Quantum-Fluctuation-Controlled Coherent Spin Dynamics of Rb atoms in Optical Lattices

1. Quantum-Fluctuation-Controlled Coherent Spin Dynamics of Rb atoms in Optical Lattices Fei Zhou University of British Columbia, Vancouver Collaborators: J. L. Song and Gordon Semenoff (UBC), X. L. Cui (UBC/IOP, ACS), $$: Office of the Dean of Science, UBCNSERC (Canada), A.P. Sloan foundation (New York) Canadian Institute for Advanced Research

2. Coherent dynamics: A.C.Josephsoneffect D.S.Hall et al., PRL 81, 1543 (1998)

3. AC Josephson effects in vertical traps Anderson and Kasevich, 2000

4. Chang et al. (Champman’s group), 05. Also Schmaljohann et al. (Sengstock’s group), 04 Mean field coherent spin dynamics Widera et al (Bloch’s group),05

5. Mean field dynamics versus fluctuation-controlled dynamics MF coherent dynamics: driven by mean field interaction energies; occur at a ms-100ms time scale; can be a measure of scattering lengths. Quantum Fluctuation-Controlled dynamics: driven by fluctuations; occur at relatively longer time scale; a direct measure of zero point motion of many-body degrees of freedom. easily tuned by optical lattice potentials. We recently worked on a) dynamics driven by fluctuations of a global order parameter; b) Non-mean-field dynamics induced mainly by fluctuations of an intermediate wavelength.

6. Two-body S-wave scattering lengths in different channels(in atomic units; a.u.=0.529A) a0 a2 a4 2-body ground states 87Rb (F=1) 105.8 (0.6) 105.0 (0.6) N/A F=2 ** 87Rb (F=2) 88.8 (1) 94.8 (1) 103.6 (1) F=0 ** ** Roberts (Wieman’s group), 1998; Klause et al (Chris Greene’s group), 2001. Quantum spin-nematic superfluids of F=2 rubidium atoms --- quantum fluctuation-induced nematic order --- quantum fluctuation-controlled coherent dynamics

7. Quant.-Fluc. Induced Uniaxial-Biaxial Transition(F=2 atoms) Rb U, B are degenerate in Mean field approx. This particular transition is induced by spin fluctuations. |2,0> |2,2>+|2,-2> Spin wavefunctions are plotted in spherical coordinates. U: uniaxial nematic; B: Biaxial nematics; C: cyclic;F:ferromagnetic; Song, GWS and FZ, 07; Turner, Barnett, Demler and Vishwanath,07.

8. Uniaxial versus biaxial for Rb atoms z x z y • Invariant under a dihedral-4 group: • 90, 180, 270 rotations around (0,0,1);2) 180 rotations around (1,0,0), (0,1,0), (1,1,0), (1,-1,0)plus a pi phase shift. Invariant under any rotation around the z-axis In the mean field approx, the states specified by xi are degenerate.

9. 1/3-quantum vortices in condensates of F= 2 atoms Schematic of the manifold (Semenoff and Zhou, PRL, 07) • Discrete symmetries • I, and 1800 rotation around x,y,z; • b) 1200 rotation around (1,1,1), (-1,1,1), (-1, -1, 1) and (1,-1, 1) • accompanied by a Berry phase 1200; • c) 2400 degree rotation around (1,1,1), (-1,1,1), (-1,-1,1) and (1,-1, 1) • accompanied by a Berry phase 2400.

10. Quantum-Fluctuation Induced Nematic Order Energy versus spin configurations (Analogous to the Lamb Shift )

11. Quantum-fluctuation controlled spin dynamics of F=2 Rb atoms (Song, FZ, 2007, to appear) 1) New type of dynamics not driven by GP potentials; 2) Potentially calibrate correlated fluctuations or critical exponents using coherent dynamics. MF interactions project out a five-dimension nematic submanifold (out of total 10-dimenion manifold) where GP potential is flat. We studied QFCSD in this Mean Field Ground State Submanifold.

12. QFCSD (Song, FZ, 07) In traps, quantum fluctuations induce a potential barrierr which Is less than 0.001 pk (=1mG B field) and dynamics 10^{-3}Hz. Difficult to study in experiments because of noise-induced quadratic Zeeman effect and finite life time of condensates. 1) In optical lattices, we find that the barrier height is enhanced by 4 or 5 orders when the potential depth V is increased. Frequencies (of spatially uniform population oscillations) can be increased to a few tens of Hz; 2) Enhancement is due to stronger spin-dependent interactions and especially much larger effective masses; 3) Thermal fluctuations can further enhance QFCSD; 4) QFCSD have unique quadratic Zeeman coupling dependence.

13. Energy splitting between |2,0> and |2,2>+|2,-2> condensates versus optical lattice potential depth

14. Oscillation (around uniaxial nematic |2,0>) frequency optical lattice potential depth V

15. Fluctuation-Induced potential at a finite quadratic Zeeman coupling (10pk or about 30mG)

16. Oscillation frequency (around |2,2>+|2,-2> state) versus Zeeman coupling

17. MFdynamics QFCSD Frequency versus quadratic Zeeman (around biaxial point) Also threshold versus potential depth V

18. |2,0> |2,2>+|2,-2> Dynamical instability phase diagram

19. Population oscillations with finite spin losses (life time 200ms and in finite traps; V=10 Recoil energy)

20. Energy splitting between |2,0> and |2,2>+|2,-2> at finite temperatures

21. Summary of QFCD 1) A novel class of non mean field or non GP dynamics; 2) Simulate radiative corrections, SSB or order from disorder; 3) Calibrate correlated quantum fluctuations and probe the physics near quantum critical points. Casmir-Polder forces, Obrecht et al (Cornell’s group), PRL, 2007