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					       New physics with polar molecules
           Eugene Demler        Harvard University

 Collaborators: E. Altman, A. Aspect, E. Dalla Torre,
 T. Giamarchi, M. Greiner, T. Kitagawa, D.W. Wang
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
                Ultracold molecules MURI Kickoff, Univ. of Maryland, 2009
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)
Second order interference from paired states
                  Theory: Altman et al., PRA 70:13603 (2004)
 n(k)

                                            n(r’)



            kF        k
                                            n(r)
            BCS


             BEC
                             n(r, r' )  n(r)  n(r' )

                                n(r,r) BCS  0
Momentum correlations in paired fermions
              Experiments: Greiner et al., PRL 94:110401 (2005)
   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
Two particle interference

       Coincidence count on detectors
       measures two particle interference




          c–c
          phase controlled by beam
          splitters and mirrors
           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
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
     Trapping ions and polar molecules
Trapped ions      Ultracold polar molecules


                                                    E




                     Noise spectrum is 1/f
                     Monroe (2006), Chuang (2008)
                     Short range
                     spatial correlations
         Effective coupling to external noise
         +   +    +      +   +     +    +        +      +     +
         -   -    -      -   -     -    -        -      -     -




- Decay of crystal correlations remains power-law.
- Decay exponent tuned by the 1/f noise power.
                                            Kc   2D
   Novel phase transitions tuned by a       2    superfluid
   competition of noise and quantum                           1D critical
   fluctuations                                  2D crystal
                                                                     F0 /h
Dynamics with dipolar interactions
Interplay of dynamical and roton instabilities

         D.W. Wang, E. Demler, arXiv:0812.1838
 Moving condensate in an optical lattice. Dynamical instability
  Theory: Niu et al. PRA (01), Smerzi et al. PRL (02)
  Experiment: Fallani et al. PRL (04)

                    v




 Origin of dynamical instability:
 negative effective mass                        Amplification of
                                                density fluctuations

unstable                      unstable
                                                                       r
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
Interplay of dynamical instability and roton softening
               momentum of the condensate
                k0=0.4p     k0=0.6p
                                            momentum
                                            perpendicular
                                            to the pancakes
as=1.88a0

                                                   momentum
                                                   in the plane
as=-0.48a0



 as=-1.88a0
Decay of Bloch oscillations in systems
   with tunable scattering length
Finite decay rate of Bloch oscillations even as as -> 0
Importance of magnetic dipolar interactions

          M. Fattori et al., PRL 100:80405 (2008)
              Summary


• 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

				
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