Quantum Noise Analysis of Spin Systems Realized with Cold Atoms

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Quantum Noise Analysisof Spin SystemsRealized
with Cold Atoms

• Robert Cherng
• Eugene Demler
• cond-mat/0609748

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Noise and Correlationsin Cold Atoms
Theory Altman et al., PRA 7013603
(2004) Experiment Folling et al., Nature 434481
(2005)
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Outline

• Goal Characterize many-body states of spin
  systems in cold atoms
• Approach Quantum noise analysis of magnetization
• Full distribution function can reveal physics
  more transparently than individual moments
• Prospects for experiments

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Spin Systems with Cold Atoms
Cold collisions Mandel et al., Nature (2003),
Jaksch et al., PRL (1999) Bose Hubbard Kuklov
and Svistunov, PRL (2003), Duan et al., PRL
(2003) Review Lewenstein cond-mat/0606771
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Quantum Noise of Magnetization
Distribution Function
Finite Moments
Generating Function
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Transverse Field Ising Model
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Distribution Functions
?
?
?
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Counting Dual Domain Walls
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Counting Dual Domain Walls
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Counting Dual Domain Walls
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Counting Dual Domain Walls
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Counting Dual Domain Walls
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Distribution Functions
?
?
?
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Splitting as Topological or Dual Order Parameter
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Experimental Prospects

• Difficulties low-dimensionality, spatial
  resolution, accurate statistics
• Ideal experiment high resolution in situ imaging
  with single atom sensitivity
• Quantum polarization spectroscopy (Lewenstein et
  al. cond-mat/0608306)

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Polarization Spectroscopy
y
Need small depumping and photon absorption
z
Resolve second moment
Resolve single spin noise
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Conclusions

• Characterize many-body spin systems through
  quantum noise analysis
• Full distribution function can reveal underlying
  physics (e.g. even/odd splitting for Pn(Mz) for
  Ising Model)
• M. Lukin, E. Altman, A. Polkovnikov, L. Levitov,
  V. Gritsev, NDSEG
• cond-mat/0609748