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arXiv:1607.02509 · Physical Review Letters

Anomalous Conductances in an Ultracold Quantum Wire

Márton Kanász-Nagy, L. I. Glazman, Tilman Esslinger, Eugene Demler

Published Dec 16, 2016• 33 citations
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Abstract

We analyze the recently measured anomalous transport properties of an ultracold gas through a ballistic constriction [S. Krinner et al., Proc. Natl. Acad. Sci. U.S.A. 113, 8144 (2016)]. The quantized conductance observed at weak interactions increases severalfold as the gas is made strongly interacting, which cannot be explained by the Landauer theory of single-channel transport. We show that this phenomenon is due to the multichannel Andreev reflections at the edges of the constriction, where the interaction and confinement result in a superconducting state. Andreev processes convert atoms of otherwise reflecting channels into the condensate propagating through the constriction, leading to a significant excess conductance. Furthermore, we find the spin conductance being suppressed by superconductivity; the agreement with experiment provides an additional support for our model.

DOI
10.1103/physrevlett.117.255302

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We analyze the recently measured anomalous transport properties of an ultracold gas through a ballistic constriction [S. Krinner et al., Proc. Natl. Acad. Sci. U.S.A. 113, 8144 (2016)]. The quantized conductance observed at weak interactions increases severalfold as the gas is made strongly interacting, which cannot be explained by the Landauer theory of single-channel transport. We show that this phenomenon is due to the multichannel Andreev reflections at the edges of the constriction, where the interaction and confinement result in a superconducting state. Andreev processes convert atoms of otherwise reflecting channels into the condensate propagating through the constriction, leading to a significant excess conductance. Furthermore, we find the spin conductance being suppressed by superconductivity; the agreement with experiment provides an additional support for our model.
Motivated by a recent experiment in ultracold atoms [S. Krinner et al., Proc. Natl. Acad. Sci. U.S.A. 113, 8144 (2016)PNASA60027-842410.1073/pnas.1601812113], we analyze transport of attractively interacting fermions through a one-dimensional wire near the superfluid transition. We show that in a ballistic regime where the conductance is quantized in the absence of interaction, the conductance is renormalized by superfluid fluctuations in reservoirs. In particular, the particle conductance is strongly enhanced, and the conductance plateau is blurred by emergent bosonic pair transport. For spin transport, in addition to the contact resistance, the wire itself is resistive, leading to a suppression of the measured spin conductance. Our results are qualitatively consistent with the experimental observations.
We study particle and spin transport in a single-mode quantum point contact, using a charge neutral, quantum degenerate Fermi gas with tunable, attractive interactions. This yields the spin and particle conductance of the point contact as a function of chemical potential or confinement. The measurements cover a regime from weak attraction, where quantized conductance is observed, to the resonantly interacting superfluid. Spin conductance exhibits a broad maximum when varying the chemical potential at moderate interactions, which signals the emergence of Cooper pairing. In contrast, the particle conductance is unexpectedly enhanced even before the gas is expected to turn into a superfluid, continuously rising from the plateau at [Formula: see text] for weak interactions to plateau-like features at nonuniversal values as high as [Formula: see text] for intermediate interactions. For strong interactions, the particle conductance plateaus disappear and the spin conductance gets suppressed, confirming the spin-insulating character of a superfluid. Our observations document the breakdown of universal conductance quantization as many-body correlations appear. The observed anomalous quantization challenges a Fermi liquid description of the normal phase, shedding new light on the nature of the strongly attractive Fermi gas.
We analyze theoretically the quantization of conductance occurring with cold bosonic atoms trapped in two reservoirs connected by a constriction with an attractive gate potential. We focus on temperatures slightly above the condensation threshold in the reservoirs. We show that a conductance step occurs, coinciding with the appearance of a condensate in the constriction. Conductance relies on a collective process involving the quantum condensation of an atom into an elementary excitation and the subsequent quantum evaporation of an atom, in contrast with ballistic fermion transport. The value of the bosonic conductance plateau is strongly enhanced compared to fermions and explicitly depends on temperature. We highlight the role of the repulsive interactions between the bosons in preventing them from collapsing into the constriction. We also point out the differences between the bosonic and fermionic thermoelectric effects in the quantized conductance regime.
Recent experiments have revealed that the temperature dependence of the conductance of quasiballistic quantum wires bears characteristic features of the Luttinger-liquid state. In this paper, the conductance of an N-channel quantum wire is calculated within the model of N coupled Luttinger liquids and under the assumption of weak disorder. It is shown that as the number of channels increases, a crossover from the Luttinger-liquid to the Fermi-liquid behavior occurs. This crossover manifests itself in the 1/N decrease of the scaling exponent of the temperature dependence. An exact expression for the scaling exponent for the case of N coupled Luttinger chains is obtained, and the large N limit is studied for the case of a quantum wire. The case of N=2 for electrons with spin is analyzed in detail, and a qualitative agreement with the experiment is achieved.
A quantum phase transition is an unequivocal signature of strongly correlated many-body physics. Signatures of such phenomena are yet to be observed in ballistic transport through quantum wires. Recent developments in quantum wires have made it possible to enhance the interaction between the electrons. Here we show that hitherto unexplained anticrossing between conduction energy subbands, observed in such experiments, can be explained through a simple yet effective discretized model which undergoes a second-order quantum phase transition within the Ising universality class. Accordingly, we observe how the charge distribution, transverse to the direction of the wire, will vary across the phase transition. We show that data coming from three different samples with differing electron densities and gate voltages show a remarkable universal scaling behavior, determined by the relevant critical exponent, which is only possible near a quantum phase transition.
We propose a method by which the quantization of the Hall conductance can be directly measured in the transport of a one-dimensional atomic gas. Our approach builds on two main ingredients: (1) a constriction optical potential, which generates a mesoscopic channel connected to two reservoirs, and (2) a time-periodic modulation of the channel specifically designed to generate motion along an additional synthetic dimension. This fictitious dimension is spanned by the harmonic oscillator modes associated with the tightly confined channel, and hence, the corresponding “lattice sites” are intimately related to the energy of the system. We analyze the quantum-transport properties of this hybrid two-dimensional system, highlighting the appealing features offered by the synthetic dimension. In particular, we demonstrate how the energetic nature of the synthetic dimension combined with the quasienergy spectrum of the periodically driven channel allows for the direct and unambiguous observation of the quantized Hall effect in a two-reservoir geometry. Our work illustrates how topological properties of matter can be accessed in a minimal one-dimensional setup, with direct and practical experimental consequences.