A few-fermion BCS superconductor · A few-fermion BCS superconductor J. Lofthouse & G.J. Conduit...
Transcript of A few-fermion BCS superconductor · A few-fermion BCS superconductor J. Lofthouse & G.J. Conduit...
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A few-fermion BCS superconductor
J. Lofthouse & G.J. Conduit
Theory of Condensed Matter Group, Department of Physics, Cambridge
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Superconductivity and Scale in Quantum Systems
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Experimental Realization of a Cold Atom Gas
6Li atom
Up spin electron
Down spin electron
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A Model of a Cold Atom Gas
• Optical trap modeled by 3-D QHO
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3-D QHO Orbitals
x
y
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3-D QHO Orbitals
x
y
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3-D QHO Orbitals
x
y
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3-D QHO Orbitals
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Non-Interacting System Ground State
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Non-Interacting System Ground State
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Non-Interacting System Ground State
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Non-Interacting System Ground State
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Non-Interacting System Ground State
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Quantum Monte-Carlo
• Non-interacting system orbitals suitable basis for weak interactions
• G.S. Energy Monte-Carlo integration
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Superfluid Hamiltonian in External Trap
• Pairwise attractive interactions between up and down spins
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Effect of Interactions on Degeneracy
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Effect of Interactions on Degeneracy
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Effect of Interactions on Degeneracy
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Interaction Energy
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Interaction Energy
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Interaction Energy
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System Geometry
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System Geometry
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System Geometry
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Pairing Effect
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Pairing Effect
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Asymmetric Trap
Non-interacting energy of N = 8 state Kept constant for
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Asymmetric Trap
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Summary
• Unique opportunity to realize a few body interacting system
• Link between microscopic physics and macroscopic phenomenology
• DMC simulations allowed us to probe attractive interactions
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BCS state
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BCS state
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BCS state
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BCS FFLO state
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BCS FFLO state
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BCS FFLO state
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BCS FFLO state
Δ(r )=Δ0 Δ(r )=Δ0ei q⋅r
q
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nx
ny
Available states
0,0
0,1 1,1
1,0
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nx
ny
Available states
0,0
0,1 1,1
1,0
1,1
1,0
1,1 1,10,1
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nx
ny
2 atoms in a spherical trap
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nx
ny
2 atoms in a spherical trap
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nx
ny
3 atoms in a spherical trap
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nx
ny
3 atoms in a spherical trap
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nx
ny
3 atoms in a spherical trap
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3 atoms in a spherical trap
nx
ny
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2 atoms in a spherical trap
Δ(r)=〈ψ∣c↑(r)c↓(r)∣ψ〉
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2 atoms in a spherical trap
Δ̄(r )Δ(0)=〈ψ∣c↓† (r)c↑
† (r)c↑(0)c↓(0)∣ψ〉
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2 atoms in a spherical trap
θ
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3 atoms in a spherical trap
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3 atoms in a spherical trap
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Where does the extra majority spin reside?
x
Δ
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Where does the extra majority spin reside?
x
Δ
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3 atoms in a spherical trap
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3 atoms in a spherical trap
θ
ρ↑-ρ↑
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Phase diagram
ω∥=2ω⊥
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Phase diagram
nx=1 ny=1
nz=1
or
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Phase diagram
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Phase diagram
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Phase diagram
Doubly degenerate
Singly degenerate
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Few trapped fermions offers chance to observe spatiallymodulated pairing
Trap ellipticity and central barrier are experimentalprobes of the pairing state
Summary
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Appendix: System Geometry
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Appendix: System Geometry
Hamiltonian for outermost electron
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Appendix: System Geometry
Hamiltonian for outermost electron
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Appendix: System Geometry
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Appendix: System Geometry
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Appendix: Magnetised Fermionic Gases
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Appendix: Magnestised fermionic gases
• N = 14
M = 0 M = 6/2 =3
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-0.4 -0.3 -0.2 -0.1 0 0.1 0.2 0.3 0.417
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19
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Appendix: Asymmetric Trap
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Trapping potential
ω⊥
ω∥V=1
2 [ω⊥2 (x2+ y2)+ω∥
2 z2 ]
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One trapped atom
E=12ω∥+ω⊥
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Two trapped atoms
E=ω∥+2ω⊥
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Three trapped atoms
E=52ω∥+3ω⊥
E=32ω∥+4ω⊥
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Three trapped atoms
E=52ω∥+3ω⊥+√ ω∥ω∥+ωBV B(2+ ω∥ω∥+ωB )
E=32ω∥+4ω⊥+3√ ω∥ω∥+ωBV B
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Three trapped atoms
E=52ω∥+3ω⊥+√ ω∥ω∥+ωBV B(2+ ω∥ω∥+ωB )+ aa∥ω⊥√
2π(32−4√2π V Bω∥+ωB )
E=32ω∥+4ω⊥+3√ ω∥ω∥+ωBV B+ aa∥ω⊥√
2π(32−6√2π V Bω∥+ωB )
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