Transcript BOSE-EINSTEIN CONDENSATION IN TRENTO

INFM
University
of Trento
University of Trento
BOSE-EINSTEIN
CONDENSATION IN TRENTO
SUPERFLUIDITY IN
TRAPPED GASES
Inauguration meeting, Trento 14-15 March 2003
BOSE-EINSTEIN CONDENSATION
vs
SUPERFLUIDITY
OLD PUZZLE IN
CONDENSED MATTER PHYSICS
LINK BETWEEN
BEC AND SUPERFLUIDITY
PROVIDED BY
ORDER PARAMETER
 =
n
1/2
iS
e
S = phase
n
v
= condensate density
= ( h / 2p m)  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 phonons
Second 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
m=0
radial
m=0
axial
m=2,-2
radial
ideal gas
collisional
ideal gas
collisionless
Collective oscillations, T=0 BEC, Mit 97
exp:
  1.57z
theory (HD):
  5 / 2  z  1.58 z
Hydrodynamics predicts anisotropic
expansion 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
( x + y
2
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 at Mit, 2001
Vortex lattices
Measurement of angular
momentum
•SPLITTING between
m=+2 and m=-2
quadrupole frequencies
(Zambelli and Stringari,
1998)
•PRECESSION
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
  m / m*z
DIPOLE OSCILLATION
Cataliotti et al, Science 293, 843 (2001)
  m / m z
*
m  h / d J
*
2
2
 J  tunneling rate
d
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
IS HYDRODYNAMIC BEHAVIOUR SAFE
CRITERIUM TO PROBE FERMI
SUPERFLUIDITY ?
• 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
akF=1 JILA (Regal and Jin, Feb 2003)
HOW TO DISTINGUISH
BETWEEN SUPERFLUID AND
COLLISIONAL
HYDRODYNAMICS
LOOK AT ROTATIONAL
EFFECTS
Irrotational hydrodynamics
(superfluids)
vs
rotational 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 MOMENTUM
vs
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