Dieter Jaksch, Irreversible loading of optical lattices Rotation of cold atoms University of Oxford Christopher Foot

Dieter Jaksch, 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

Dieter Jaksch, BEC 10 5 rubidium atoms. Temperature ~ 50 nK Density ~ cm -3 Magnetic coils and vacuum cell TOP trap Time-orbiting potential

Dieter Jaksch, TOP trap

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

Dieter Jaksch, u The velocity field  gradient u Hence velocity field is irrotational u Circulation around a closed contour is quantised Zero circulation = irrotational flow Non-zero circulation = vortices ħ ħ ħ Quantised circulation in a quantum fluid

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

Dieter Jaksch, Described in book: Bose-Einstein Condensation Pitaevskii & Stringari Oxford University Press 2003 Scissors mode results

Dieter Jaksch, Types of flow

Dieter Jaksch, Rotation of the confining magnetic potential BEC Impart angular momentum using rotating elliptical potential

Dieter Jaksch, Nucleation of a single vortex

Dieter Jaksch,  Critical frequency  c  2 u Line II : stability boundary for the quadrupole II branch.  Vortices nucleated below  c. Thresholds for vortex nucleation Eleanor Hodby et al = Rotation frequency maximum rotation freq.

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

Dieter Jaksch,  Critical frequency  c  2 u Line II : stability boundary for the quadrupole II branch.  Vortices nucleated below  c. Thresholds for vortex nucleation Eleanor Hodby et al = Rotation frequency maximum rotation freq.

Dieter Jaksch, Nucleation of a single vortex

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

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

Dieter Jaksch, Observing the Tilting Mode ( side view of the vortex array )

Dieter Jaksch, Precession of angle of condensate with vortex lattice

Dieter Jaksch, Precession of angle of condensate with vortex lattice = Hz = 8.4 ± 0.4 ħ

Dieter Jaksch, 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

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

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

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

Dieter Jaksch, Contours of a quadrupole magnetic field div B  quadrupole coils ON |B|  constant Apply RF with TOP coils

Dieter Jaksch, Atoms trapped on a magnetic field contour B 0 rf = 0.3 G B 0 rf = 0.24 G B 0 rf = 0.18 G B 0 rf = 0.12 GB 0 rf = 0.06 G

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

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

Dieter Jaksch, Trapping potential: Static + RF fields

Dieter Jaksch, Ring shaped cloud of atoms (March 2007) Eileen Nugent & Chris Foot: application to persistent currents

Dieter Jaksch, Rotating atoms in the ring trap 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, Persistent current 1. Original plug 2. Deform plug 3. Rotate deformation Bill Phillip’s team at NIST, Gaithersburg have reported seeing a persistent current in a recent preprint

Dieter Jaksch, 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

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

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

Dieter Jaksch, Mathematical equivalence of rotation on cold atoms and the effect of a magnetic field on charged particles (electrons) Coriolis force: F = 2m v x  Lorentz force: F = q(E  v x B ) q B eff ↔ 2m  For electron, q  e Cyclotron frequency,  c  eB  2  rot m 

Dieter Jaksch, Effective magnetic fields via rotation Neutral atom in rotating frame Electron under magnetic field

Dieter Jaksch, Energy levels of a rotating 2-D harmonic oscillator 0 at rest rotating        

Dieter Jaksch, Landau levels  2D harmonic oscillator levelsDegenerate Landau levels Energy levels of 2D harmonic oscillator Near degeneracy as    . Interactions mix single particle states  strongly correlated multi-particle states

Dieter Jaksch, Fractional quantum Hall states FQHE states predicted in BEC at fast rotation frequencies: Wilkin and Gunn, Ho, Paredes et al., Cooper et al,… Read-RezayiMoore-Read Composite fermionsLaughlin Vortex lattice Zoo of strongly correlated states Lindemann criterion suggests that the vortex lattice melts when N  Number of atoms N v Number of vortices ( cf. filling factor, )

Dieter Jaksch, Optical lattice in the rotating frame

Dieter Jaksch, Atoms in a rotating lattice Phase shift from hopping around one lattice cell is   Theory: R. Palmer & D. Jaksch, Phys. Rev. Lett. 96, (2006)   eB eff d 2    h h/e  d  = flux through loop h/e  flux quantum

Dieter Jaksch, The Hofstadter butterfly 0 1 E A = Area

Dieter Jaksch, The Hofstadter butterfly 0 1 E B E n  B E

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

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

Dieter Jaksch, Experiment in Oxford Microscope for quantum matter.

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

Dieter Jaksch, Movie of rotating lattice Movie prepared by Ross Williams, Oxford.

Dieter Jaksch, 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?

Dieter Jaksch, 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