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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 - PowerPoint PPT Presentation
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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
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“Ultracold gases – from the experimenters’

perspective (II)”Wolfgang Ketterle

Massachusetts Institute of TechnologyMIT-Harvard Center for Ultracold Atoms

7/13/06Innsbruck ICAP Summer School

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Bose-Einstein condensation

• Ideal Bose gas• Weakly interacting homogenous Bose gas• Inhomogeneous Bose gas• Superfluid hydrodynamics

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Ideal BEC

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The shadow of a cloud of bosonsas the temperature is decreased

(Ballistic expansion for a fixed time-of-flight)

Temperature is linearly related to the rf frequency which controls the evaporation

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BEC @ JILA, June ‘95(Rubidium)

BEC @ MIT, Sept. ‘95 (Sodium)

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1-(T/Tc)3

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Homogeneous BEC

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Propagation of sound

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Excitation of sound

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Excitation of sound

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Excitation of sound

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0.5mm

Sound = propagating density perturbations

1.3 ms per frame

Laser beam

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

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Quantum depletionor

How to observe the transition from aquantum 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

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What is the wavefunction of a condensate?

Ideal gas:

0 Nq

Interacting gas:

† †0 p q r sH U a a a a † †

0 0 0 p pH U a a a a

20 0 ...

N Nq q q p q p

0 ( )H U r

Quantum depletion

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Quantum depletion in 3-dimensional free space

021.5

4

Mn U

He II: 90 %

Gaseous BEC: 0.2 %

Optical lattice: Increase n and Meff

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Quantum Depletion

Free space Lattice

: tunneling rate

: on-site interaction

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2-D Mask Gaussian Fit

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2-D Mask Gaussian Fit

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Observed quantum depletion > 50 %

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Dispersion relation

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AbsorptionimageLaser light Condensate

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AbsorptionimageLaser light Condensate

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AbsorptionimageLaser light Condensate

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+ excitation

Laser light Condensate

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+ excitation

Laser light Condensate

Measuremomentum qand frequency

dynamic structure factor

S(q,)

analogous toneutron scatteringfrom 4He

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Laser light Condensate

dynamic structure factor

S(q,)

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Laser light Condensate

dynamic structure factor

S(q,)

Optical stimulation

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large momentum(two single-photon recoil)

Large and small momentum transfer to atoms

small momentum

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low density“free particles”S(q)=1

high density“phonons”S(q)=q/2mc<1

frequency shift

Spectrum of small-angle Bragg scattering

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large q

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large q

small q

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Inhomogeneous BEC

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

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250m

Lower Temperature

2 K 200 nK

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250m

Lower Temperature

2 K 200 nK

BEC peak Thermal wings, Temperature

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BEC peak

Thermal wings, Temperature

rms width of harmonic oscillator ground state 7 m (repulsive) interactions interesting many-body physics

300 m

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Signatures of BEC: Anisotropic expansion

1 ms 5 ms 10 ms

20 ms 30 ms 45 ms

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Length and energy scales in BEC

Size of the atom a 3 nmSeparation betweenatoms n-1/3 200 nm

Matter wavelength dB 1 m

Size of confinement aosc 30m

a << n-1/3 dB < aosc

BECGas!

kBTs-wave >> kBTc kBT >< 2

Healing length 2 2m

> Uint

=(h2/m)na

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Vortices

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Spinning a Bose-Einstein condensate

Rotatinggreen laser beams

The rotating bucket experiment with a superfluid gas 100,000 thinner than air

Two-component vortex Boulder, 1999Single-component vortices Paris, 1999 Boulder, 2000 MIT 2001 Oxford 2001

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non-rotating rotating (160 vortices)

Rotating condensates

J. Abo-Shaeer, C. Raman, J.M. Vogels, W.Ketterle, Science, 4/20/2001

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Sodium BEC in the magnetic trap

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-21 dB-18 dB

Green beam Power(arb. scale)

Immediately afterstirring

After 500 ms offree evolution

-15 dB-12 dB-9 dB-6 dB-3 dB0 dB

Resonant Drive:

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Hydrodynamics

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Absorption 0% 100%

16 ms 23 ms 28 ms 41 ms 48 ms

Collective excitations(observed in ballistic expansion)

MIT, 1996

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Shape oscillations

“Non-destructive” observation of a time-dependent wave function

350m

5 milliseconds per frame

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m=0 quadrupole-type oscillation at 29 Hz

Low T

High T

Stamper-Kurn, Miesner, Inouye, Andrews, W.K, PRL 81, 500 (1998)

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Tc

condensate

thermal cloud

Landau damping(Popov, Szefalusky, Condor,Liu, Stringari, Pitaevskii, Fedichev, Shlyapnikov, Burnett,Edwards, Clark, Stoof, Olshanii)

Temperature dependence offrequency“Beyond-mean field theory”(Giorgini)

1.569(4)1.580 (prediction by Stringari)

oscz=

Onset of hydrodynamicbehavior

collisionless oscillation

hydrodynamic oscillation

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Excitation of surface modes m=l

Radial cross sectionof 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.

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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)

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Hexadecapole oscillation ( = 4)

Hex

adec

apol

e

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“Ultracold gases – from the experimenters’

perspective (III)”Wolfgang Ketterle

Massachusetts Institute of TechnologyMIT-Harvard Center for Ultracold Atoms

7/14/06Innsbruck ICAP Summer School

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The new frontier:Strong interactions and

correlations

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Strongly correlated bosons in optical lattices

The Superfluid to Mott Insulator Transition

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BEC in 3D optical lattice

Courtesy Markus Greiner

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The Superfluid-Mott Insulator transitionDeep Lattices – Mott InsulatorShallow Lattices - Superfluid

tunneling term between neighboring sites

xdxw

m

aU 34

2

)(4

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

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The Superfluid-Mott Insulator transition

5 Erec 9 Erec

Shallow Lattices - Superfluid

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5 Erec 9 Erec 12 Erec 15 Erec 20 Erec

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

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The Superfluid-Mott Insulator Transition in Optical Lattices

MI phase transition

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Cold fermions

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Lithium Sodium

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BosonsParticles with an even number of protons, neutrons and electrons

FermionsParticles 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

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Two kinds of fermions

Fermi sea: Atoms are not coherent No superfluidity

Pairs of fermionsParticles with an even number of protons, neutrons and electrons

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At absolute zero temperature …

Pairs of fermionsParticles with an even number of protons, neutrons and electrons

Bose-Einstein condensation atoms as waves superfluidity

Two kinds of fermionsParticles with an odd number of protons, neutrons and electrons

Fermi sea: Atoms are not coherent No superfluidity

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Two kinds of fermionsParticles with an odd number of protons, neutrons and electrons

Fermi sea: Atoms are not coherent No superfluidity

Weak attractive interactions

Cooper pairslarger than interatomic distancemomentum correlations BCS superfluidity

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Bose Einstein condensate of molecules

BCS Superconductor

Atom pairs Electron pairs

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Molecular BEC BCS superfluid

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Molecular BEC BCS superfluid

Magnetic field

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Molecular BEC BCS superfluidCrossover superfluid

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First observation: C. A. Regal et al., Phys. Rev. Lett. 92, 040403 (2004)

Observation of Pair Condensates!

Initialtemperature:

T / TF = 0.05T / TF = 0.1T / TF = 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)

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„Phase diagram“ for pair condensation

kF|a| > 1

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