Title “Ultracold gases – from the experimenters’ perspective (II)” Wolfgang Ketterle Massachusetts Institute of Technology MIT-Harvard Center for Ultracold Atoms 7/13/06 Innsbruck ICAP Summer School

Subtitle Bose-Einstein condensation Ideal Bose gas Weakly interacting homogenous Bose gas Inhomogeneous Bose gas Superfluid hydrodynamics

Subtitle Ideal BEC

BEC B&W The shadow of a cloud of bosons as the temperature is decreased (Ballistic expansion for a fixed time-of-flight) Temperature is linearly related to the rf frequency which controls the evaporation

BEC at JILA and MIT JILA, June ‘95 (Rubidium) MIT, Sept. ‘95 (Sodium)

Mixed cloud in phase contrast

Condensate fraction 1-(T/T c ) 3

Subtitle Homogeneous BEC

Sound propagation Propagation of sound

Exciting sound I Excitation of sound

Exciting sound I Excitation of sound

Exciting sound I Excitation of sound

Sound = propagating density perturbations 1.3 ms per frame Sound propagation Laser beam

Speed of sound results (M. Andrews, D.M. Kurn, H.-J. Miesner, D.S. Durfee, C.G. Townsend, S. Inouye, W.K., PRL 79, 549 (1997))

Quantum depletion or How to observe the transition from a quantum gas to a quantum liquid K. Xu, Y. Liu, D.E. Miller, J.K. Chin, W. Setiawan, W.K., PRL 96, (2006). In 1D: Zürich

What is the wavefunction of a condensate? Ideal gas: Interacting gas: Quantum depletion

Quantum depletion in 3-dimensional free space He II: 90 % Gaseous BEC: 0.2 % Optical lattice: Increase n and M eff

Quantum Depletion Free space Lattice : tunneling rate : on-site interaction

2-D Mask Gaussian Fit

Observed quantum depletion > 50 %

Sound propagation Dispersion relation

Light scattering I Absorption image Laser light Condensate

Light scattering II Absorption image Laser light Condensate

Light scattering III Absorption image Laser light Condensate

+ excitation Light scattering IV Laser light Condensate

+ excitation Light scattering V Laser light Condensate Measure momentum q and frequency dynamic structure factor S(q, ) analogous to neutron scattering from 4 He

Light scattering VI Laser light Condensate dynamic structure factor S(q, )

Light scattering VII Laser light Condensate dynamic structure factor S(q, ) Atoms scatter off a light grating = Bragg spectroscopy Optical stimulation

Bogoliubov dispersion relation

Large and small momentum transfer large momentum (two single-photon recoil) Large and small momentum transfer to atoms small momentum

Small q Bragg scattering - spectra low density “free particles” S(q)=1 high density “phonons” S(q)=q/2mc<1 frequency shift Spectrum of small-angle Bragg scattering

Mean-field shift I large q

Mean-field shift I large q small q

Subtitle Inhomogeneous BEC

A live condensate in the magnetic trap (seen by dark-ground imaging) Phase transition, dark ground

Phase transition, phase contrast

BEC peak Thermal wings,  Temperature

Mixed cloud in phase contrast BEC peak Thermal wings,  Temperature rms width of harmonic oscillator ground state 7  m  (repulsive) interactions  interesting many-body physics 300  m

TOF movie

Signatures of BEC: Anisotropic expansion Anisotropic expansion

Length and energy scales k B T s-wave >> k B T c  k B T >   < 2  Healing length 2  2  m > U int =(h 2 /m)na

Subtitle Vortices

Spinning a BEC Spinning a Bose-Einstein condensate Rotating green laser beams The rotating bucket experiment with a superfluid gas 100,000 thinner than air Two-component vortex Boulder, 1999 Single-component vortices Paris, 1999 Boulder, 2000 MIT 2001 Oxford 2001

Centrifugal distortion non-rotatingrotating (160 vortices) Rotating condensates J. Abo-Shaeer, C. Raman, J.M. Vogels, W.Ketterle, Science, 4/20/2001

Sodium BEC in the magnetic trap

-21 dB-18 dB Green beam Power (arb. scale) Immediately after stirring After 500 ms of free evolution -15 dB-12 dB-9 dB-6 dB-3 dB0 dB Resonant Drive:

Subtitle Hydrodynamics

Collective excitations (observed in ballistic expansion) Collective excitation in TOF MIT, 1996

Shape oscillations “Non-destructive” observation of a time-dependent wave function 5 milliseconds per frame Shape oscillation

m=0 quadrupole-type oscillation at 29 Hz Movie, quadrupole oscillation Low T High T Stamper-Kurn, Miesner, Inouye, Andrews, W.K, PRL 81, 500 (1998)

Results on temp. dep. frequencies and damping TcTc condensate thermal cloud Landau damping (Popov, Szefalusky, Condor, Liu, Stringari, Pitaevskii, Fedichev, Shlyapnikov, Burnett, Edwards, Clark, Stoof, Olshanii) Temperature dependence of frequency “Beyond-mean field theory” (Giorgini) 1.569(4) (prediction by Stringari)  osc  z = Onset of hydrodynamic behavior collisionless oscillation hydrodynamic oscillation

Excitation of surface modes Excitation of surface modes m=  l Radial cross section of condensate Focused IR beam Rapid switching between points (10 … 100 kHz) Slow variation of intensity or position Excitation of standing and travelling waves Theory on surface modes: Stringari et al., Pethick et al.

Quadrupole raw images Observation of m=2, l=2 collective excitation Time of flight (20 msec), standing wave excitation In-situ phase-contrast imaging (2 msec per frame) rotating excitation R. Onofrio, D.S. Durfee, C. Raman, M. Köhl, C.E. Kuklewicz, W.K., Phys. Rev. Lett. 84, 810 (2000)

Hexadecapole results Hexadecapole oscillation ( = 4) Hexadecapole

Title “Ultracold gases – from the experimenters’ perspective (III)” Wolfgang Ketterle Massachusetts Institute of Technology MIT-Harvard Center for Ultracold Atoms 7/14/06 Innsbruck ICAP Summer School

Title The new frontier: Strong interactions and correlations

Strongly correlated bosons in optical lattices The Superfluid to Mott Insulator Transition

BEC in 3D optical lattice Courtesy Markus Greiner

The Superfluid-Mott Insulator transition Deep Lattices – Mott Insulator Shallow Lattices - Superfluid tunneling term between neighboring sites a = s-wave scattering length Energy offset due to external harmonic confinement. Not in condensed matter systems. on-site interaction Other exp: Mainz, Zurich, NIST Gaithersburg, Innsbruck, MPQ and others

The Superfluid-Mott Insulator transition 5 E rec 9 E rec Shallow Lattices - Superfluid

5 E rec 9 E rec 12 E rec 15 E rec 20 E rec Diagnostics: Loss of Coherence Excitation Spectrum Noise Correlations As the lattice depth is increased, J decreases exponentially, and U increases. For J/U<<1, number fluctuations are suppressed, and the atoms are localized Deep Lattices – Mott Insulator Microwave Spectroscopy The Superfluid-Mott Insulator transition

The Superfluid-Mott Insulator Transition in Optical Lattices MI phase transition

Cold fermions

Li Na cooling movie LithiumSodium

Bosons Particles with an even number of protons, neutrons and electrons Fermions Particles with an odd number of protons, neutrons and electrons Bose-Einstein condensation  atoms as waves  superfluidity At absolute zero temperature … Fermi sea:  Atoms are not coherent  No superfluidity

Two kinds of fermions Fermi sea:  Atoms are not coherent  No superfluidity Pairs of fermions Particles with an even number of protons, neutrons and electrons

At absolute zero temperature … Pairs of fermions Particles with an even number of protons, neutrons and electrons Bose-Einstein condensation  atoms as waves  superfluidity Two kinds of fermions Particles with an odd number of protons, neutrons and electrons Fermi sea:  Atoms are not coherent  No superfluidity

Two kinds of fermions Particles with an odd number of protons, neutrons and electrons Fermi sea:  Atoms are not coherent  No superfluidity Weak attractive interactions Cooper pairs larger than interatomic distance momentum correlations  BCS superfluidity

Bose Einstein condensate of molecules BCS Superconductor Atom pairs Electron pairs

Molecular BEC BCS superfluid

Molecular BEC BCS superfluid Magnetic field

Molecular BEC BCS superfluidCrossover superfluid

First observation: C. A. Regal et al., Phys. Rev. Lett. 92, (2004) Observation of Pair Condensates! Initial temperature: T / T F = 0.05T / T F = 0.1T / T F = 0.2 M.W. Zwierlein, C.A. Stan, C.H. Schunck, S.M.F. Raupach, A.J. Kerman, W.K. Phys. Rev. Lett. 92, (2004). At 900 G (above dissociation limit of molecules)

„Phase diagram“ for pair condensation k F |a| > 1