Anomalous Transport in a Unitary Fermi gas Shun Uchino RIKEN The - PowerPoint PPT Presentation

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 gas Husmann, Uchino et al., Science 350 , 1498 (2015). Anomalous transport of normal Fermi gas M. Ueda at Univ. Tokyo, RIKEN

More is different Superconductivity Quamtum Hall effect Kondo effect

More is different Superconductivity Quamtum Hall effect Kondo effect Each phenomenon possesses a peculiar transport property

Atomtronics mesoscropic conduction channel left right • Two terminal transport setup realized in Esslinger’s group@ETH • Transfer of atoms between reservoirs occurs through

Quantum point contact Wees et al., PRL 60 , 848 (1988). Electron system Cold atoms Krinner et al., Nature 517 , 64 (2015). 3D 3D 1D

Quantum point contact 3D 1D 3D Krinner et al., Nature 517 , 64 (2015). Conductance quantization (Landauer’s formula) G = 1 hN ch N ch : number of conduction channels

M. Randeria, E. Taylor, Annual Review of Condensed matter physics 5, 209 (2014). BCS-BEC crossover What happens for superfluid reservoirs?

Connecting two neutron stars? Harvard-Smithsonian Center for Astrophysics

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] Problem No existing theory to explain the experiment

Tunneling Hamiltonian Left Right t H = H bulk + H T 0 1 p 2 X @X X X 2 mc † c † i, p + q , ↑ c † H bulk = i, p , σ c i, p , σ − g i, − p , ↓ c i, − k , ↓ c i, k + q , ↑ A p i = L,R σ = ↑ , ↓ p , q , k ( c † L, p , σ c R, k , σ + c † X H T = t R, k , σ c L, p , σ ) p , k , σ

Superfluid(superconducting) fluctuation? enhanced by superconducting fluctuations. Aslamazov-Larkin correction • In superconductor materials, the conductivity is known to be Π AL ( q , ω ) = • 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! ≈ · · ·

Preformed-pair current in tunneling Hamiltonian 3D 2D · · · 4 3 G p [ 1 / h ] 2 1 0 0.0 0.2 0.4 0.6 0.8 1.0 ( T - T c )/ T c

Comparison (single-transport channel) !"# %"# T/T F = 0 . 075 )"( T/T F = 0 . 1 ! !"## ! ! " " # )"# $"( $"# !"( !"# !"# !"$ !"% !"& !"' $"# ! ! ! ! !$# #"& #") ! !"#$ ! ! " " # • The comparison is made by assuming 3D reservoirs #"% #"( #"$ • Consistent with experimental observations #"! !"# !"$ !"% !"& !"' $"# ! ! ! !

( gate potential, trapping, interaction dependence ) Comparison 5 3.0 1 1 k F a =- 1.2 k F a =- 0.9 2.5 4 G mass [ 1 / h ] G mass [ 1 / h ] 1 1 2.0 k F a =- 1.1 k F a =- 1.6 3 1.5 1 1 k F a =- 2.1 k F a =- 2.1 2 1.0 1 0.5 0 0.0 12 14 16 18 20 22 24 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 Horizontal confinement [ kHz ] Gate potential [ μ K ] • Energy dependence of t is incorporated • Again consistent with experimental observations

Summary Nonlinear current-bias characteristics Multiple Andreev reflections D. Husmann, SU et al., Science 350 , 1498 (2015). 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 • Superfluid transport in a unitary Fermi gas • Anomalous conductance in attractively-interacting fermions