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Download Ketterle lecture notes July 13th - Quantum Optics and Spectroscopy
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“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 Bose-Einstein condensation • Ideal Bose gas • Weakly interacting homogenous Bose gas • Inhomogeneous Bose gas • Superfluid hydrodynamics Ideal BEC 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 @ JILA, June ‘95 (Rubidium) BEC @ MIT, Sept. ‘95 (Sodium) 1-(T/Tc)3 Homogeneous BEC Propagation of sound Excitation of sound Excitation of sound Excitation of sound Sound = propagating density perturbations 0.5 mm Laser beam 1.3 ms per frame (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 In 1D: Zürich K. Xu, Y. Liu, D.E. Miller, J.K. Chin, W. Setiawan, W.K., PRL 96, 180405 (2006). What is the wavefunction of a condensate? Ideal gas: q0 N H U 0 (r ) Interacting gas: † † H U0 a p aq ar as q0 N H U0a0 a0 a a q 0 † † p p N 2 q p q p ... Quantum depletion Quantum depletion in 3-dimensional free space 1.5 n M 4 2 U0 Gaseous BEC: 0.2 % He II: 90 % Optical lattice: Increase n and Meff Quantum Depletion Free space Lattice : tunneling rate : on-site interaction 2-D Mask Gaussian Fit 2-D Mask Gaussian Fit Observed quantum depletion > 50 % Dispersion relation Laser light Condensate Absorption image Laser light Condensate Absorption image Laser light Condensate Absorption image Laser light Condensate + excitation Laser light Condensate Measure momentum q and frequency n + excitation dynamic structure factor S(q,n) analogous to neutron scattering from 4He Laser light Condensate dynamic structure factor S(q,n) Laser light Condensate Optical stimulation dynamic structure factor S(q,n) Large and small momentum transfer to atoms large momentum (two single-photon recoil) small momentum Spectrum of small-angle Bragg scattering low density “free particles” S(q)=1 high density “phonons” S(q)=q/2mc<1 frequency shift large q large q small q Inhomogeneous BEC A live condensate in the magnetic trap (seen by dark-ground imaging) BEC peak Thermal wings, Temperature BEC peak 300 m Thermal wings, Temperature rms width of harmonic oscillator ground state 7 m (repulsive) interactions interesting many-body physics Signatures of BEC: Anisotropic expansion 1 ms 5 ms 10 ms 20 ms 30 ms 45 ms Length and energy scales in BEC Size of the atom Separation between atoms Matter wavelength n dB 200 nm 1 m Healing length 2x 2m Size of confinement a -1/3 << n kBTs-wave >> kBTc Gas! a -1/3 3 nm aosc 30m dB < 2x < aosc kBT BEC > Uint > =(h2/m)na Vortices Spinning a Bose-Einstein condensate The rotating bucket experiment with a superfluid gas 100,000 thinner than air Rotating green laser beams Two-component vortex Boulder, 1999 Single-component vortices Paris, 1999 Boulder, 2000 MIT 2001 Oxford 2001 Rotating condensates non-rotating rotating (160 vortices) J. Abo-Shaeer, C. Raman, J.M. Vogels, W.Ketterle, Science, 4/20/2001 Sodium BEC in the magnetic trap Resonant Drive: Green beam Power (arb. scale) -21 -18 -15 -12 -9 -6 -3 0 dB Immediately after stirring After 500 ms of free evolution Hydrodynamics Collective excitations (observed in ballistic expansion) 16 ms 23 ms Absorption 0% 28 ms 41 ms 48 ms 100% MIT, 1996 Shape oscillations “Non-destructive” observation of a time-dependent wave function 350 m 5 milliseconds per frame m=0 quadrupole-type oscillation at 29 Hz Low T High T Stamper-Kurn, Miesner, Inouye, Andrews, W.K, PRL 81, 500 (1998) Tc collisionless oscillation osc/z= 1.569(4) hydrodynamic oscillation 1.580 (prediction by Stringari) thermal cloud Temperature dependence of frequency condensate “Beyond-mean field theory” Onset of hydrodynamic behavior (Giorgini) Landau damping (Popov, Szefalusky, Condor, Liu, Stringari, Pitaevskii, Fedichev, Shlyapnikov, Burnett, Edwards, Clark, Stoof, Olshanii) 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. 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 Hexadecapole oscillation ( = 4) “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 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 Shallow Lattices - Superfluid Deep Lattices – Mott Insulator Energy offset due to external harmonic confinement. Not in condensed matter systems. tunneling term between neighboring sites on-site interaction 4 2 a 4 w( x) d 3 x U m a = s-wave scattering length Other exp: Mainz, Zurich, NIST Gaithersburg, Innsbruck, MPQ and others The Superfluid-Mott Insulator transition Shallow Lattices - Superfluid 5 Erec 9 Erec The Superfluid-Mott Insulator transition Deep Lattices – Mott Insulator 5 Erec 9 Erec 12 Erec 15 Erec 20 Erec Diagnostics: Loss of Coherence Excitation Spectrum Noise Correlations Microwave Spectroscopy 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 The Superfluid-Mott Insulator Transition in Optical Lattices MI phase transition Cold fermions Lithium Sodium At absolute zero temperature … Bosons Particles with an even number of protons, neutrons and electrons Bose-Einstein condensation atoms as waves superfluidity Fermions Particles with an odd number of protons, neutrons and electrons Fermi sea: Atoms are not coherent No superfluidity Pairs of fermions Particles with an even number of protons, neutrons and electrons Two kinds of fermions Fermi sea: Atoms are not coherent No superfluidity 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 Weak attractive interactions Cooper pairs larger than interatomic distance momentum correlations BCS superfluidity Two kinds of fermions Particles with an odd number of protons, neutrons and electrons Fermi sea: Atoms are not coherent No superfluidity Atom pairs Bose Einstein condensate of molecules Electron pairs BCS Superconductor BEC BCS supe BEC Magnetic field BCS supe BEC Crossover superfluid BCS supe Observation of Pair Condensates! At 900 G (above dissociation limit of molecules) Initial T / TF = 0.2 temperature: T / TF = 0.1 T / TF = 0.05 First observation: C. A. Regal et al., Phys. Rev. Lett. 92, 040403 (2004) M.W. Zwierlein, C.A. Stan, C.H. Schunck, S.M.F. Raupach, A.J. Kerman, W.K. Phys. Rev. Lett. 92, 120403 (2004). „Phase diagram“ for pair condensation kF|a| > 1