Non-equilibrium Dynamics in Ultracold Fermionic and Bosonic Gases Michael KöhlK ETH Zürich Z (www.quantumoptics.ethz.ch( www.quantumoptics.ethz.ch)
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
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.
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
Fermions in a 3D optical lattice
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
Atoms: 40 K Optical lattice: 826 nm
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
Observed Fermi surfaces theory experiment conductive state filling band insulator M. Köhl et al., Phys. Rev. Lett. 94, 080403 (2005).
Quantum phases in the lattice band insulator Mott insulator conducting state nn = nn = 0 0< nn < 1 1 study formation of molecules
Molecules in a lattice deep lattice = array of harmonic oscillators energy [ħω] 8 6 4 2 0-2 Two interacting particles in a harmonic oscillator -3-2 -1 0 1 2 3 scattering length a s [a ho ] scattering length [a 0 ] Feshbach resonance 3000 sweep 0-3000 200 220 magnetic field [G]
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, 210401 (2005)
Results Binding energy Molecule fraction nn T. Stöferle, H. Moritz, K. Günter, M. Köhl, T. Esslinger, Phys. Rev. Lett. 96, 030401 (2006); M. Köhl, Phys. Rev. A 73, 031601(R) (2006).
Going the other direction energy [ħω] 8 6 4 2 0-2 Two interacting particles in a harmonic oscillator -3-2 -1 0 1 2 3 scattering length a s [a ho ] noninteracting scattering length [a 0 ] Feshbach resonance 3000 sweep 0-3000 220 240 magnetic field [G] sweep across Feshbach resonance 1 st Brillouin zone M. Köhl et al., Phys. Rev. Lett. 94, 080403 (2005). Theory: Diener & Ho, cond-mat/0507253, H. G. Katzgraber et al., cond-mat/0510194. observe atoms in higher bands
Bose-Fermi mixtures (in equilibrium )
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
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/0604139 (2006)
Non-equilibrium formation of long-range order during Bose-Einstein condensation
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, 080402 (2002). How does long-range order evolve? λ db probe spatial coherence φ 1? φ 2 φ 3 φ 4 φ
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) 2 1 2 1 } slit separation
Two frequency output coupling T. Bourdel et al., Phys. Rev. A 73, 063618 (2006). I. Bloch, T. Hänsch, T. Esslinger, Nature 403, 166 (2000).
Preparing a non-equilibrium atom cloud Maxwell Boltzmann distribution above T c p(e) evaporation frequency time t=0 E
Interferences during Condensation visibility density
Formation of a Bose condensate
Density growth vs. coherence growth time [ms] no evidence for quasi-condensates.
First order correlation function 1.0 0.8 0.6 Visibility 0.4 0.2 0 275 375 175 75
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.
Acknowledgements Fermions Ken Günter Henning Moritz Thilo Stöferle Cavity QED Thomas Bourdel Tobias Donner Anton Öttl Stephan Ritter Michael Köhl Tilman Esslinger