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arXiv:2203.04059 · Physical Review A

Vortex creation, annihilation, and nonlinear dynamics in atomic vapors

Pierre Azam, Adam Griffin, Sergey Nazarenko, Robin Kaiser

Published Apr 14, 2022• 20 citations
arXivHTMLPDF

Abstract

We exploit techniques for generating vortices and controlling their interactions in an optical beam in a nonlinear atomic vapor. A precise control of the vortex positions allows us to observe strong interactions leading to vortex dynamics involving annihilations. With this improved controlled nonlinear system, we get closer to the pure hydrodynamic regime than in previous experiments while a wavefront sensor offers us a direct access to the fluid's density and velocity. Finally, we developed a relative phase shift method which mimics a time evolution process without changing nonlinear parameters. These observations are an important step toward the experimental implementation of a two-dimensional turbulent state.

DOI
10.1103/physreva.105.043510

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We exploit techniques for generating vortices and controlling their interactions in an optical beam in a nonlinear atomic vapor. A precise control of the vortex positions allows us to observe strong interactions leading to vortex dynamics involving annihilations. With this improved controlled nonlinear system, we get closer to the pure hydrodynamic regime than in previous experiments while a wavefront sensor offers us a direct access to the fluid's density and velocity. Finally, we developed a relative phase shift method which mimics a time evolution process without changing nonlinear parameters. These observations are an important step toward the experimental implementation of a two-dimensional turbulent state.
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.
Abstract Optical vortices, which are beams with spiral‐shaped wavefronts and screw phase dislocations, have potential for supporting high‐capacity optical communications. In this study, the generation of 1D and 2D vortex‐beam arrays is theoretically proposed and experimentally demonstrated by introducing novel forked‐photonic lattices in a three‐level 85 Rb atomic medium. Such forked‐photonic lattices are established through the interference of Gaussian and vortex coupling beams. The input Gaussian probe beam that travels through this lattice experiences phase superposition and is diffracted into vortex‐beam arrays. Moreover, the relative efficiency of the high‐order diffractions can be enhanced by tuning the two‐photon detuning and power of the coupling beams. The enriched diffractive arrays of a vortex probe beam propagating in such forked‐photonic lattices are also presented. The experimental results agree well with those of the numerical simulations. This work suggests that atomic systems are a fertile platform for creating and controlling vortex‐beam arrays, and that they can shed light on ongoing exploration in the fields of optical manipulation and quantum information processing.
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.
Methods to generate, manipulate, and measure optical and atomic fields with global or local angular momentum have a wide range of applications in both fundamental physics research and technology development. In optics, the engineering of angular momentum states of light can aid studies of orbital angular momentum (OAM) exchange between light and matter. The engineering of optical angular momentum states can also be used to increase the bandwidth of optical communications or serve as a means to distribute quantum keys, for example. Similar capabilities in Bose-Einstein condensates are being investigated to improve our understanding of superfluid dynamics, superconductivity, and turbulence, the last of which is widely considered to be one of most ubiquitous yet poorly understood subjects in physics. The first part of this two-part dissertation presents an analysis of techniques for measuring and manipulating quantized vortices in BECs. The second part of this dissertation presents theoretical and numerical analyses of new methods to engineer the OAM spectra of optical beams. The superfluid dynamics of a BEC are often well described by a nonlinear Schrodinger equation. The nonlinearity arises from interatomic scattering and enables BECs to support quantized vortices, which have quantized circulation and are fundamental structural elements of quantum turbulence. With the experimental tools to dynamically manipulate and measure quantized vortices, BECs are proving to be a useful medium for testing the theoretical predictions of quantum turbulence. In this dissertation we analyze a method for making minimally destructive in situ observations of quantized vortices in a BEC. Secondly, we numerically study a mechanism to imprint vortex dipoles in a BEC. With these advancements, more robust experiments of vortex dynamics and quantum turbulence will be within reach. A more complete understanding of quantum turbulence will enable principles of microscopic fluid flow to be related to the statistical properties of turbulence in a superfluid. In the second part of this dissertation we explore frequency mixing, a subset of nonlinear optical processes in which one or more input optical beam(s) are converted into one or more output beams with different optical frequencies. The ability of parametric nonlinear processes such as second harmonic generation or parametric amplification to manipulate the OAM spectra of optical beams is an active area of research. In a theoretical and numerical investigation, two complimentary methods for sculpting the OAM spectra are developed. The first method employs second harmonic generation with two non-collinear input beams to develop a broad spectrum of OAM states in an optical field. The second method utilizes parametric amplification with collinear input beams to develop an OAM-dependent gain or attenuation, termed dichroism for OAM, to effectively narrow the OAM spectrum of an optical beam. The theoretical principles developed in this dissertation enhance our understanding of how nonlinear processes can be used to engineer the OAM spectra of optical beams and could serve as methods to increase the bandwidth of an optical signal by multiplexing over a range of OAM states.
Nonlinear holography is a powerful technique for shaping beams at new optical frequencies. Selectively reconstructing target wavefront information from multichannel nonlinear holography is challenging due to the critical phase-matching condition. Herein, we propose a scheme for all-optical controlled multichannel nonlinear holography using four-wave mixing (FWM) in Rb vapor. A dispersion-controlled wavevector was dynamically tuned to achieve a full phase-matching condition for efficient target wavefront reconstruction. We adjusted the frequency and intensity of the control beam to selectively reconstruct annular vortex arrays in the FWM signal. Four switchable holographic channels were established for beam shaping via experimental parameter optimization. Our study demonstrates that the atomic system is ideal for studying nonlinear control of structured light and aids in constructing all-optical multichannel devices for classical and quantum information processing.
We experimentally generate a vortex beam through a four-wave mixing (FWM) process after satisfying the phase-matching condition in a rubidium atomic vapor cell with a photonic band gap (PBG) structure. The observed FWM vortex can also be viewed as the reflected part of the launched probe vortex from the PBG. Further, we investigate the propagation behaviors, including the spatial shift and splitting of the probe and FWM vortices in the medium with enhanced Kerr nonlinearity induced by electromagnetically induced transparency. This Letter can be useful for better understanding and manipulating the applications involving the interactions between optical vortices and the medium.