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Anomalous Transport in a Unitary Fermi gas
Shun Uchino RIKEN
The Sumitomo Foundation
Uchino and Ueda, arXiv:1608.01070
T. Esslinger’s group at ETH(Lithium team) T. Giamarchi at Univ. Geneva
Transport of superfluid Fermi gasHusmann, Uchino et al., Science 350, 1498 (2015).
Anomalous transport of normal Fermi gasM. Ueda at Univ. Tokyo, RIKEN
More is differentSuperconductivity Quamtum Hall effect
Kondo effect
More is differentSuperconductivity Quamtum Hall effect
Kondo effect
Each phenomenon possesses a peculiar transport property
Atomtronics
• Two terminal transport setup realized in Esslinger’s group@ETH
• Transfer of atoms between reservoirs occurs through mesoscropic conduction channel
left
right
Quantum point contact
Wees et al., PRL 60, 848 (1988).
Electron system Cold atoms
Krinner et al., Nature 517, 64 (2015).
3D 3D1D
Quantum point contact
3D1D
Nch : number of conduction channels
G =1
hNch
3D
Krinner et al., Nature 517, 64 (2015).
Conductance quantization (Landauer’s formula)
M. Randeria, E. Taylor, Annual Review of Condensed matter physics 5, 209 (2014).
BCS-BEC crossover
What happens for superfluid reservoirs?
Harvard-Smithsonian Center for Astrophysics
Connecting two neutron stars?
Nonlinear current-bias characteristics (Low temperature data)
Husmann, Uchino et al., Science 350, 1498 (2015).
Nonlinear current-bias characteristics (Low temperature data)
Husmann, Uchino et al., Science 350, 1498 (2015).
Red curve: theory based on Keldysh formalism
Nonlinear current-bias characteristics (Low temperature data)
Experiment can be explained by a theory with multiple Andreev reflections (Quasi-particle+pair tunneling)
Husmann, Uchino et al., Science 350, 1498 (2015).
Blonder et al., PRB 25, 4515(1982) Averin and Bardas, PRL 75, 1831(1995)
Anomalous conductance measurement
S. Krinner et al., PNAS 201601812 (2016).
Confinement potential[kHz]
ProblemNo existing theory to explain the experiment
Tunneling HamiltonianH = Hbulk +HT
Hbulk =X
i=L,R
0
@X
p
X
�=",#
p2
2mc†i,p,�ci,p,� � g
X
p,q,k
c†i,p+q,"c†i,�p,#ci,�k,#ci,k+q,"
1
A
HT = tX
p,k,�
(c†L,p,�cR,k,� + c†R,k,�cL,p,�)
Left Rightt
Superfluid(superconducting) fluctuation?• In superconductor materials, the conductivity is known to be enhanced by superconducting fluctuations.
⇧AL(q,!) =
Aslamazov-Larkin correction
• Physically, above represents transport of preformed pairs
Preformed-pair current in tunneling Hamiltonian Leading diagram is already fourth order in t
⇡
· · ·
n-th order diagram of the fluctuation-pair contribution
Nonlinear response theory must be applied!
· · ·
0.0 0.2 0.4 0.6 0.8 1.00
1
2
3
4
(T-Tc)/TcGp[1
/h]
2D3D
Preformed-pair current in tunneling Hamiltonian
Comparison (single-transport channel)!"#
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• The comparison is made by assuming 3D reservoirs
• Consistent with experimental observations
T/TF = 0.1T/TF = 0.075
Comparison (gate potential, trapping, interaction dependence)
• Energy dependence of t is incorporated
1kF a
=-1.1
1kF a
=-0.9
1kF a
=-2.1
12 14 16 18 20 22 240.0
0.5
1.0
1.5
2.0
2.5
3.0
Horizontal confinement [kHz]
Gmass[1
/h]
1kF a
=-1.6
1kF a
=-1.2
1kF a
=-2.1
0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.90
1
2
3
4
5
Gate potential [μK]
Gmass[1
/h]
• Again consistent with experimental observations
Summary• Superfluid transport in a unitary Fermi gas
Nonlinear current-bias characteristicsMultiple Andreev reflections
D. Husmann, SU et al., Science 350, 1498 (2015).
• Anomalous conductance in attractively-interacting fermions
Transport of preformed pairs
Breakdown of Landauer’s formula
SU and M. Ueda, arXiv:1608.01070
Another scenario: M. Kanasz-Nagy et al., arXiv:1607.02509