Molecules and Cooper pairs in Ultracold Gases Krynica 2005 Krzysztof Góral Marzena Szymanska Thorsten Köhler Joshua Milstein Keith Burnett

Outline 1. History 2. Feshbach Resonances 3. Atom-Molecule Coherences 4. BEC Molecules to BCS Pairs 5. Molecular Projection 6. Future work

T HE W ASHINGTON P OST F RIDAY, J ULY 14, 1995

31 new BECs reported

Molecule Of the Year The Bose-Einstein Condensate

Fermions Bosons Bose-Einstein Condensation Quantum Degenerate Hulet et al. (2003)

Jin et al. (2004) Molecular Condensation & Fermionic Superfluidity Jin et al. (2004) Repulsive Interactions Molecular bound states Attractive Interactions Many-body paired states

Jin et al. (2004) Molecular Condensation & Fermionic Superfluidity Jin et al. (2004) Repulsive Interactions Molecular bound states Attractive Interactions Many-body paired states

Tuneable Interactions a s >0 a s <0 s-wave a s >0, repulsive 2-body bound states a s <0, attractive

Feshbach resonances Single resonance state approximation

Formal Feshbach Result

Entrance channel dominated resonance

Feshbach molecules can be huge!

Molecular binding energies 85 Rb * N.R. Claussen et al., Phys. Rev. A 67, (2003); S. Kokkelmans, private communication.

Ramsey interferometry

Ramsey Interferometer

Ramsey fringes

The NLSE Gross-Pitaevskii Equation Collective modes Superfluidity Vortex formation Non-linear Atomic Optics

Microscopic quantum dynamics method Non-Markovian non-linear Schrödinger equation Zero momentum plane wave of the relative motion of two atoms in the entrance channel

Simulation Results For molecular Condensate

Decaying Oscillations

Oscillation frequency

Jin et al. (2004) Molecular Condensation & Fermionic Superfluidity Jin et al. (2004) Repulsive Interactions Molecular bound states Attractive Interactions Many-body paired states

“BCS-Superfluid” Overlapping Pairs Edge of Fermi Surface Spatial k+q -k+q -k’+q’ k’+q’ 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

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 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 pairs BEC Limit

BCS-Limit Spatially overlap Intermediate Limit Bound pairs Distinctly fermions Bound pairs Distinctly 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.

T HE W ASHINGTON P OST F RIDAY, J ULY 14, 1995

31 new BECs reported

Molecule Of the Year The Bose-Einstein Condensate