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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