Non-equilibrium Dynamics in Ultracold Fermionic and Bosonic Gases

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1 Non-equilibrium Dynamics in Ultracold Fermionic and Bosonic Gases Michael KöhlK ETH Zürich Z (

2 Introduction Why should a condensed matter physicist be interested in experiments with cold atomic gases? Three reasons 1. Purity an excellent system for studying 2. Tunability non-equilibrium physics 3. Long coherence times

3 Correlated systems in quantum gases Quantum phases in optical lattices BEC-BCS crossover ETH, Hamburg, LENS, Munich/Mainz, MIT, NIST, Yale/Stanford Duke, ENS, Innsbruck, JILA, MIT, Rice, Low-dimensional systems 1D 2D Quantized vortices ENS, ETH, LENS, Mainz, MIT, NIST, Penn State, ENS, JILA, MIT, Oxford, GeorgiaTech, Correlation functions can be measured directly.

4 Outline 1. Fermionic atoms in a 3D optical lattice with time-dependent interactions 2. Non-equilibrium formation of long-range order during Bose-Einstein condensation

5 Fermions in a 3D optical lattice

6 Interaction of an atom with a laser field Induced electric dipole potential: V = 1 2 α E 2 ac polarizability of the atom electric field of the laser Two options: ωl < ωa ωl > ωa red detuned blue detuned Optical lattice λ /2 400nm

7 Atoms: 40 K Optical lattice: 826 nm

8 Fermi-Hubbard model H J cˆ cˆ U nˆ nˆ ( μ ) nˆ = + ε i, σ j, σ i i i, σ i, σ < i, j>, σ i i, σ tunneling interactions filling confinement dimensionality time dependent tuning is possible

9 Observed Fermi surfaces theory experiment conductive state filling band insulator M. Köhl et al., Phys. Rev. Lett. 94, (2005).

10 Quantum phases in the lattice band insulator Mott insulator conducting state nn = nn = 0 0< nn < 1 1 study formation of molecules

11 Molecules in a lattice deep lattice = array of harmonic oscillators energy [ħω] Two interacting particles in a harmonic oscillator scattering length a s [a ho ] scattering length [a 0 ] Feshbach resonance 3000 sweep magnetic field [G]

12 Radio-frequency spectroscopy noninteracting ground state apply RF pulse bound state m F -9/2-7/2-5/2 E B bound-bound spectroscopy In homogeneous systems: C. Regal et al., Nature 424, 47 (2003) C. Chin et al., Science 305, 1128 (2004) In a one-dimensional system: H. Moritz, T. Stöferle, K. Günter, M. Köhl, T.Esslinger, Phys. Rev. Lett. 94, (2005)

13 Results Binding energy Molecule fraction nn T. Stöferle, H. Moritz, K. Günter, M. Köhl, T. Esslinger, Phys. Rev. Lett. 96, (2006); M. Köhl, Phys. Rev. A 73, (R) (2006).

14 Going the other direction energy [ħω] Two interacting particles in a harmonic oscillator scattering length a s [a ho ] noninteracting scattering length [a 0 ] Feshbach resonance 3000 sweep magnetic field [G] sweep across Feshbach resonance 1 st Brillouin zone M. Köhl et al., Phys. Rev. Lett. 94, (2005). Theory: Diener & Ho, cond-mat/ , H. G. Katzgraber et al., cond-mat/ observe atoms in higher bands

15 Bose-Fermi mixtures (in equilibrium )

16 Adding fermions to a Bose condensate 87 Rb K Similiar to 3 He/ 4 He mixtures (but in a lattice) Depletion of the Bose-Einstein condensate Polarons, fermion-phonon coupling with v F =v S Composite fermions

17 Experimental results k y -π/a π/ak x k=0: Bose-Einstein condensate k 0: depletion K. Günter, T. Stöferle, H. Moritz, M. Köhl, T. Esslinger, PRL, in press; cond-mat/ (2006)

18 Non-equilibrium formation of long-range order during Bose-Einstein condensation

19 Growth of Bose-Einstein condensates Evolution of density is quantitatively understood H. J. Miesner et al., Science 279, 1005 (1998); M. Köhl et al., Phys. Rev. Lett. 88, (2002). How does long-range order evolve? λ db probe spatial coherence φ 1? φ 2 φ 3 φ 4 φ

20 Young s double slit experiment ψ ( r ) 1 source ψ ( r ) 2 screen Visibility V measures first order correlation function V g ( r r) = ψ ( r ) ψ( r) (1) } slit separation

21 Two frequency output coupling T. Bourdel et al., Phys. Rev. A 73, (2006). I. Bloch, T. Hänsch, T. Esslinger, Nature 403, 166 (2000).

22 Preparing a non-equilibrium atom cloud Maxwell Boltzmann distribution above T c p(e) evaporation frequency time t=0 E

23 Interferences during Condensation visibility density

24 Formation of a Bose condensate

25 Density growth vs. coherence growth time [ms] no evidence for quasi-condensates.

26 First order correlation function Visibility

27 Conclusion Atomic quantum gases are a great system to study non-equilibrium dynamics. Time-dependent interactions between fermions in lattices. Non-equilibrium dynamics at the Bose-Einstein phase transition.

28 Acknowledgements Fermions Ken Günter Henning Moritz Thilo Stöferle Cavity QED Thomas Bourdel Tobias Donner Anton Öttl Stephan Ritter Michael Köhl Tilman Esslinger