Ground State Description of Single Vortex in Atomic Fermi Gas: From BCS to BEC

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Ground State Description of Single Vortex in
Atomic Fermi Gas From BCS to BEC
Ref cond-mat/0510647

• Chih-Chun Chien,Y.He,Q.Chen,K.Levin
• University of Chicago
• (Thanks to N.Nygaard)

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Introduction

• Motivation Quantized vortex is strong evidence
  of superfluidity.
• Goal Use a unified theory to describe the
  evolution of a single vortex in an atomic Fermi
  gas in the BCS-BEC crossover.

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Methodology

• Solve Bogoliubov-de Gennes equation with the
  assumption that the ground state is the
  Leggett-BCS ground state (D and m solved
  self-consistently).

(T0, 1 channel)

• Deep-BEC Limit (composite bosons)

Assumptions
slow-varying (Pieri Strinati PRL 03)

Gross-Pitaevskii theory with corrections
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Vortex in deep-BEC Limit
(Neglect the z-dependence)
(Total depletion in the core center)
(Black sold line GP. Blue dash line GP w/ g3)
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Vortex in BCS-BEC crossover
deep-BEC
Unitary
Order parameter always vanishes at core center
BCS
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Vortex in BCS-BEC crossover
deep-BEC
Total depletion
Partial depletion (unpaired fermions)
Unitary
Almost no depletion
BCS
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Density Depletion and Core Size
BCS
BCS
Unitary
BEC
Unitary
BEC
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Local Density of States (LDOS)
Definition
(constant)
Total number of states
Total number of particles (occupied states)
Black dash line r0 (center) . Red solid line
r25/kF (bulk)
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Local Density of States (LDOS)

• Two contributions to core density depletion
• Unoccupied discrete state shifts spectral weight
• Redistribution of spectral weight of continuum
  states

Black dash line r0 (center) . Red solid line
r25/kF (bulk)
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Local Density of States (LDOS)
Quasi-bound state (almost unoccupied)
Discrete state (unoccupied)
Bound state (partially occupied)
Black dash line r0 (center) . Red solid line
r25/kF (bulk)
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Local Density of States (LDOS)
Redistribution of continuum states (Compared to
bulk)
Black dash line r0 (center) . Red solid line
r25/kF (bulk)
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Summary

• We use a unified theory to study vortex in
  BCS-BEC crossover
• BdG theory in the deep-BEC limit is equivalent to
  GP theory (with corrections).
• We show the structure, density, core size of
  single vortex in the BCS-BEC crossover.
• We use LDOS to attribute core density depletion
  to unoccupied discrete state and redistribution
  of continuum.

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Comparisons with other works

• Sensarma et. al. (cond-mat/0510761) Similar
  observations, but we show that discrete states
  are not important in BEC limit.
• Machida et. al. (PRL 94, 140401) They attributed
  core density depletion to closed channel bosons
  (2-channel model).
• Yu et. al. (PRL 90, 161101) Only BCS Unitary.
  They attribute core density depletion to
  Hartree-Fock term.
• Nygaard et. al. (PRL 90, 210402) Detailed work
  in BCS. We benefit from their work.