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arXiv:2401.10132 · Physics of Fluids

Trapped vortex dynamics implemented in composite Bessel beams

Andrew A. Voitiv, Mark E. Siemens, Mark T. Lusk

Published Jan 1, 2024• 2 citations
arXivHTMLPDF

Abstract

The divergence-free nature of Bessel beams can be harnessed to effectively trap optical vortices in free space laser propagation. We show how to generate arbitrary vortex configurations in Bessel traps to investigate few-body vortex interactions within a dynamically evolving fluid of light, which is a formal analog to a non-interacting Bose gas. We implement—theoretically and experimentally—initial conditions of vortex configurations first predicted in harmonically trapped quantum fluids, in the limit of weak atomic interactions, and model and measure the resultant dynamics. These hard trap dynamics are distinct from the harmonic trap predictions due to the non-local interactions that occur among the hard-wall boundary and steep phase gradients that nucleate other vortices. By simultaneously presenting experimental demonstrations with the theoretical proposal, we validate the potential application of using Bessel hard-wall traps as testing grounds for engineering few-body vortex interactions within trapped, two-dimensional compressible fluids.

DOI
10.1063/5.0187870

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The divergence-free nature of Bessel beams can be harnessed to effectively trap optical vortices in free space laser propagation. We show how to generate arbitrary vortex configurations in Bessel traps to investigate few-body vortex interactions within a dynamically evolving fluid of light, which is a formal analog to a non-interacting Bose gas. We implement—theoretically and experimentally—initial conditions of vortex configurations first predicted in harmonically trapped quantum fluids, in the limit of weak atomic interactions, and model and measure the resultant dynamics. These hard trap dynamics are distinct from the harmonic trap predictions due to the non-local interactions that occur among the hard-wall boundary and steep phase gradients that nucleate other vortices. By simultaneously presenting experimental demonstrations with the theoretical proposal, we validate the potential application of using Bessel hard-wall traps as testing grounds for engineering few-body vortex interactions within trapped, two-dimensional compressible fluids.
We propose a method to controllably create free-space, “hard-trapped” two-dimensional fluids with Bessel-Gaussian beam superpositions. We use these systems to experimentally demonstrate several vortex dynamics that resemble dynamics numerically predicted in weakly-interacting quantum fluids. Theoretically, we perform a Bessel-mode decomposition on an initial state containing an arrangement of optical vortices. The experiment is performed using a laser beam that is structured holographically with a spatial light modulator that contains the initial condition of the reconstructed field from the theoretical decomposition. This works allows for the experimental verification of many numerically predicted dynamics or the discovery of new dynamics from experiment.
Linear combinations of Bessel beams can be used to effectively trap light within cylindrical domains. Such hard traps can be used to produce states that exhibit stationary arrays of optical vortices from the perspective of a steadily rotating frame. These patterned singularities can be engineered to have singularities of the same or mixed charges and the requisite rotation rates are quantized even though the setting is purely linear. A hydrodynamic interpretation is that the vortices are at rest within a compressible, two-dimensional fluid of light.
Dilute gas Bose-Einstein condensates (BECs) provide unique and powerful experimental platforms to study fluid turbulence. Some aspects of BEC hydrodynamics are specific to atomic quantum fluids such as quantized vortices and flexible trapping geometries. However, there are features of turbulence that are universal and simpler to understand in such systems. BECs are also of interest in fundamental physics in their own right and a rich synthesis of theory and experiment has yielded powerful numerical methods to simulate and study BEC dynamics. In this dissertation I present two experiments, one conducted and one proposed, describing novel aspects of the generation and detection of vorticity in Bose-Einstein condensates. Models of BEC dynamics at zero temperature are provided by the Gross-Pitaevskii equation. Simple and fast numerical solutions of this equation have yielded a wealth of literature. However, in experimental reality the atomic ensemble exists at a finite temperature and consists of a BEC coexisting with a thermal cloud of non-condensed atoms. The interaction between the condensate and the thermal fraction yields rich and complex physics that require more advanced models. We present an experiment demonstrating the relaxation dynamics of a BEC in a rotating trap perturbed by a repulsive laser barrier. The data provided by this experiment are valuable to further development of theoretical models that incorporate interactions between the BEC and noncondensed atoms. In the field of quantum fluid dynamics, an experimental method to determine the position and circulation of vortices is a highly sought-after capability. Onsager's point-vortex model of turbulence completely determines the kinetic energy spectrum of an incompressible fluid by these degrees of freedom. We present proof-of-principle simulations that describe a new method of spatially sampling the velocity field of a two-dimensional BEC by using an optical lattice analogously to a Shack-Hartmann Wavefront Sensor. Extracting vortex information from the appropriately sampled velocity field can be accomplished either qualitatively or with detection algorithms. This method requires minimal experimental infrastructure and is generally applicable across atomic species. The implications of measuring a condensate velocity field are broad and these initial results provide the first step towards realizing a valuable tool in BEC physics.
Recent studies have confirmed the coupling of optical vortices, such as Laguerre-Gaussian and Bessel-Gaussian modes, to quadrupole-active atomic transitions. This interaction has been shown to be enhanced considerably in the case of Laguerre-Gaussian beams due to the gradient coupling, particularly, in the case of a relatively large winding number. Here, we consider the trapping and the dynamics of atoms in the optical quadrupole potential generated by two coaxial counterpropagating optical vortex beams. We focus on the atomic transition $6{\phantom{\rule{0.16em}{0ex}}}^{2}{S}_{1/2}\ensuremath{\rightarrow}5{\phantom{\rule{0.16em}{0ex}}}^{2}{D}_{5/2}$ in Cs which is a dipole-forbidden but a quadrupole-allowed transition. We show how this atomic transition engages with the optical vortex fields at near resonance, leading to atom trapping in the optical quadrupole potential well accompanied by translational motion. We show how the optical forces generate the motion of the atoms trapped within the quadrupole potential, illustrating the results using typical experimentally accessible parameters.
The nonequilibrium dynamics of vortices in two-dimensional quantum fluids can be predicted by accounting for the way in which vortex ellipticity is coupled to the gradient in background fluid density. In the absence of nonlinear interactions, a harmonically trapped fluid can be analyzed analytically to show that single vortices will move in an elliptic trajectory that has the same orientation and aspect ratio as the vortex projection itself. This allows the vortex ellipticity to be estimated through observation of its trajectory. A combination of analysis and numerical simulation is then used to show that nonlinear interactions cause the vortex orientation to precess, and that the rate of vortex precession is once again mimicked by a precession of the elliptical trajectory. Both vortex ellipticity and rate of precession can therefore be inferred by observing its motion in a trap. An ability to anticipate and control local vortex structure and vortex trajectory is expected to prove useful in designing few-vortex systems in which ellipticity is a ubiquitous, as-yet-unharnessed feature.
We study controlled methods of preparing vortex configurations in atomic Bose-Einstein condensates and their use in the studies of fundamental vortex scattering, reconnection processes, and superfluid sound emission. We explore techniques of imprinting vortex rings by means of coherently driving internal atomic transitions with electromagnetic fields which exhibit singular phase profiles. In particular, we show that a vortex ring can be prepared by two focused co-propagating Gaussian laser beams. More complex vortex systems may also be imprinted by directly superposing simpler field configurations or by programming their phase profiles on optical holograms. We analyze specific examples of two merging vortex rings in a trapped two-species 87Rb^{87}\mathrm{Rb}87Rb gas. We calculate the radiated sound energy in the reconnection process and show that the vortex relaxation and the redistribution of sound energy can be controlled by the imprinting process. As another creation technique, we study engineering pairs of two-dimensional point vortices in the condensates using a `light roadblock' in ultraslow light propagation. We show how this can be used to study vortex collisions in compressible superfluids and how these collisions result in energy dissipation via phonons and, sometimes, annihilation of vortex pairs.