1. 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

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

3. Subtitle Ideal BEC

22. 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

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

24. Mixed cloud in phase contrast

25. Condensate fraction 1-(T/T c ) 3

29. Subtitle Homogeneous BEC

42. Sound propagation Propagation of sound

43. Exciting sound I Excitation of sound

44. Exciting sound I Excitation of sound

45. Exciting sound I Excitation of sound

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

47. 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))

51. 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, 180405 (2006). In 1D: Zürich

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

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

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

55. 2-D Mask Gaussian Fit

57. Observed quantum depletion > 50 %

58. Sound propagation Dispersion relation

60. Light scattering I Absorption image Laser light Condensate

61. Light scattering II Absorption image Laser light Condensate

62. Light scattering III Absorption image Laser light Condensate

63. + excitation Light scattering IV Laser light Condensate

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

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

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

67. Bogoliubov dispersion relation

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

69. 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

70. Mean-field shift I large q

71. Mean-field shift I large q small q

72. Subtitle Inhomogeneous BEC

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

83. Phase transition, phase contrast

84. BEC peak Thermal wings,  Temperature

85. 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

86. TOF movie

87. Signatures of BEC: Anisotropic expansion Anisotropic expansion

89. 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

90. Subtitle Vortices

92. 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

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

94. Sodium BEC in the magnetic trap

95. -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:

96. Subtitle Hydrodynamics

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

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

110. 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)

111. 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) 1.580 (prediction by Stringari)  osc  z = Onset of hydrodynamic behavior collisionless oscillation hydrodynamic oscillation

112. 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.

113. 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)

114. Hexadecapole results Hexadecapole oscillation ( = 4) Hexadecapole

115. 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

116. Title The new frontier: Strong interactions and correlations

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

118. BEC in 3D optical lattice Courtesy Markus Greiner

119. 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

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

121. 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

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

123. Cold fermions

124. Li Na cooling movie LithiumSodium

125. 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

129. 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

130. 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

131. 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

137. Bose Einstein condensate of molecules BCS Superconductor Atom pairs Electron pairs

138. Molecular BEC BCS superfluid

139. Molecular BEC BCS superfluid Magnetic field

140. Molecular BEC BCS superfluidCrossover superfluid

146. First observation: C. A. Regal et al., Phys. Rev. Lett. 92, 040403 (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, 120403 (2004). At 900 G (above dissociation limit of molecules)

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