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

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

Fei ZhouUniversity of British Columbia, Vancouver

Collaborators: J. L. Song and Gordon Semenoff (UBC), X. L. Cui (UBC/IOP, ACS),

$$: Office of the Dean of Science, UBC NSERC (Canada), A.P. Sloan foundation (New York)

Canadian Institute for Advanced Research

Coherent dynamics: A.C. Josephson effect

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D.S.Hall et al., PRL 81, 1543 (1998)

AC Josephson effects in vertical traps

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Anderson and Kasevich, 2000

Chang et al. (Champman’s group), 05.Also Schmaljohann et al. (Sengstock’s group), 04

Widera et al (Bloch’s group),05Mean field coherent spin dynamics

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.

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

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.

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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>

Uniaxial versus biaxial for Rb atoms

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Invariant under a dihedral-4 group:1) 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.

z

z

y

x

)2,2|2,2(|2

1sin0,2|cos

In the mean field approx, the states specified by xi are degenerate.

1/3-quantum vortices in condensates of F= 2 atoms

Discrete symmetriesa) 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.

Schematic of the manifold(Semenoff and Zhou, PRL, 07)

Quantum-Fluctuation Induced Nematic Order

Energy versus spin configurations (Analogous to the Lamb Shift )

)2,2|2,2(|2

1sin0,2|cos

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.

)2,2|2,2(|2

1)(sin0,2|)(cos tt

QFCSD (Song, FZ, 07)

In traps, quantum fluctuations induce a potential barrierr whichIs 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 by4 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.

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

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

)2,2|2,2(|2

1cos0,2| tA

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

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

0,2|)2,2|2,2(|2

1cos tA

Frequency versus quadratic Zeeman (around biaxial point)Also threshold versus potential depth V

MF dynamics

QFCSD

Dynamical instability phase diagram

|2,0>

|2,2>+|2,-2>

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

Energy splitting between |2,0> and |2,2>+|2,-2>

at finite temperatures

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