Quantum phase transitions across pwave Feshbach resonance

1
Quantum phase transitions acrossp-wave Feshbach
resonance
with Victor Gurarie (CU Boulder) Anton
Andreev (U. Washington) for details see,
Gurarie, L.R., Andreev, cond-mat/0410620
support by NSF Materials Theory, Packard
Foundation
2
Outline

• Motivation
• Predictions
• Model
• Analysis
• Phase transitions
• Conclusions

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Motivation

• discovery of p-wave Feshbach resonances in 40K
  (Jin), 6Li (Salomon)
• demonstration of s-wave FR-driven paired
  superfluidity
• richness of nonzero L superfluids (3He,
  Ruthenates, high-Tcs,)
• realization of a fractional quantum Hall state
• narrowness of p-wave FR small parameter
  (cf. s-wave)
• quantitatively accurate predictions

Regal, et al
Regal, et al
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Predictions

• novel vortices (Volovik, Liu)
• FQHE phenomenology (Read and Green)

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s-wave Feshbach resonant scattering
Timmermans, et al Holland, et al Stoof, et al
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s-wave resonant superfluidity
Griffin, et al Levin, et al
Timmermans, et al Holland, et al Stoof, et al
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p-wave Feshbach resonant scattering
naturally narrow!
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p-wave resonant superfluidity
Ho, Diener Ohashi
Sa de Melo, et al Cheng, Yip

• narrow resonance
• complex vector order parameter
• sample states

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Mean-field theory

• superfluid ground state
• excitation spectrum

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Isotropic resonance at T0

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Dipolar-interaction FR splitting
Ticknor, et al
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P-wave superfluid phases
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T0 phase diagrams
also see Cheng, Yip 05
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Finite T phase diagram
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Gapless gapped superfluid transitions
also see Sa de Melo, et al
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px i py superfluid in 2D

• same as the Pfaffian (Moore-Read) state in
  quantum Hall effect
• excitations with non-Abelian statistics
• topological classification in terms of uk and vk
• gapped ? gapped superfluid transition at ???
• suggested to be used as qubits for quantum
  computers

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Conclusions

• quantitatively accurate description of crossover
  and transitions
• with ?????F as small parameter for
  narrow resonance
• px and px i py superfluid states
• superfluid ? superfluid finite T and quantum
  phase transitions
• need generalization to a trap and detailed
  exploration of
• phenomenology

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Numbers for various s-FBR
Petrov
TF 2 ?K ? l 10,000 Å ?0 1/(2m r02) r0 h4
/(m2 g2)