Strongly Correlated Systems of Ultracold Atoms

Theory work at CUA

New Era in Cold Atoms Research

Focus on Systems with Strong Interactions • Optical lattices • Feshbach resonances • Low dimensional systems • Systems with long range interactions (Coulomb interaction for trapped ions, dipolar interactions for polar molecules)

Quantum Simulations of Condensed Matter Systems using Ultracold Atomic Gases

Preparation of many-body states SYNERGY BETWEEN THEORY AND EXPERIMENT Detection and Characterization Phase Diagrams

Preparation of many-body states

Doublon decay in a compressible state How to get rid of the excess energy U?

Decay probability Doublon can decay into a pair of quasiparticles with many particle-hole pairs Consider processes which maximize the number of particle-hole excitations Experiment: ETH, Zurich Theory: Harvard Perturbation theory to order n=U/t

Observation of superexchange in a double well potential Theory: A.M. Rey et al., PRL (2007) Experiment: S. Trotzky et al., Science (2008)

J ex

Use magnetic field gradient to prepare a state Observe oscillations between and states Experimental measurements of superexchange J ex . Comparison to first principle calculations

1D: XXZ dynamics starting from the classical Neel state Coherent time evolution starting with Y (t=0) =

QLRO

Equilibrium phase diagram D • • DMRG • XZ model: exact solution D >1: sine-Gordon Bethe ansatz solution Time,

Jt

Fermions in optical lattice: surprise of the attractive Hubbard model Anomalous radius increase Experiments by I. Bloch et al.

High temperature expansion of the Hubbard model Theory: Mainz+Harvard Competition of attraction and entropy

DETECTION AND CHARACTERIZATION PHASE DIAGRAMS

Experiments with 2D Bose gas

Hadzibabic, Dalibard et al., Nature 441:1118 (2006) Time of flight

z x

Experiments with 1D Bose gas Hofferberth et al. Nature Physics (2008)

Interference of independent 1d condensates S. Hofferberth et al., Nature Physics (2008) Experiments: Vienna; Theory: Harvard Higher order correlation functions probed by noise in interference

OUTLOOK: NONEQUILIBRIUM DYNAMICS NEW PERSPECTIVE ON MANY-BODY SYSTEMS

Dynamics in 1d: Ramsey interference Interaction induced collapse of Ramsey fringes. Ramsey fringe visibility Spin echo time Experiments in 1d tubes: A. Widera et al. B. PRL (2008)

Interaction induced collapse of Ramsey fringes in one dimensional systems Luttinger liquid approach How to distinguish decoherence due to many-body dynamics?

Evolution of spin distribution functions Only q=0 mode shows complete spin echo Finite q modes continue decay The net visibility is a result of competition between q=0 and other modes

OUTLOOK: QUANTUM MANY-BODY SYSTEMS IN THE PRESENSE OF NONEQUILIBRIUM NOISE NEW PERSPECTIVE ON MANY-BODY SYSTEMS

Trapping ions and polar molecules Trapped ions Ultracold polar molecules Noise spectrum is

1/f

Monroe (2006), Chuang (2008) Short range spatial correlations

E

Effective coupling to external noise + + + + + + + + + + (Quantum) Langevin dynamics: Thermal bath External noise Dissipative coupling to bath needed to ensure steady state (removes the energy pumped in by the external noise).

Physical implementation: continuous cooling

Wigner crystal correlations - Decay of crystal correlations remains power-law. - Decay exponent tuned by the 1/f noise power.

• Powerlaw correlations and response in the critical steady state • Novel phase transitions tuned by a competition of noise and quantum fluctuations 2

K

c 2D superfluid 1D critical 2D crystal

F 0

/ h

Quantum Simulations of Condensed Matter Systems using Ultracold Atomic Gases

Preparation of many-body states SYNERGY BETWEEN THEORY AND EXPERIMENT Detection and Characterization Phase Diagrams