Ordering and Entropy Production Across Quantum Phase Transitions

1
Ordering and Entropy Production Across Quantum
Phase Transitions

• Robert Cherng (Harvard)
• Leonid Levitov (MIT)
• cond-mat/0512689
• MIT UROP, NDSEG

2
QPT in Quantum Gases

• Mott transition in 3D and 1D
• Controllable environment, long coherence time
• Non-equilibrium dynamics of QPT accessible

3D - Greiner et al., Nature (2002) 1D Stoferle
et al. PRL (2004)
3
Kibble-Zurek Theory

• Causality ? defect formation
• Critical scaling ? ????/(1z?)
• Limitations
• classical not quantum theory
• structure of defect formation?

Disordered
Ordered
4
1D Transverse Ising Model

• Toy model for QPT
• Exact non-equilibrium solution for g(t)vt via
  Fermionization

Disordered
Ordered
Disordered
5
Entropy Production

• Coherent dynamics ? globally a pure quantum state
  
• Locally a mixed state of classical configurations
  with finite entropy!

Typical Configuration
6
Entropy of Defects

• Defect density ?n
• Classical gas s -?n log?n
• Fast driving vv s -?n log?n
• Slow driving vv s ?n
• More orderly defect arrangement for slow
  driving!

7
Spin Correlations

• Exact asymptotics via theory of Toeplitz
  determinants
• Correlations have oscillatory behavior at slow
  driving

8
Quantum Gases in Optical Lattices

• Spin chains via ultracold bosons in optical
  lattices
• Detect spin ordering via noise correlations

Spin exchange Mandel et al., Nature (2003),
Duan et al., PRL (2003) Noise correlations
Folling et al., Nature (2005), Altman et al., PRA
(2004)
9
Conclusions

• Non-equilibrium QPT dynamics in the transverse
  Ising model
• Entropy production in coarse-grained local
  picture
• Pattern of defect formation at slow driving
  rate
• Connections to ultracold quantum gases