“Ultracold gases – from the experimenters’

perspective (II)”Wolfgang Ketterle

Massachusetts Institute of TechnologyMIT-Harvard Center for Ultracold Atoms

7/13/06Innsbruck 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 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

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

0.5mm

Sound = propagating density perturbations

1.3 ms per frame

Laser beam

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

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

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

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

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

AbsorptionimageLaser light Condensate

AbsorptionimageLaser light Condensate

AbsorptionimageLaser light Condensate

+ excitation

Laser light Condensate

+ excitation

Laser light Condensate

Measuremomentum qand frequency

dynamic structure factor

S(q,)

analogous toneutron scatteringfrom 4He

Laser light Condensate

dynamic structure factor

S(q,)

Laser light Condensate

dynamic structure factor

S(q,)

Optical stimulation

large momentum(two single-photon recoil)

Large and small momentum transfer to atoms

small momentum

low density“free particles”S(q)=1

high density“phonons”S(q)=q/2mc<1

frequency shift

Spectrum of small-angle Bragg scattering

large q

large q

small q

Inhomogeneous BEC

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

250m

Lower Temperature

2 K 200 nK

250m

Lower Temperature

2 K 200 nK

BEC peak Thermal wings, Temperature

BEC peak

Thermal wings, Temperature

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

300 m

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 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

Vortices

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

non-rotating rotating (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 afterstirring

After 500 ms offree evolution

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

Resonant Drive:

Hydrodynamics

Absorption 0% 100%

16 ms 23 ms 28 ms 41 ms 48 ms

Collective excitations(observed in ballistic expansion)

MIT, 1996

Shape oscillations

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

350m

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

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

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.

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 oscillation ( = 4)

Hex

adec

apol

e

“Ultracold gases – from the experimenters’

perspective (III)”Wolfgang Ketterle

Massachusetts Institute of TechnologyMIT-Harvard Center for Ultracold Atoms

7/14/06Innsbruck 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 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

The Superfluid-Mott Insulator transition

5 Erec 9 Erec

Shallow Lattices - Superfluid

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

The Superfluid-Mott Insulator Transition in Optical Lattices

MI phase transition

Cold fermions

Lithium Sodium

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

Two kinds of fermions

Fermi sea: Atoms are not coherent No superfluidity

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

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

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

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, 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)

„Phase diagram“ for pair condensation

kF|a| > 1