Dynamics of a Mobile Impurity in a One-Dimensional Bose Liquid

Mathematical results on some models describing the motion of a tracer particle through a Bose-Einstein condensate are described. In the limit of a very dense, very weakly interacting Bose gas and for a very large particle mass, the dynamics of the coupled system is determined by classical non-linear Hamiltonian equations of motion. The particle's motion exhibits deceleration corresponding to friction (with memory) caused by the emission of Cerenkov radiation of gapless modes ...

We study controllable friction in a system consisting of a dark soliton in a one-dimensional Bose-Einstein condensate coupled to a non-interacting Fermi gas. The fermions act as impurity atoms, not part of the original condensate, that scatter off of the soliton. We study semi-classical dynamics of the dark soliton, a particle-like object with negative mass, and calculate its friction coefficient. Surprisingly, it depends periodically on the ratio of interspecies (impurity-co...

We numerically study the relaxation dynamics of a single, heavy impurity atom interacting with a finite one- or two-dimensional, ultracold Bose-gas. While there is a clear separation of time scales between processes resulting from single- and two-phonon scattering in three spatial dimensions, the thermalization in lower dimensions is dominated by two-phonon processes. This is due to infrared divergencies in the corresponding scattering rates in the thermodynamic limit, which ...

We estimate the changes in the condensate ground state energy induced by one or more "sizable" impurities. By "sizable", we mean an impurity whose size is within a few orders of magnitude of the trap size and not necessarily atomic in scale. A sizable impurity will "drill" a hole in the condensate wave function and alter the condensate energy. The question is whether this microscopic change can be detected macroscopically because of the Bose-Einstein condensation effect. We d...

We experimentally investigate the quantum motion of an impurity atom that is immersed in a strongly interacting one-dimensional Bose liquid and is subject to an external force. We find that the momentum distribution of the impurity exhibits characteristic Bragg reflections at the edge of an emergent Brillouin zone. While Bragg reflections are typically associated with lattice structures, in our strongly correlated quantum liquid they result from the interplay of short-range c...

Dissipative forces are ubiquitous and thus constitute an essential part of realistic physical theories. However, quantization of dissipation has remained an open challenge for nearly a century. We construct a quantum counterpart of classical friction, a velocity-dependent force acting against the direction of motion. In particular, a translationary invariant Lindblad equation is derived satisfying the appropriate dynamical relations for the coordinate and momentum (i.e., the ...

The existence of frictionless flow below a critical velocity for obstacles moving in a superfluid is well established in the context of the mean-field Gross-Pitaevskii theory. We calculate the next order correction due to quantum and thermal fluctuations and find a non-zero force acting on a delta-function impurity moving through a quasi-one-dimensional Bose-Einstein condensate at all subcritical velocities and at all temperatures. The force occurs due to an imbalance in the ...

We study the ground state of a one-dimensional (1D) trapped Bose gas with two mobile impurity particles. To investigate this set-up, we develop a variational procedure in which the coordinates of the impurity particles are slow-like variables. We validate our method using the exact results obtained for small systems. Then, we discuss energies and pair densities for systems that contain of the order of one hundred atoms. We show that bosonic non-interacting impurities cluster....

In this paper, we consider the quantum version of the hamiltonian model describing friction introduced in [BDB]. This model consists of a particle which interacts with a bosonic reservoir representing a homogeneous medium through which the particle moves. We show that if the particle is confined, then the Hamiltonian admits a ground state if and only if a suitable infrared condition is satisfied. The latter is violated in the case of linear friction, but satisfied when the fr...

We unravel the nonequilibrium dynamics of two fermionic impurities immersed in a one-dimensional bosonic gas following an interspecies interaction quench from weak to strong repulsions. Monitoring the temporal evolution of the single-particle density of each species we reveal the existence of four distinct dynamical regimes. For weak interspecies repulsions both species either perform a breathing motion or the impurity density splits into two parts which interact and disperse...