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arXiv:0903.4823 · Physical Review Letters

Quantum Transport through a Tonks-Girardeau Gas

Stefan Palzer, Christoph Zipkes, Carlo Sias, Michael Köhl

Published Oct 8, 2009• 227 citations
arXivHTMLPDF

Abstract

We investigate the propagation of spin impurity atoms through a strongly interacting one-dimensional Bose gas. The initially well localized impurities are accelerated by a constant force, very much analogous to electrons subject to a bias voltage, and propagate as a one-dimensional impurity spin wave packet. We follow the motion of the impurities in situ and characterize the interaction induced dynamics. We observe a very complex nonequilibrium dynamics, including the emergence of large density fluctuations in the remaining Bose gas, and multiple scattering events leading to dissipation of the impurity's motion.

DOI
10.1103/physrevlett.103.150601

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We investigate the propagation of spin impurity atoms through a strongly interacting one-dimensional Bose gas. The initially well localized impurities are accelerated by a constant force, very much analogous to electrons subject to a bias voltage, and propagate as a one-dimensional impurity spin wave packet. We follow the motion of the impurities in situ and characterize the interaction induced dynamics. We observe a very complex nonequilibrium dynamics, including the emergence of large density fluctuations in the remaining Bose gas, and multiple scattering events leading to dissipation of the impurity's motion.
Using near-exact numerical simulations, we study the propagation of an impurity through a one-dimensional Bose lattice gas for varying bosonic interaction strengths and filling factors at zero temperature. The impurity is coupled to the Bose gas and confined to a separate tilted lattice. The precise nature of the transport of the impurity is specific to the excitation spectrum of the Bose gas, which allows one to measure properties of the Bose gas nondestructively, in principle, by observing the impurity; here we focus on the spatial and momentum distributions of the impurity as well as its reduced density matrix. For instance, we show it is possible to determine whether the Bose gas is commensurately filled as well as the bandwidth and gap in its excitation spectrum. Moreover, we show that the impurity acts as a witness to the crossover of its environment from the weakly to the strongly interacting regime, i.e., from a superfluid to a Mott insulator or Tonks-Girardeau lattice gas, and the effects on the impurity in both of these strongly interacting regimes are clearly distinguishable. Finally, we find that the spatial coherence of the impurity is related to its propagation through the Bose gas.
The nonequilibrium dynamics of spin impurity atoms in a strongly interacting one-dimensional (1D) Bose gas under the gravity field is studied. We show that due to the nonequilibrium preparation of the initial state as well as the interaction between the impurity atoms and other bosons, a counterintuitive phenomenon may emerge: the impurity atoms could propagate upward automatically in the gravity field. The effects of the strength of interaction, the gradient of the gravity field, as well as the different configurations of the initial state are investigated by studying the time-dependent evolution of the 1D strongly interacting bosonic system using time-evolving block decimation (TEBD) method. A profound connection between this counterintuitive phenomenon and the repulsive bound pair is also revealed.
We study the motion of an impurity under the action of a constant force through a one-dimensional system of weakly-interacting bosons. The interplay of the impurity-boson interaction, the boson-boson interaction, and the driving force gives rise to a rich dynamics. We focus on the influence of a finite external force. Under these far-from-equilibrium conditions, we show that in a wide range of forces, one part of the momentum transferred to the system is periodically channeled into the Bose gas through the emission of dispersive density shock waves, solitons, density waves and the creation of additional phase gradients. As a result, the impurity velocity does not increase indefinitely, but periodically oscillates in time around the drift velocity. We uncover and characterize different dynamical regimes in a wide range of the impurity-boson coupling, the impurity mass and the external force. At a sufficiently large force, the Bloch oscillations cease and the impurity exhibits an unlimited acceleration.
We investigate the time evolution of the momentum of an impurity atom injected into a degenerate Tonks-Girardeau gas. We establish that given an initial momentum p0{p}_{0}p0​ the impurity relaxes to a steady state with a nonvanishing momentum ${p}_{\ensuremath{\infty}}.$ The nature of the steady state is found to depend drastically on whether the masses of the impurity and the host are equal. This is due to multiple coherent scattering processes leading to a resonant interaction between the impurity and the host in the case of equal masses. The dependence of ${p}_{\ensuremath{\infty}}$ on p0{p}_{0}p0​ remains nontrivial even in the limit of vanishing interaction between the impurity and host particles. In this limit ${p}_{\ensuremath{\infty}}({p}_{0})$ is found explicitly.
The frictionless motion of an object through a fluid medium is commonly viewed as a hallmark of superfluidity. According to Landau, kinematic constraints prohibit superfluid behavior in one-dimensional (1D) bosonic systems. Here, using ultracold atoms, we show how a microscopic impurity can propagate through a strongly interacting 1D Bose gas without any friction, at odds with conventional expectations. We inject the impurity with initial velocities ranging from the subsonic to supersonic regime, and subsequently track its dynamics. For supersonic initial velocities, we observe the formation of a shock wave and a remarkably fast relaxation to a stationary regime, on a time scale that increases with decreasing impurity velocity. After reaching the stationary state, the impurity continues its motion through the system with a finite velocity. Our findings demonstrate how quantum effects can conspire to eliminate dissipation of a microscopic object immersed in a quantum fluid, thereby bringing novel insights into the propagation of matter and information in the quantum realm.
The nonequilibrium dynamics of an impurity immersed with a finite velocity into a one-dimensional system of weakly interacting bosons is studied within the framework of the time-dependent Gross-Pitaevskii equation. We uncover and characterize different regimes of relaxation dynamics. We find that the final impurity velocity remains constant in a large interval of sufficiently big and realistic initial velocities. The underlying physical mechanism is the emission of the dispersive density shock waves that carry away the excess of the initial impurity momentum, while locally the system remains in the same stationary state. In contrast, a heavy impurity with the same coupling constant relaxes differently and the regime of constant final velocity disappears. Furthermore, a fast heavy impurity exhibits damped velocity oscillations in time before reaching a stationary state. This process is accompanied by the oscillations of the local depletion of the boson density around the impurity, until their positions coincide and they continue the motion together. Decreasing the impurity-boson coupling or increasing the strength of repulsion between bosons, the oscillations get amplified. In the case of a heavy impurity with the mass bigger than the critical one, the ground-state energy as a function of momentum exhibits cusps and metastable branches. We show that they manifest themselves by a soliton emission, a considerable slowing down of the relaxation, and a change of the impurity direction of motion with respect to the initial one.