ondensed Matter models for any-body systems of ultracold atom Eugene Demler Harvard University ollaborators: hud Altman, Robert Cherng, Adilet Imambekov, ladimir Gritsev, Takuya Kitagawa, Susanne Pielawa, avid Pekker, Rajdeep Sensarma xperiments: loch et al., Esslinger et al., chmiedmayer et al., Stamper-Kurn et al. Harvard- MIT
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Condensed Matter models for many-body systems of ultracold atoms Eugene Demler Harvard University Collaborators: Ehud Altman, Robert Cherng, Adilet Imambekov,
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Condensed Matter models for many-body systems of ultracold atoms Eugene Demler Harvard University
Collaborators:Ehud Altman, Robert Cherng, Adilet Imambekov, Vladimir Gritsev, Takuya Kitagawa, Susanne Pielawa,David Pekker, Rajdeep Sensarma
Experiments: Bloch et al., Esslinger et al., Schmiedmayer et al., Stamper-Kurn et al.
Harvard-MIT
New Tricks for Old Dogs,Old Tricks for New Dogs
Condensed Matter models for many-body systems of ultracold atoms
Dipolar interactions. Magnetoroton softening, spin textures, supersolid. New issues: averaging over Larmor precession, coupling of spin textures and vorticesR. Cherng, V. Gritsev. In collaboration with D. Stamper-Kurn
Luttinger liquid. Ramsey interferometry and many-body decoherence in 1d. New issues: nonequilibrium dynamics, analysis of quantum noise.V. Gritsev, T. Kitagawa, S. Pielawa. In collaboration with expt. groups of I. Bloch and J. Schmiedmayer
Hubbard model. Fermions in optical lattice.
Decay of repulsively bound pairs. New issues: nonequilibrium dynamics in strongly interacting regime.D. Pekker, R. Sensarma, E. Altman. In collaboration with expt. group of T. Esslinger
Summary
Dipolar interactions in spinor condensates.Magnetoroton softening and spin texturesR. Cherng, V. Gritsev. In collaboration with D. Stamper-Kurn
Roton minimum in 4He
Glyde, J. Low. Temp. Phys. 93 861
Phase diagram of 4He
Possible supersolid phase in 4He
A.F. Andreev and I.M. Lifshits (1969):Melting of vacancies in a crystal due to strong quantum fluctuations.
Also G. Chester (1970); A.J. Leggett (1970)
D. Kirzhnits, Y. Nepomnyashchii (1970),T. Schneider and C.P. Enz (1971).Formation of the supersolid phase due tosoftening of roton excitations
Most unstable mode• |k|2 cost in kinetic energy• |k| gain in dipolar energy• l ~ 30 μm
kIm
Hz5.1,ˆ//ˆ qxB
Finding a stable ground state
Non-linear sigma model:Spin textures cause phase twists
Spinor “vector potential”Energetic Constraints
Equations of motion for η
Effective kinetic energy
Non-linear sigma model
Topological charge(net vorticity)
Spin gradient
Vortex interaction
Dipolar interaction
Spin Textures
Unit Cell
Top. Charge Q Kinetic EnergyQ<0
Q>0
Min KE
Max KE
Spin Textures: Skyrmion Stripes
Unit Cell
Top. Charge Q Kinetic Energy
Unit Cell
Top. Charge Q Kinetic Energy
Spin Textures: Skyrmion Lattice
Unit Cell
Top. Charge Q Kinetic Energy
Unit Cell
Top. Charge Q Kinetic Energy
Quantum noise as a probe of non-equilibrium dynamics
Ramsey interferometry and many-body decoherence
T. Kitagawa, A. Imambekov, S. Pielawa, J. Schmeidmayer’s group. Continues earlier work with V. Gritsev, M. Lukin, I. Bloch’s group.Phys. Rev. Lett. 100:140401 (2008)
Working with N atoms improves the precision by .
Ramsey interference
t0
1
Atomic clocks and Ramsey interference:
Two component BEC. Single mode approximation
Interaction induced collapse of Ramsey fringes
time
Ramsey fringe visibility
Experiments in 1d tubes: A. Widera et al. PRL 100:140401 (2008)
Spin echo. Time reversal experiments
Single mode approximation
Predicts perfect spin echo
The Hamiltonian can be reversed by changing a12
Spin echo. Time reversal experiments
No revival?
Expts: A. Widera et al., Phys. Rev. Lett. (2008)
Experiments done in array of tubes. Strong fluctuations in 1d systems.Single mode approximation does not apply.Need to analyze the full model
Interaction induced collapse of Ramsey fringes.Multimode analysis
Luttinger model
Changing the sign of the interaction reverses the interaction part of the Hamiltonian but not the kinetic energy
Time dependent harmonic oscillatorscan be analyzed exactly
Low energy effective theory: Luttinger liquid approach
Time-dependent harmonic oscillator
Explicit quantum mechanical wavefunction can be found
From the solution of classical problem
We solve this problem for each momentum component
See e.g. Lewis, Riesengeld (1969) Malkin, Man’ko (1970)
Interaction induced collapse of Ramsey fringesin one dimensional systems