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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