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arXiv:1809.06889 · Physical Review Letters

Mechanical Resonances of Mobile Impurities in a One-Dimensional Quantum Fluid

Thomas L. Schmidt, Giacomo Dolcetto, Chris Pedder, Karyn Le Hur, Peter P. Orth

Published Aug 13, 2019• 4 citations
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Abstract

We study a one-dimensional interacting quantum liquid hosting a pair of mobile impurities causing backscattering. We determine the effective retarded interaction between the two impurities mediated by the liquid. We show that for strong backscattering this interaction gives rise to resonances and antiresonances in the finite-frequency mobility of the impurity pair. At the antiresonances, the two impurities remain at rest even when driven by a (small) external force. At the resonances, their synchronous motion follows the external drive in phase and reaches maximum amplitude. Using a perturbative renormalization group analysis in quantum tunneling across the impurities, we study the range of validity of our model. We predict that these mechanical antiresonances are observable in experiments on ultracold atom gases confined to one dimension.

DOI
10.1103/physrevlett.123.075302

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We study the dynamics of a mobile impurity in a quantum fluid at zero temperature. Two related settings are considered. In the first setting an impurity is injected in a fluid with some initial velocity v0{\mathbf v}_0v0​, and we are interested in its velocity at infinite time, v∞{\mathbf v}_\inftyv∞​. We derive a rigorous upper bound on ∣v0−v∞∣|{\mathbf v}_0-{\mathbf v}_\infty|∣v0​−v∞​∣ for initial velocities smaller than some critical velocity. In the limit of vanishing impurity-fluid coupling this bound can be regarded as a rigorous proof of the Landau criterion of superfluidity. In the case of a finite coupling the velocity of the impurity can drop, but not to zero; the bound quantifies the maximal possible drop. In the second setting a small constant force acts on the impurity. We identify two possible regimes of the impurity dynamics -- backscattering oscillations of the impurity velocity and saturation of the velocity without oscillations. Which regime is realized depends on the spectrum of the fluid and the mass of the impurity. In particular, backscattering oscillations are possible for sufficiently heavy impurities in fluids with a roton feature of the spectrum. We critically discuss a concept of Bloch oscillations of a mobile impurity in a one-dimensional quantum fluid introduced in [Phys. Rev. Lett. 102, 070402 (2009)] and argue that this type of oscillations is absent in the thermodynamic limit.
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Virtual phonons of a quantum liquid scatter off impurities and mediate a long-range interaction, analogous to the Casimir effect. In one dimension the effect is universal and the induced interaction decays as 1/r3, much slower than the van der Waals interaction ∼1/r6, where r is the impurity separation. The sign of the effect is characterized by the product of impurity-phonon scattering amplitudes, which take a universal form and have been seen to vanish for several integrable impurity models. Thus, if the impurity parameters can be independently tuned to lie on opposite sides of such integrable points, one can observe an attractive interaction turned into a repulsive one.
We study the notion of superfluid critical velocity in one spatial dimension. It is shown that, for heavy impurities with mass M exceeding a critical mass Mc, the dispersion develops periodic metastable branches resulting in dramatic changes of dynamics in the presence of an external driving force. In contrast to smooth Bloch oscillations for M<Mc, a heavy impurity climbs metastable branches until it reaches a branch termination point or undergoes a random tunneling event, both leading to an abrupt change in velocity and an energy loss. This is predicted to lead to a nonanalytic dependence of the impurity drift velocity on small forces.
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.