Dynamical instability of the XY spiral state of ferromagnetic condensates

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Dynamical instability of the XY spiral state of
ferromagnetic condensates

• Robert Cherng (Harvard)
• NDSEG, NSF GRFP
• Vladimir Gritsev (Harvard)
• Dan Stamper-Kurn (UC Berkeley)
• Eugene Demler (Harvard)
• arXiv0710.2499
• (see also Lamacraft arXiv0710.1848)

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From spinless condensates

• Single component fields

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To spinor condensates

• Multicomponent fields
• (F1 87Rb)

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Order parameters

• Spinor fields (F1 87Rb)
• Magnetization
• Nematicity

Fa
Qab
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Order parameters

• Spinor fields (F1 87Rb)
• Magnetization
• Nematicity

Spin textures
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Spin textures in spinor condensates
Prepare condensate with uniform magnetization
Apply magnetic field gradient
What is the fate of the XY spiral state?
see Higbie et. al., PRL 95, 050401 (2005).
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High resolution magnetometry
Vengalattore et. al. , PRL 97, 200801 (2007)
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Dissolving spin textures
DSK, unpublished
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Spinor Hamiltonian

• Quadratic Zeeman term q favors Fa0
• Spin dependent interaction gs favors Fa?0
• Conservation of Fz magnetic field does not
  enter through linear Zeeman term

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Collective mode analysis
F condensate dFk collective mode ?k
excitation energy ? spiral wavevector

• F is a metastable stationary state
• Dynamical instability imaginary ?k indicating
  exponential growth of fluctuations

Analyze in rotating frame
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Spectrum of collective modes
q0.2 Hz, fz0
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fz0 Phase diagram
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Instability for small q

• Near SO(3) rotationally symmetric limit
• Instability driven by fluctuations in the
  direction of magnetization
• Finite q provides energy barrier stable for
  ?2/2mltq

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Instability for large q
Unwind XY magnetization
Via magnitude fluctuations

• Near phase transition to polar state
• Instability driven by fluctuations in the
  magnitude of magnetization
• (qc-q) measures distance from critical point
  stable for ?2/2mlt(qc-q)/3

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Conclusions

• Spiral spin textures unwind due to dynamical
  instability
• small q rotations out of plane
• large q rotations within plane
• Adiabatic/sudden limits, length/time scales,
  aspect ratio, dipolar interactions
• V. Gritsev, D. Stamper-Kurn, E. Demler
• arXiv0710.2499

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Spinor Hamiltonian
Spin dependent interactions
g0n215 Hz, gsn8 Hz
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Adiabatic vs. sudden Limits
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Longitudinal Magnetization
fz0.05
fz0.5
Adiabatic
Sudden
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Fragmentation length/time scales
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Mean-field solution
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Collective Modes