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Science Discovery

Research of Vortex Nucleation in Bose-Einstein Condensates

Li Ji

Published Jan 1, 2017• 0 citations
Publisher

Abstract

Vortex nucleation is the key technology to realize quantum gyroscope in Bose-Einstein Condensates (BEC). Through mass investigation and research, the recent research status of vortex nucleation in Bose-Einstein Condensates is presented, the theory and experimentation about imprinting phase, rotating the potential trap and transferring the orbital angular momentum of a photon to generate BEC vortex are analyzed and compared in detail, furthermore, an improved method of rotating the potential trap to generate vortex is proposed. Quantum gyroscope based on BEC vortex has the potential advantages of realizing the ultra high sensitivity and small volume of quantum gyroscope. This paper aims to promote the development of quantum vortex gyroscope, which attracts extensive attention of domestic scholars.

DOI
10.11648/j.sd.20170501.11

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Vortex nucleation is the key technology to realize quantum gyroscope in Bose-Einstein Condensates (BEC). Through mass investigation and research, the recent research status of vortex nucleation in Bose-Einstein Condensates is presented, the theory and experimentation about imprinting phase, rotating the potential trap and transferring the orbital angular momentum of a photon to generate BEC vortex are analyzed and compared in detail, furthermore, an improved method of rotating the potential trap to generate vortex is proposed. Quantum gyroscope based on BEC vortex has the potential advantages of realizing the ultra high sensitivity and small volume of quantum gyroscope. This paper aims to promote the development of quantum vortex gyroscope, which attracts extensive attention of domestic scholars.
With high precision and sensitivity, quantum gyroscope has become a research hotspot of inertial technology in recent years. Because the Bose-Einstein Condensate (BEC) in atomic gas has more condensate atoms, atomic gas is pure and thin, and there is no friction in atoms, the matter–wave gyroscopy with counter-rotating vortex superpositions has great potential of higher sensitivity, higher precision, and miniaturization. The basic mechanism and sensitivity of the matter– wave gyroscopy with counter-rotating vortex superpositions were analyzed, and the interaction between superposition of vortex beams and BEC atomic gases were studied, it is Stimulated Raman Adiabatic Passage (STIRAP). In the study, the outstanding issue that the gyroscopy is difficult to obtain stable vortices with high order orbital angular momentum was clarified by theoretical derivation on the base of Gross-Pitaevskii equation which is the basic equation in BEC. For solving the above problems, the scheme which is easy to achieve based on Sombrero potential trap was proposed.
This paper presents the recent research status of quantum gyroscope and superfluid gyroscope based on the new physical effects of cryogenic Bose-Einstein condensation.The physical effects,operating principles and technical status of the two new types of gyroscopes were described.The quantum gyroscope is based on the Sagnac effect of mater wave,and its precision is several orders higher than that of optical gyroscope.The superfluid gyroscope is based on the superfluid’s low-viscosity and the quantum’s vortex properties,and can obtain super-high precision in principle.At last,the paper analyzes the development prospect of the two types of gyroscopes.
A method to produce a spin-dependent rotating potential using near-resonant circularly polarized laser beams is proposed. It is shown that half-quantum vortices are nucleated in a spinor Bose-Einstein condensate (BEC) with an antiferromagnetic interaction. In contrast to the vortex nucleation in a scalar BEC, the spin-vortex nucleation occurs at a low rotation frequency ($\ensuremath{\simeq}0.1{\ensuremath{\omega}}_{\ensuremath{\perp}}$ with ${\ensuremath{\omega}}_{\ensuremath{\perp}}$ being the radial trap frequency) in a short nucleation time $\ensuremath{\simeq}50\phantom{\rule{0.3em}{0ex}}\mathrm{ms}$ without dissipation. A method for nondestructive measurement of half-quantum vortices is discussed.
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.
We study the generation of vortices in rotating Bose-Einstein condensates, a situation that has been realized in a recent experiment [K. W. Madison, F. Chevy, W. Wohlleben, and J. Dalibard, Phys. Rev. Lett. 84 806 (2000)]. By combining a linear stability analysis with the global optimization of the nonlinear free-energy functional, we study the regimes that can be reached in current experiments. We find a hysteresis phenomenon in the vortex nucleation due to the metastabilization of the vortexless condensate. We also prove that for a fast enough rotating trap, the ground state of the condensate hosts one or more bent vortex lines.