1 / 50

Rotation of cold atoms

Irreversible loading of optical lattices. Rotation of cold atoms. Christopher Foot. University of Oxford. Outline. Superfluidity – tested by the response to rotation TOP trap  rotating elliptical potential Observation of the scissors mode Nucleation of vortices

xuxa
Download Presentation

Rotation of cold atoms

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Irreversible loading of optical lattices Rotation of cold atoms Christopher Foot University of Oxford

  2. Outline • Superfluidity – tested by the response to rotation • TOP trap  rotating elliptical potential • Observation of the scissors mode • Nucleation of vortices • Superfluid gyroscope • Ring trap for cold atoms • Rotating optical lattice  artificial B-field

  3. Magnetic coils and vacuum cell TOP trap Time-orbiting potential BEC 105 rubidium atoms. Temperature ~ 50 nK Density ~ 1014 cm-3

  4. TOP trap

  5. Shape of BEC in a TOP trap Pancake (oblate) rather than a cigar (prolate), or `baguette-shaped’ as in Ioffe traps.

  6. Quantised circulation in a quantum fluid ħ • The velocity field  gradient • Hence velocity field is irrotational • Circulation around a closed contour is quantised ħ ħ • Zero circulation = irrotational flow • Non-zero circulation = vortices

  7. Excitation of scissors mode Trap tilted adiabatically to angle   Trap suddenly rotated by -2 2 Cloud oscillates about new equilibrium position c.f. torsion pendulum

  8. Thermal cloud - two frequencies 1 0 5 f = 481(1) Hz 1 f = 226.4(0.6) Hz 0 ) g 2 e d - 5 ( e  = 13(3) Hz l g n - 1 0 A - 1 5 Angle (deg.) - 2 0 5 1 0 1 5 2 0 T i m e ( m s ) Condensate - single frequency 1 0 5 f = 382(1) Hz 0 scis ) g e d - 5 (  = 15(5) Hz e l g n - 1 0 A - 1 5 Angle (deg.) - 2 0 5 1 0 1 5 2 0 T i m e ( m s ) f = 127.6(0.9) Hz radial Scissors mode results Described in book: Bose-Einstein Condensation Pitaevskii & Stringari Oxford University Press 2003

  9. Types of flow

  10. BEC Rotation of the confining magnetic potential Impart angular momentum using rotating elliptical potential

  11. Nucleation of a single vortex

  12. Thresholds for vortex nucleation = Rotation frequency maximum rotation freq. • Critical frequency Wc = 1/2 • Line II : stability boundary for the quadrupole II branch. • Vortices nucleated below Wc. Eleanor Hodby et al

  13. Rotational also introduces ‘centrifugal’ term into the Hamiltonian Radial harmonic potential ‘Centrifugal’ term Radial trapping decreases as   

  14. Thresholds for vortex nucleation = Rotation frequency maximum rotation freq. • Critical frequency Wc = 1/2 • Line II : stability boundary for the quadrupole II branch. • Vortices nucleated below Wc. Eleanor Hodby et al

  15. Nucleation of a single vortex

  16. Scissors mode + vortex = ‘Superfluid gyroscope’ Numerical simulation by Nilsen, McPeake & McCann, Queens University, Belfast

  17. Nucleation of an array of vortices Nathan Smith Will Heathcote Chris Foot, Oxford Other experiments: ENS, MIT, JILA

  18. Observing the Tilting Mode ( side view of the vortex array )

  19. Precession of angle of condensate with vortex lattice

  20. Precession of angle of condensate with vortex lattice = 27.75 Hz < lz> = 8.4 ± 0.4 ħ

  21. Outline • Superfluidity – tested by the response to rotation • TOP trap  rotating elliptical potential • Observation of the scissors mode • Nucleation of vortices • Superfluid gyroscope • Ring trap for cold atoms • Rotating optical lattice  artificial B-field

  22. RF-dressed magentic potentials Modify magnetic trap using RF radiation • Proposed by: • O. Zobay and B. Garroway, PRL 86 (2001), 1195-1198. • Other Experiments: • Helen Perrin, Paris Nord, France. • Schmiedmayer Group: double well potential on an atom chip

  23. Modification of a magnetostatic trap by RF radiation magnetic potential avoided crossings MF= -1 rf MF= 0 rf x rf rf MF= +1 F=1 hyperfine level of Rb-87 rf rf rf rf Proposed by Zobay & Garraway PRL (2001) dressed-atom picture

  24. Modification of a magnetostatic trap by RF radiation dressed-atom potential magnetic potential MF= -1 rf rf rf MF= 0 rf x x rf rf rf rf MF= +1 F=1 hyperfine level of Rb-87 Proposed by Zobay & Garraway PRL (2001)

  25. Contours of a quadrupole magnetic field |B|= constant div B = 0 quadrupole coils ON Apply RF with TOP coils

  26. Atoms trapped on a magnetic field contour B0rf = 0.3 G B0rf = 0.18 G B0rf = 0.24 G B0rf = 0.12 G B0rf = 0.06 G

  27. Two-dimensional trapping of Bose gas • Weak radial confinement by the magnetic trap • Squeeze atoms between two sheets of light • Creates a thin sheet of atoms = 2D Bose gas z BEC z = 2 kHz  = 10 Hz Physics of 2-D systems

  28. Combined optical and magnetic trap = ring trap Contours of constant magnetic potential z x Light sheets confine atoms to plane z = const. rf rf x rf rf

  29. Trapping potential: Static + RF fields

  30. Ring shaped cloud of atoms (March 2007) Eileen Nugent & Chris Foot: application to persistent currents

  31. Rotating atoms in the ring trap 1. Original plug 3. Rotate deformation 2. Deform plug Persistent current Bill Phillip’s team at NIST, Gaithersburg have reported seeing a persistent current in a recent preprint Detection of current using scheme proposed in “Superfluid toroidal currents in atomic condensates ”, E. Nugent, D. McPeake and J.F. McCann, Phys Rev A 68, 063606.

  32. Outline • Superfluidity – tested by the response to rotation • TOP trap  rotating elliptical potential • Observation of the scissors mode • Nucleation of vortices • Superfluid gyroscope • Ring trap for cold atoms (persistent current) • Rotating optical lattice  artificial B-field

  33. Overview of cold atoms/molecules Atoms in optical lattices: Physics of strongly correlated systems Dilute quantum gases: BEC Fermi gas Cold molecules Quantum Information Processing Condensed Matter Physics Quantum fluids: superfluid helium

  34. Hamiltonian of atoms in optical lattice = Hamiltonian of CMP system Simulation of Condensed Matter Systems E.g. Fractional Quantum Hall Effect

  35. Mathematical equivalence of rotation on cold atoms and the effect of a magnetic field on charged particles (electrons) • Coriolis force: F = 2mvx • Lorentz force: F = q(E + vxB ) • q Beff↔ 2m  • For electron, q = -e • Cyclotron frequency, c= eB= 2rot  m

  36. Effective magnetic fields via rotation Neutral atom in rotating frame Electron under magnetic field

  37. Energy levels of a rotating 2-D harmonic oscillator at rest rotating 6 6 5 5 4 4 3 3  + 2 2 -1 +1  -  1 1 0 0 0 -3 -2 -1 0 1 2 3 -3 -2 -1 0 1 2 3

  38. Landau levels  Energy levels of 2D harmonic oscillator 6 5 4 3 2 1 0 -3 -2 -1 0 1 2 3 2D harmonic oscillator levels Degenerate Landau levels Near degeneracy as    . Interactions mix single particle states  strongly correlated multi-particle states

  39. Composite fermions Moore-Read Laughlin Vortex lattice Read-Rezayi Fractional quantum Hall states FQHE states predicted in BEC at fast rotation frequencies: Wilkin and Gunn, Ho, Paredes et al.,Cooper et al,… N=Number of atoms ( cf. filling factor,  ) Nv Number of vortices Zoo of strongly correlated states Lindemann criterion suggests that the vortex lattice melts when

  40. Optical lattice in the rotating frame

  41. Atoms in a rotating lattice Theory: R. Palmer & D. Jaksch, Phys. Rev. Lett. 96, 180407 (2006) • Phase shift from hopping around one lattice cell is   = flux through loop  d  = eBeff d2= h/e= flux quantum h h/e

  42. The Hofstadter butterfly E 0 1 A = Area

  43. The Hofstadter butterfly E E 0 1 En  B B

  44. The Hofstadter butterfly E 0 1 R.N. Palmer and D. Jaksch, Phys. Rev. Lett. 96, 180407 (2006)

  45. High-field FQHE The optical lattice setup allows to explore parameter regimes which are not accessible otherwise  beyond mimicking condensed matter

  46. Experiment in Oxford Microscope for quantum matter.

  47. Two-dimensional rotating optical lattice Confinement along z by two sheets of laser light (not shown). High NA lens Funded by ESF EuroQUAM programme

  48. Movie of rotating lattice Movie prepared by Ross Williams, Oxford.

  49. Summary • Scissors mode and vortices • Superfluidity • Magnetic trap + rf = ring potential for atoms in the dressed state • persistent current? • Rotating optical lattice gives term in atomic Hamiltonian analogous to an applied magnetic field of a charged particle (e.g. electron) • Highly correlated quantum states as in Fractional Quantum Hall Effect • Other experiments along the way?

  50. Acknowledgments People: • Chris Foot • Eileen Nugent • Ross Williams • Amita Deb • Ben Sheard • Ben Fletcher • Ben Sherlock • Min Sung Yoon • Marcus Gildemeister • Herbert Crepaz • Sara Al-Assam* Funding: • Engineering and Physical Sciences Research Council • European Science Foundation *Jointly supervised by Dieter Jaksch

More Related