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arXiv:0710.2914 · Physical Review Letters

Andreev-Like Reflections with Cold Atoms

Andrew J. Daley, P. Zoller, Björn Trauzettel

Published Mar 20, 2008• 25 citations
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Abstract

We propose a setup in which Andreev-like reflections predicted for 1D transport systems could be observed time dependently using cold atoms in a 1D optical lattice. Using time-dependent density matrix renormalization group methods we analyze the wave packet dynamics as a density excitation propagates across a boundary in the interaction strength. These phenomena exhibit good correspondence with predictions from Luttinger liquid models and could be observed in current experiments in the context of the Bose-Hubbard model.

DOI
10.1103/physrevlett.100.110404

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We propose a setup in which Andreev-like reflections predicted for 1D transport systems could be observed time dependently using cold atoms in a 1D optical lattice. Using time-dependent density matrix renormalization group methods we analyze the wave packet dynamics as a density excitation propagates across a boundary in the interaction strength. These phenomena exhibit good correspondence with predictions from Luttinger liquid models and could be observed in current experiments in the context of the Bose-Hubbard model.
In this paper, we study a strongly correlated quantum system that has become amenable to experiment by the advent of ultracold bosonic atoms in optical lattices, a chain of two different bosonic constituents. Excitations in this system are first considered within the framework of bosonization and the Luttinger liquid theory which are applicable if the Luttinger liquid parameters are determined numerically. The occurrence of a bosonic counterpart of fermionic spin–charge separation is signalled by a characteristic two-peak structure in the spectral functions found by dynamical density-matrix renormalization group (DMRG) in good agreement with analytical predictions. Experimentally, single-particle excitations as probed by spectral functions are currently not accessible in cold atoms. Therefore we consider the modifications needed for current experiments, namely the investigation of the real-time evolution of density perturbations instead of single-particle excitations, a slight inequivalence between the two intraspecies interactions in actual experiments, and the presence of a confining trap potential. Using time-dependent DMRG, we show that only quantitative modifications occur. With an eye to the simulation of strongly correlated quantum systems far from equilibrium, we detect a strong dependence of the time-evolution of entanglement entropy on the initial perturbation.
We investigate the propagation of density-wave packets in a Bose-Hubbard model using the adaptive time-dependent density-matrix renormalization group method. We discuss the decay of the amplitude with time and the dependence of the velocity on density, interaction strength, and the height of the perturbation in a numerically exact way, covering arbitrary interactions and amplitudes of the perturbation. In addition, we investigate the effect of self-steepening due to the amplitude dependence of the velocity and discuss the possibilities for an experimental detection of the moving wave packet in time-of-flight pictures. By comparing the sound velocity to theoretical predictions, we determine the limits of a Gross-Pitaevskii- or Bogoliubov-type description and the regime where repulsive one-dimensional Bose gases exhibit fermionic behavior.
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.
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Recent experiments have demonstrated single-site resolved observation of cold atoms in optical lattices. Thus, in the future it may be possible to take repeated snapshots of an interacting quantum many-body system during the course of its evolution. Here we address the impact of the resulting quantum (anti-)Zeno physics on the many-body dynamics. We use the time-dependent density-matrix renormalization group to obtain the time evolution of the full wave function, which is then periodically projected in order to simulate realizations of stroboscopic measurements. For the example of a one-dimensional lattice of spinless fermions with nearest-neighbor interactions, we find regimes for which many-particle configurations are stabilized or destabilized, depending on the interaction strength and the time between observations.
Recent experimental realizations of artificial gauge fields for cold atoms are promising for generating steady states carrying a mass current in strongly correlated systems, such as the Bose-Hubbard model. Moreover, a homogeneous condensate confined by hard-wall potentials from laser sheets has been demonstrated, which provides opportunities for probing the intrinsic transport properties of isolated quantum systems. Using the time-dependent density matrix renormalization group, we analyze the effect of the lattice and interaction strength on the current generated by a quench in the artificial vector potential when the density varies from low values (continuum limit) up to integer filling in the Mott-insulator regime. There is no observable mass current deep in the Mott-insulator state as one may expect. Other observable quantities used to characterize the quasisteady state in the bulk of the system are the Drude weight and entanglement entropy production rate. The latter in particular provides a striking signature of the superfluid--Mott-insulator transition. Furthermore, an interesting property of the superfluid state is the formation of shock and rarefaction waves at the boundaries due to the hard-wall confining potentials. We provide results for the height and the speed of the shock front that propagates from the boundary toward the center of the lattice. Our results should be verifiable with current experimental capabilities.