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Phase imprinting of vortices in Bose-Einstein condensates using shaped light

Jasper Smits

Published Jan 1, 2016• 0 citations
OpenAlex

Abstract

Vorticity in superfluids has been studied for decades. In atomic BECs, vorticity was induced by stirring with laser beams. In this thesis, phase imprinting is introduced as an alternative method to induce vorticity in a BEC. By using a Liquid Crystal-on-Silicon spatial light modulator the phase of a laser beam can be shaped into any spatial profile, limited only by the imaging resolution. By using this shaped light in a two-photon Raman transfer, the phase of the electromagnetic field is transferred on to the Bose-condensed atoms.\n\nSimulations are performed for light containing a single phase winding, taking into account that the vortex in this beam has a finite vortex core size due to limited imaging resolution. It follows that the finite core size has an incomplete transfer as a result, but the phase winding is imprinted on to the atoms transferred to the second component.\n\nAlso, experimentally the two-photon Raman transition which is needed has been realised. However, the transfer process is impeded by a different two-photon process occuring at the same time, and by superradiant Rayleigh scattering. Recommendations are given to suppress these effects and successfully imprint the phase from the shaped light on to the atoms.

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Vorticity in superfluids has been studied for decades. In atomic BECs, vorticity was induced by stirring with laser beams. In this thesis, phase imprinting is introduced as an alternative method to induce vorticity in a BEC. By using a Liquid Crystal-on-Silicon spatial light modulator the phase of a laser beam can be shaped into any spatial profile, limited only by the imaging resolution. By using this shaped light in a two-photon Raman transfer, the phase of the electromagnetic field is transferred on to the Bose-condensed atoms.\n\nSimulations are performed for light containing a single phase winding, taking into account that the vortex in this beam has a finite vortex core size due to limited imaging resolution. It follows that the finite core size has an incomplete transfer as a result, but the phase winding is imprinted on to the atoms transferred to the second component.\n\nAlso, experimentally the two-photon Raman transition which is needed has been realised. However, the transfer process is impeded by a different two-photon process occuring at the same time, and by superradiant Rayleigh scattering. Recommendations are given to suppress these effects and successfully imprint the phase from the shaped light on to the atoms.
In this paper we demonstrate a technique that can create non-equilibrium vortex configurations with almost arbitrary charge and geometry in a Bose-Einstein condensate. We coherently transfer orbital angular momentum from a holographically generated light beam to a 87Rb condensate using a two-photon stimulated Raman process. Using matter wave interferometry, we verify the phase pattern imprinted onto the atomic wave function for a single vortex and a vortex-antivortex pair. In addition to their phase winding, the vortices created with this technique have an associated hyperfine spin texture.
In this paper we demonstrate a technique that can create non-equilibrium vortex configurations with almost arbitrary charge and geometry in a Bose-Einstein condensate. We coherently transfer orbital angular momentum from a holographically generated light beam to a 87Rb condensate using a two-photon stimulated Raman process. Using matter wave interferometry, we verify the phase pattern imprinted onto the atomic wave function for a single vortex and a vortex-antivortex pair. In addition to their phase winding, the vortices created with this technique have an associated hyperfine spin texture.
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.
We demonstrate numerically the efficient generation of vortices in Bose-Einstein condensates (BECs) by using a ``phase imprinting'' method. The method consists of passing a far-off-resonant laser pulse through an absorption plate with an azimuthally dependent absorption coefficient, imaging the laser beam onto a BEC, and thus creating the corresponding nondissipative Stark-shift potential and condensate phase shift. In our calculations we take into account experimental imperfections. We also propose an interference method to detect vortices by coherently pushing part of the condensate using optically induced Bragg scattering.
We propose a method to prepare states of given quantized circulation in annular Bose-Einstein condensates (BEC) confined in a ring trap using the method of phase imprinting without relying on a two-photon angular momentum transfer. The desired phase profile is imprinted on the atomic wave function using a short light pulse with a tailored intensity pattern generated with a spatial light modulator. We demonstrate the realization of ``helicoidal'' intensity profiles suitable for this purpose. Due to the diffraction limit, the theoretical steplike intensity profile is not achievable in practice. We investigate the effect of imprinting an intensity profile smoothed by a finite optical resolution onto the annular BEC with a numerical simulation of the time-dependent Gross-Pitaevskii equation. This allows us to optimize the intensity pattern for a given target circulation to compensate for the limited resolution.
Quantum vortices in superfluid Bose Einstein condensates (BECs) are excellent candidates\nfor studying hydrodynamic phenomena, such as turbulence and chaos, due to the\nquantization of vortex circulation and the absence of dissipation in BECs. Since the early\n2000s, many experimental groups have successfully observed vortices in dilute atomic\nBECs.\n\nThis work mainly focuses on creating quantum chaos with a few vortices in a twodimensional\nBEC of Rubidium􀀀87. We use graphics processing unit (GPU) computing methods to simulate our BEC trapped inside a harmonic potential with tight trapping in one direction. The quantum vortices are created by rotating the condensate. After generating the ground state of the BEC with a small number of singly charged vortices with positive phase winding, we imprint a 4\\pi phase winding on top of one vortex in the opposite orientation to that of the original vortex. This phase imprinting annihilates the preexisting vortex and creates a new singly-charged vortex with negative phase winding. Due to the high resolution of our system and an excellent vortex tracking algorithm, the location of phase imprinting can be delicately controlled.\n\nBoth the individual vortex dynamics and the dynamics of the entire system of vortices\nafter flipping a vortex have shown strong signs of chaos. This chaotic nature is\nfurther confirmed both qualitatively and quantitatively by employing two chaos indicators\non our numerical results. These chaos indicators are the Lyapunov exponent spectrum\nand the Smaller ALignment Index (SALI). The Lyapunov exponent remains positive and\nconverges to a positive value during an experimentally realistic time period, which is the\nsmoking gun for chaotic behaviour.