University of Trento

INFM

BOSE-EINSTEIN CONDENSATION IN TRENTO

SUPERFLUIDITY IN TRAPPED GASES

University of Trento

Inauguration meeting, Trento 14-15 March 2003

BOSE-EINSTEIN CONDENSATIONvs

SUPERFLUIDITY

OLD PUZZLE IN

CONDENSED MATTER PHYSICS

LINK BETWEEN BEC AND SUPERFLUIDITY

PROVIDED BY

ORDER PARAMETER

= n1/2 eiS

S = phase

n = condensate density

v = ( h / 2m) S = superfluid velocity

(IRROTATIONALITY ! )

SUPERFLUIDITY IN TRAPPED GASES

• Dynamics (sound, oscillations, expansion)

• Rotational effects (scissors and vortices)

• Josephson effect

• Fermi gases

IRROTATIONAL HYDRODYNAMICS

(Bose and Fermi superfluids)

HD equations hold in local density approximation (healing length << R; local

description of chemical potential)

• Dilute BEC gas

(a<<d)

• Dilute Fermi gas (a<<d)

PREDICTIONS OF IRROTATIONAL

HYDRODYNAMICS

• BOGOLIUBOV SOUND

• COLLECTIVE OSCILLATIONS

• ANISOTROPIC EXPANSION

Sound in a Bose gas

Mit, 97

Measurement of Bogoliubov amplitudes

Theory ( double Bragg pulse)First pulse generates phononsSecond pulse measures their momentum distribution Brunello et al. PRL85, 4422(2000)

Exp: Vogels et al. PRL88, 060402 (2002)

Collective oscillations in hydrodynamic regime (cigar trap)

BEC superfluid

ideal gas collisional

ideal gas collisionless

m=0

radial

m=0

axial

m=2,-2

radial

Collective oscillations, T=0 BEC, Mit 97

exp:

theory (HD):

z 57.1

zz 58.12/5

Hydrodynamics predicts anisotropicexpansion of the condensate

SUPERFLUIDITY IN TRAPPED GASES

• Dynamics (sound, oscillations, expansion)

• Rotational effects (scissors and vortices)

• Josephson effect

• Fermi gases

Scissors mode

Scissors mode below Tc :

the superfluid oscillates with frequency

( x2 + y

2 )1/2

Scissors mode above Tc : the gas oscillates with frequencies

| x y |

Guery-Odelin and Stringari, PRL 83, 4452 (1999)

Scissors at Oxford Marago’et al, PRL 84, 2056 (2000)

above Tc

below Tc

QUANTIZED VORTICES

( r , ) = ( r ) e i

• Circulation of velocity is quantized. Quantum of circulation: h/m

• First obtained at Jila (phase imprinting)

• Realized at ENS by rotating the trap at “high”angular velocity

• Nucleation of vortices associated with instabilities against surface deformation

Quantized vortices at ENS (2001)F. Chevy et al.

Vortex lattices

Vortex lattices at Mit, 2001

•SPLITTING between m=+2 and m=-2 quadrupole frequencies (Zambelli and Stringari, 1998)

•PRECESSION

Measurement of angular momentum

Shape precession in the presence of a quantized vortex (Jila 2001)

Measurement of angular momentum in BEC gas (Chevy et al., PRL 85, 2223 (2000))

SUPERFLUIDITY IN TRAPPED GASES

• Dynamics (sound, oscillations, expansion)

• Rotational effects (scissors and vortices)

• Josephson effect

• Fermi gases

JOSEPHSON OSCILLATIONS

• CONDENSATE TRAPPED IN OPTICAL LATTICE +HARMONIC TRAPPING

• CONDENSATE CAN COHERENTLY TUNNEL THROUGH THE BARRIERS

zmm */

DIPOLE OSCILLATION Cataliotti et al, Science 293, 843 (2001)

d

dhm

mm

J

J

z

22*

*

/

/

tunneling rate

distance between wells

Josephson oscillation in optical trap Cataliotti et al. Science 293, 843 (2001)

SUPERFLUIDITY IN TRAPPED GASES

• Dynamics (sound, oscillations, expansion)

• Rotational effects (scissors and vortices)

• Josephson effect

• Fermi gases

RECENT WORK ON RESONANCE SUPERFLUIDITY

(Holland, Griffin, Timmermans, Stoof, Combescot)

• Availability of Feshbach resonances permits to reach favourable conditions for superfluidity

• BCS-BEC crossover (Randeria, 1993)

Hydrodynamics predicts anisotropic expansion in Fermi superfluids

(Menotti et al, PRL 89, 250402(2002))

Evidence for hydrodynamic anisotropic expansion in a cold Fermi gas (O’Hara et al,

Science, Dec. 2003)

O’Hara et al, Science, Dec 2003

• IN THE PRESENCE OF FESHBACH RESONANCE MEAN FREE PATH CAN BECOME SMALLER THAN SIZE OF THE SYSTEM GIVING RISE TO COLLISIONAL REGIME EVEN IN NORMAL PHASE

IS HYDRODYNAMIC BEHAVIOUR SAFE CRITERIUM TO PROBE FERMI

SUPERFLUIDITY ?

akF=1 JILA (Regal and Jin, Feb 2003)

HOW TO DISTINGUISH BETWEEN SUPERFLUID AND

COLLISIONAL HYDRODYNAMICS

LOOK AT ROTATIONAL EFFECTS

Irrotational hydrodynamics (superfluids)

vsrotational hydrodynamics

(normal fluids)

ROTATIONAL HYDRODYNAMICS HOLDS IF

NORMAL GAS IS COLLISIONAL or

SUPERFLUID HAS MANY VORTICES (diffused vorticity), Cozzini and Stringari, PRA in press

SPLITTING OF QUADRUPOLE FREQUENCIES PREDICTED BY

ROTATIONAL HYDRODYNAMICS:

consistent with rigid value estimate of angular momentum in

SPLITTING OF QUADRUPOLE FREQUENCIES IN BEC GAS WITH

MANY VORTICES (JILA, 2001)

HOW TO PROBE SUPERFLUIDITY IN A COLD FERMI GAS

ROTATE A SLIGHTLY DEFORMED TRAP AT SMALL ANGULAR VELOCITY (NO VORTICES)

• SUPERFLUID. No angular momentum. No quadrupole frequency splitting

• NON SUPERFLUID. Collisions thermalize the system to rigid rotation. Quadrupole frequencies are splitted.

ANGULAR MOMENTUMvs

ANGULAR VELOCITY

OTHER TOPICS RELATED TO SUPERFLUIDITY

• Critical velocity and critical angular velocity

• Systems of reduced dimensionality

• Phase transition to Mott insulator phase

• Superfluidity vs. disorder

MAIN CONCLUSION

• TRAPPED ATOMIC GASES: WELL SUITED TO EXPLORE THE EFFECTS OF SUPERFLUIDITY

• MORE IN NEXT TALKS