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Molecules and Cooper pairs in Ultracold Gases
Krynica 2005
Krzysztof Góral Marzena Szymanska
Thorsten KöhlerJoshua MilsteinKeith Burnett
Outline
1. History
2. Feshbach Resonances
3. Atom-Molecule Coherences
4. BEC Molecules to BCS Pairs
5. Molecular Projection
6. Future work
THE WASHINGTON POST FRIDAY, JULY 14, 1995
31 new BECs reported
MoleculeOf theYear
The Bose-Einstein Condensate
FermionsBosons
Bose-Einstein Condensation
QuantumDegenerate
Hule
t et a
l . (2003)
Jin e
t al. (2
00
4)
Molecular Condensation&
Fermionic Superfluidity
Jin e
t al. (2
00
4)
Repulsive Interactions Molecular
bound states
Attractive InteractionsMany-body
paired states
Physics Programme Spend : 2035-2036
ELVIS IMPERSONATION0.9%
Quantum Computing4.8%
PIZZA DELIVERY0.7%
BOOZE11.8%
TRAVEL1.4%
SQUANDERED0.2%
BEC80.1%
Physics Programme Spend : 2035-2036
ELVIS IMPERSONATION0.9%
Quantum Computing4.8%
PIZZA DELIVERY0.7%
BOOZE11.8%
TRAVEL1.4%
SQUANDERED0.2%
BEC-BCS80.1%
Jin e
t al. (2
00
4)
Molecular Condensation&
Fermionic Superfluidity
Jin e
t al. (2
00
4)
Repulsive Interactions Molecular
bound states
Attractive InteractionsMany-body
paired states
Tuneable Interactions
as>0
as<0
s-wave
as>0, repulsive2-body bound
states
as<0, attractive
Feshbach resonances
22
2 2( ) ( )B BH B bg bg cl cl V Bm
2 ( ) ( ) ( )B bgV B bg V r bg bg W r cl
( ) ( , )clcl W r bg cl V B r cl
22 ( ) ( )cl res res resV B E B
m
Single resonance state approximation
Formal Feshbach Result
Entrance channel dominated resonance
Feshbach molecules can be huge!
Molecular binding energies85Rb
* N.R. Claussen et al., Phys. Rev. A 67, 060701 (2003); S. Kokkelmans, private communication.
Ramsey interferometry
Ramsey Interferometer
Ramsey fringes
The NLSE Gross-Pitaevskii Equation
Collective modesSuperfluidityVortex formationNon-linear Atomic Optics
Microscopic quantum dynamics method
0
22
* 2
( , ) ( ) ( , )2
( , ) ( , ) ( , )
trap
t
i t V tt m
t d h t
x x x
x x
Non-Markovian non-linear Schrödinger equation
32 2( , ) (2 ) ( ) 0, ( ) ( , ) 0,B Bh t t bg V t U t bg
0,bg Zero momentum plane wave of the relative motion of two atoms in the entrance channel
Simulation Results For molecular Condensate
DecayingOscillations
Oscillation frequency
Jin e
t al. (2
00
4)
Molecular Condensation&
Fermionic Superfluidity
Jin e
t al. (2
00
4)
Repulsive Interactions Molecular
bound states
Attractive InteractionsMany-body
paired states
“BCS-Superfluid”Overlapping Pairs
Edge of Fermi Surface
Spatial
k+q
-k+q
-k’+q’
k’+q’
k
-k-k
k
q q’
q’’
Momentum
“Crossover Regime”Clusters
Smeared Fermi Surface
“Crossover Regime”Clusters
Smeared Fermi Surface
“BEC-Superfluid”Distinct Pairs
No Fermi Surface
BCS-BEC in K
Gap Equations for BCS-BEC
1) Single channel system works fine close to resonance.Two channel works over wider range. 2) Mean-Field Theory Solution
BCS-BEC in K
BCS-BEC in K
BCS-BEC in K
BCS-BEC in K
BCS-BEC in K
Condensate BCS-BEC in K
Overlap zero at around half a Gauss above
resonance
BCS-BEC in K
“BCS-Superfluid”Overlapping Pairs
Edge of Fermi Surface
Spatial
k+q
-k+q
-k’+q’
k’+q’
k
-k-k
k
q q’
q’’
Momentum
“Crossover Regime”Clusters
Smeared Fermi Surface
“Crossover Regime”Clusters
Smeared Fermi Surface
“BEC-Superfluid”Distinct Pairs
No Fermi Surface
Fee-Fi-Fo-Fum Cluster Model
Dynamics/Thermodynamics of Small Clusters
Variational Approach: Gaussian Wavepackets
Non-interacting
Four independent particles
Four independent particles
Discrete, bound pairsDiscrete, bound pairs
BEC LimitBEC Limit
BCS-Limit
Spatially overlapSpatially overlap
Intermediate Limit
Bound pairsDistinctly fermions
Bound pairsDistinctly fermions
Acknowledgments
The Royal Society and Wolfson Foundation
EPSRC
EU Cold Quantum Gases Network
EC Marie Curie Fellowships
Summary
1.New era of strong correlation studies
2.Dynamical aspects are crucial
3.Much theory to be done.
THE WASHINGTON POST FRIDAY, JULY 14, 1995
31 new BECs reported
MoleculeOf theYear
The Bose-Einstein Condensate