1. New physics with polar molecules Eugene Demler Harvard University Outline: Measurements of molecular wavefunctions using noise correlations Quantum critical states and phase transitions in the presence of non equilibrium noise Dynamics of systems with dipolar interactions: interplay of roton and dynamical instabilities Collaborators: E. Altman, A. Aspect, E. Dalla Torre, T. Giamarchi, M. Greiner, T. Kitagawa, D.W. Wang Ultracold molecules MURI Kickoff, Univ. of Maryland, 2009

2. How to measure wavefunctions of molecules From noise correlations to phase sensitive measurements in systems of ultra-cold atoms T. Kitagawa, A. Aspect, M. Greiner, E. Demler Following up on earlier experiments of D. Jin et al. PRL (2005)

3. Second order interference from paired states n(r) n(r’) n(k) k BCS BEC k F Theory: Altman et al., PRA 70:13603 (2004)

4. Momentum correlations in paired fermions Experiments: Greiner et al., PRL 94:110401 (2005)

5. How to measure the molecular wavefunction? How to measure the non-trivial symmetry of y (p)? We want to measure the relative phase between components of the molecule at different wavevectors

6. Two particle interference Coincidence count on detectors measures two particle interference c – c phase controlled by beam splitters and mirrors

7. Two particle interference Implementation for atoms: Bragg pulse before expansion Bragg pulse mixes states k and –p = k-G -k and p =-k+G Coincidence count for states k and p depends on two particle interference and measures phase of the molecule wavefunction

8. Quantum critical states and phase transitions in the presence of non equilibrium noise E. G. Dalla Torre, E. Demler, T. Giamarchi, E. Altman, arXiv:0908.0868

9. Trapped ions Ultracold polar molecules E Trapping ions and polar molecules Noise spectrum is 1/f Monroe (2006), Chuang (2008) Short range spatial correlations

10. Effective coupling to external noise + - + - + - + - + - + - + - + - + - + - - Decay of crystal correlations remains power-law. - Decay exponent tuned by the 1/f noise power. Novel phase transitions tuned by a competition of noise and quantum fluctuations 2 KcKc F 0 /  2D superfluid 2D crystal 1D critical

11. Dynamics with dipolar interactions Interplay of dynamical and roton instabilities D.W. Wang, E. Demler, arXiv:0812.1838

12. Moving condensate in an optical lattice. Dynamical instability v Theory: Niu et al. PRA (01), Smerzi et al. PRL (02) Experiment: Fallani et al. PRL (04) Origin of dynamical instability: negative effective mass unstable r Amplification of density fluctuations

13. Roton spectrum in pancake polar condensates Santos, Shlyapnikov, Lewenstein (2000) Fischer (2006) Origin of roton softening Repulsion at long distances Attraction at short distances Stability of the supersolid phase is a subject of debate

14. Interplay of dynamical instability and roton softening momentum in the plane momentum perpendicular to the pancakes a s =1.88a 0 a s =-0.48a 0 a s =-1.88a 0 momentum of the condensate k 0 =0.4 p k 0 =0.6 p

15. Decay of Bloch oscillations in systems with tunable scattering length M. Fattori et al., PRL 100:80405 (2008) Finite decay rate of Bloch oscillations even as a s -> 0 Importance of magnetic dipolar interactions

16. Measurements of molecular wavefunctions using noise correlations Quantum critical states and phase transitions in the presence of non equilibrium noise Dynamics of systems with dipolar interactions: interplay of roton and dynamical instabilities Summary