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arXiv:cond-mat/0703610 · Physical Review Letters

Dynamics of One-Dimensional Bose Liquids: Andreev-Like Reflection at Y Junctions and the Absence of the Aharonov-Bohm Effect

Akiyuki Tokuno, Masaki Oshikawa, Eugene Demler

Published Apr 8, 2008• 55 citations
arXivHTMLPDF

Abstract

We study one-dimensional Bose liquids of interacting ultracold atoms in the Y-shaped potential when each branch is filled with atoms. We find that the excitation packet incident on a single Y junction should experience a negative density reflection analogous to the Andreev reflection at normal-superconductor interfaces, although the present system does not contain fermions. In a ring-interferometer-type configuration, we find that the transport is completely insensitive to the (effective) flux contained in the ring, in contrast with the Aharonov-Bohm effect of a single particle in the same geometry.

DOI
10.1103/physrevlett.100.140402

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We study one-dimensional Bose liquids of interacting ultracold atoms in the Y-shaped potential when each branch is filled with atoms. We find that the excitation packet incident on a single Y junction should experience a negative density reflection analogous to the Andreev reflection at normal-superconductor interfaces, although the present system does not contain fermions. In a ring-interferometer-type configuration, we find that the transport is completely insensitive to the (effective) flux contained in the ring, in contrast with the Aharonov-Bohm effect of a single particle in the same geometry.
Abstract We study the quantum transport through two specific atomtronic circuits: a Y -junction and a ring-shaped condensate pierced by an effective magnetic flux. We demonstrate that for bosons, the two circuits display Andreev-like reflections. For the Y -junction, the transport depends on the coupling strength of the Y -junction. For the ring-shaped condensate, the transport crucially depends on the particle statistics. For interacting bosons we find that the Aharonov–Bohm interference effect is absent. By breaking the translational invariance of the ring, the flux dependence can be restored. A complementary view of the problem is obtained through a specific non-equilibrium quench protocol. We find that the steady-state is independent of the flux, however the actual time-dynamics depends on the flux. The dynamics of the full closed system can be fitted with an approximated open system approach. For all the protocols we studied, we find striking differences in the dynamics of the Bose–Hubbard model and the Gross–Pitaevskii equation.
Reflection of charge excitations at the step in the interaction strength in a Luttinger liquid can be of the Andreev type, even the interactions are purely repulsive. The region with stronger repulsion plays the role of a normal metal in a normal-metal/superconductor junction, whereas the region with weaker repulsion plays the role of a superconductor. It is shown that this quasi-Andreev reflection leads to a number of proximitylike effects, including the local enhancement (suppression) of superconducting fluctuations on the quasinormal (quasisuperconducting) side of the step and significant modification of the local density of states, as well as others. The observable consequences of these proximity effects are analyzed for the case of single- and two-particle tunneling from a normal-metal or superconducting tip into an inhomogeneous Luttinger-liquid wire.
We study the one-dimensional (1D) transport properties of an ultracold gas of Bose-Einstein condensed atoms through Aharonov-Bohm (AB) rings. Our system consists of a BoseEinstein condensate (BEC) that is outcoupled from a magnetic trap into a 1D waveguide which is made of two semiinfinite leads that join a ring geometry exposed to a magnetic flux φ. We specifically investigate the effects of a small atom-atom contact interaction strength on the AB oscillations. The main numerical tools that we use for this purpose are a mean-field Gross-Pitaevskii (GP) description and the truncated Wigner (tW) method. The latter allows for the description of incoherent transport and corresponds to a classical sampling of the evolution of the quantum bosonic many-body state through effective GP trajectories. We find that resonant transmission peaks move with an increasing interaction strength and can be suppressed for sufficiently strong interaction. We also observe that the coherent transmission blockade due to destructive interference at the AB flux φ = π is very robust with respect to the interaction strength. Aharonov-Bohm rings • Toroidal optical dipole trap Sheet beam Laguerre-Gaussian beam LG10 [1] Vlatt
A theory describing a one-dimensional Luttinger liquid in contact with a superconductor is developed. Boundary conditions for the fermion fields describing Andreev reflection at the contacts are derived and used to construct a bosonic representation of the fermions. The Josephson current through a superconductor/Luttinger liquid/superconductor junction is considered for both perfectly and poorly transmitting interfaces. In the former case, the Josephson current at low temperatures is found to be essentially unaffected by electron-electron interactions. In the latter case, significant renormalization of the Josephson current occurs. The profile of the (induced) condensate wave function in a semi-infinite Luttinger liquid in contact with a superconductor is shown to decay as a power law, the exponent depending on the sign and strength of the interactions. In the case of repulsive (attractive) interactions the decay is faster (slower) than in their absence. An equivalent method of calculating the Josephson current through a Luttinger liquid, which employs the bosonization of the system as a whole (i.e., superconductor, as well as Luttinger liquid) is developed and shown to give the results equivalent to those obtained via boundary conditions describing Andreev reflection. \textcopyright{} 1996 The American Physical Society.
Ultracold atoms in light-shaped potentials open up new ways to explore mesoscopic physics: Arbitrary trapping potentials can be engineered with only a change of the laser field. Here, we propose using ultracold atoms in light-shaped potentials to feasibly realize a cold-atom device to study one of the fundamental problems of mesoscopic physics, the Aharonov-Bohm effect: the interaction of particles with a magnetic field when traveling in a closed loop. Surprisingly, we find that the Aharonov-Bohm effect is washed out for interacting bosons, while it is present for fermions. We show that our atomic device has possible applications as a quantum simulator, Mach-Zehnder interferometer, and for tests of quantum foundation.
The Josephson current through a one-dimensional (1D) interacting electron system of length L coupled with two superconductors is studied in the presence of a barrier potential at the junction interfaces. The 1D system is treated within the framework of the Tomonaga-Luttinger liquid, in which the interaction is characterized by correlation exponents K ρ and K σ . We pay attention to the influence of Andreev reflection, which modifies the low-energy property of the 1D electron system near the junction interfaces. It is found that the critical current at low temperatures decays with increasing L as j c ∝(1/ L ) 2/ K ρ -1 , which is in striking contrast to the previous result j c ∝(1/ L ) 1/ K ρ + K σ -1 , obtained by Fazio et al. taking no account of the influence of Andreev reflection.