We study the motion of a heavy impurity in a one-dimensional Bose gas. The impurity experiences the friction force due to scattering off thermally excited quasiparticles. We present detailed analysis of an arbitrarily strong impurity-boson coupling in a wide range of temperatures within a microscopic theory. Focusing mostly on weakly interacting bosons, we derive an analytical result for the friction force and uncover new regimes of the impurity dynamics. Particularly interesting is the low-temperature T^{2} dependence of the friction force obtained for a strongly coupled impurity, which should be contrasted with the expected T^{4} scaling. This new regime applies to systems of bosons with an arbitrary repulsion strength. We finally study the evolution of the impurity with a given initial momentum. We evaluate analytically its nonstationary momentum distribution function. The impurity relaxation towards the equilibrium is a realization of the Ornstein-Uhlenbeck process in momentum space.
We study the motion of a heavy impurity in a one-dimensional Bose gas. The impurity experiences the friction force due to scattering off thermally excited quasiparticles. We present detailed analysis of an arbitrarily strong impurity-boson coupling in a wide range of temperatures within a microscopic theory. Focusing mostly on weakly interacting bosons, we derive an analytical result for the friction force and uncover new regimes of the impurity dynamics. Particularly interesting is the low-temperature T^{2} dependence of the friction force obtained for a strongly coupled impurity, which should be contrasted with the expected T^{4} scaling. This new regime applies to systems of bosons with an arbitrary repulsion strength. We finally study the evolution of the impurity with a given initial momentum. We evaluate analytically its nonstationary momentum distribution function. The impurity relaxation towards the equilibrium is a realization of the Ornstein-Uhlenbeck process in momentum space.
We study the motion of a slow quantum impurity in one-dimensional environments focusing on systems of strongly interacting bosons and weakly interacting fermions. While at zero temperature the impurity motion is frictionless, at low temperatures finite friction appears. The dominant process is the scattering of the impurity off two fermionic quasiparticles. We evaluate the friction force and show that, at low temperatures, it scales either as the fourth or the sixth power of temperature, depending on the system parameters. This is a result of the scattering of the impurity off two fermionic quasiparticles that are situated around different Fermi points. It is the dominant process at low temperatures. We also evaluate the contribution to the friction force originating from the scattering of the impurity off two fermionic quasiparticles that are situated around different Fermi points. It behaves as the tenth power of temperature.
We develop a microscopic theory of a quantum impurity propagating in a one-dimensional Bose liquid. As a result of scattering off thermally excited quasiparticles, the impurity experiences the friction. We find that, at low temperatures, the resulting force scales either as the fourth or the eighth power of temperature, depending on the system parameters. For temperatures higher than the chemical potential of the Bose liquid, the friction force is a linear function of temperature. Our approach enables us to find the friction force in the crossover region between the two limiting cases. In the integrable case, corresponding to the Yang-Gaudin model, the impurity becomes transparent for quasiparticles and thus the friction force is absent. Our results could be further generalized to study other kinetic phenomena.
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.
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.
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.
Bose polarons, quasiparticles composed of mobile impurities surrounded by cold Bose gas, can experience strong interactions mediated by the many-body environment and form bipolaron bound states. Here we present a detailed study of heavy polarons in a one-dimensional Bose gas by formulating a nonperturbative theory and complementing it with exact numerical simulations. We develop an analytic approach for weak boson-boson interactions and arbitrarily strong impurity-boson couplings. Our approach is based on a mean-field theory that accounts for deformations of the superfluid by the impurities and in this way minimizes quantum fluctuations. The mean-field equations are solved exactly in the Born-Oppenheimer approximation, leading to an analytic expression for the interaction potential of heavy polarons, which is found to be in excellent agreement with quantum Monte Carlo (QMC) results. In the strong coupling limit, the potential substantially deviates from the exponential form valid for weak coupling and has a linear shape at short distances. Taking into account the leading-order Born-Huang corrections, we calculate bipolaron binding energies for impurity-boson mass ratios as low as 3 and find excellent agreement with QMC results.