the vortex demonstrates a strong degree of localisation — away from the vortex core, the density falls off as $[1+(\rho/a)^{2}]^{-1/2}$, where $\rho$ is the distance from the core and $a$ is a controllable parameter. Such a vortex can be moved around the trap by moving the laser beams. Provided the movement speed is less than approximately half the speed of sound in the condensate, the shape of the vortex retains its structure during the movement, and the density of the second component does not get distorted as well.

We support our findings with analytical arguments based on the approximate one-dimensional Gross–Pitaevskii equation (GPE) for the dark state, which features a geometric vector potential term. Additionally, we present numerical solutions of the full GPE system describing the $\Lambda$-coupled three-level system.

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