Dynamical Instabilities of Dipolar Spinor Condensates

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Dynamical Instabilities of Dipolar Spinor
Condensates

• Robert Cherng (Harvard, NSF GRFP)
• Eugene Demler (Harvard)

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From Spinless to Spinor Condensates
Esslinger Group http//www.quantumoptics.ethz.ch/
Stamper-Kurn Group http//ultracold.physics.berkel
ey.edu/
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Spinor Condensates at Berkeley
F1 87Rb
M. Vengalattore, S. R. Leslie, J. Guzman and D.
M. Stamper-Kurn, ''Spontaneously modulated spin
textures in a dipolar spinor Bose-Einstein
condensate'', arXiv0712.4182 (Dec 2007)
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Competing Effects

• Magnetic Field
• Larmor Precession (115 Hz)
• Quadratic Zeeman (0-20 Hz)

• S-wave Scattering
• Spin independent (g0n215 Hz)
• Spin dependent (gsn8 Hz)

• Dipolar Interaction
• Anisotropic (gdn10 Hz)
• Long-ranged

• Reduced Dimensionality
• Quasi-2D geometry

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Competing Effects

• Magnetic Field
• Larmor Precession (115 Hz)
• Quadratic Zeeman (0-20 Hz)

• S-wave Scattering
• Spin independent (g0n215 Hz)
• Spin dependent (gsn8 Hz)

• Dipolar Interaction
• Anisotropic (gdn10 Hz)
• Long-ranged

• Reduced Dimensionality
• Quasi-2D geometry

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Hamiltonian
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Precessional and Quasi-2D Averaging
Rotating Frame
Gaussian Profile
Quasi-2D Time Averaged Dipolar Interaction
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Uniform Mean Field Solutions
Mean Field Parameters
?-0
Mean Field State
?-p/2
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Collective Modes
Mean Field
Equations of Motion
Collective Fluctuations (Spin, Charge)
Spin Mode dfB longitudinal magnetization df
transverse orientation Charge Mode dn 2D
density d? global phase
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Berkeley Experiments
M. Vengalattore, et. al, arXiv0712.4182
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Conclusions

• Dipolar interactions crucial for spinor
  condensates
• But effectively modified by quasi-2D and
  precession
• Variety of instabilities (ring, stripe,
  checkerboard)
• But what about the ground state?