The interplay of strong quantum correlations and far-from-equilibrium conditions can give rise to striking dynamical phenomena. We experimentally investigated the quantum motion of an impurity atom immersed in a strongly interacting one-dimensional Bose liquid and subject to an external force. We found that the momentum distribution of the impurity exhibits characteristic Bragg reflections at the edge of an emergent Brillouin zone. Although Bragg reflections are typically associated with lattice structures, in our strongly correlated quantum liquid they result from the interplay of short-range crystalline order and kinematic constraints on the many-body scattering processes in the one-dimensional system. As a consequence, the impurity exhibits periodic dynamics, reminiscent of Bloch oscillations, although the quantum liquid is translationally invariant. Our observations are supported by large-scale numerical simulations.
The interplay of strong quantum correlations and far-from-equilibrium conditions can give rise to striking dynamical phenomena. We experimentally investigated the quantum motion of an impurity atom immersed in a strongly interacting one-dimensional Bose liquid and subject to an external force. We found that the momentum distribution of the impurity exhibits characteristic Bragg reflections at the edge of an emergent Brillouin zone. Although Bragg reflections are typically associated with lattice structures, in our strongly correlated quantum liquid they result from the interplay of short-range crystalline order and kinematic constraints on the many-body scattering processes in the one-dimensional system. As a consequence, the impurity exhibits periodic dynamics, reminiscent of Bloch oscillations, although the quantum liquid is translationally invariant. Our observations are supported by large-scale numerical simulations.
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 study the out-of-equilibrium dynamics of an impurity driven by a constant external force through a system of homogeneous weakly-interacting bosons in one spatial dimension. The impurity-boson interaction is assumed to be attractive. We show that the impurity exhibits drifted Bloch oscillations in a wide range of forces in the absence of a lattice. We characterize the dynamical response of the host bosons and explain the mechanism underlying the Bloch oscillations. We analyse the behavior of the drift velocity, the Bloch amplitude and the time period of oscillations in a wide range of forces and other system parameters. In contrast to the case of repulsive impurity-boson interaction, the drift velocity exhibits a sub-linear dependence on a weak applied force, Vd∼Fα with a positive exponent α smaller than unity. The drift velocity monotonically increases with force, though the scaling behavior varies considerably across different regimes of F. Moreover, the amplitude of the velocity oscillations displays rich behavior: it first undergoes a decay with force, reaches a minimum, and then presents a revival, increasing with force.
Objects subjected to a constant force generally increase their velocity over time. This expectation fails whenever their energy is a smooth and periodic function of momentum, resulting in periodic Bloch oscillations instead. Periodic dispersions, typical of lattice systems, can also emerge in continuum media through strong interactions. Here, we study the phenomenon of such Bloch oscillations in the absence of a lattice in a paradigmatic model of integrable quantum gases: the two-component Yang-Gaudin model. We derive a generalized-hydrodynamic theory of Bloch oscillations for a finite density of impurities embedded in a homogeneous interacting background, which we show to persist superimposed to a drift due to the acceleration of the center of mass. Moreover, we show the single-impurity oscillation period is renormalized at finite impurity density when two-magnon bound states are populated. Our results are relevant for ultracold atom experiments, where impurities can be created at controllable densities.
Motivated by a recent experiment by Meinert et al. [arXiv:1608.08200], we study the dynamics of an impurity moving in the background of a harmonically trapped one-dimensional Bose gas in the hard-core limit. We show that due to the hidden ``lattice'' structure of background bosons, the impurity effectively feels a quasiperiodic potential via impurity-boson interactions that can drive the Bloch oscillation under an external force, even in the absence of real lattice potentials. Meanwhile, the inhomogeneous density of trapped bosons imposes an additional harmonic potential to the impurity, resulting in a similar oscillation dynamics but with a different period and amplitude. We show that the sign and strength of the impurity-boson coupling can significantly affect the above two potentials in determining the impurity dynamics.
We study the dynamics of an impurity of finite mass injected into a one-dimensional quantum liquid at zero temperature, either at finite velocity or at zero velocity with a force driving the impurity. We obtain accurate results using numerical simulations based on matrix product states, and find that in both cases, the impurity undergoes oscillations, however the physical mechanism is different: the driven impurity undergoes Bloch oscillations by following the ground state branch while continuously emitting phonons, whereas the undriven impurity undergoes coherent quantum oscillations at an emergent energy scale, called quantum flutter in previous work, whose amplitude grows with increasing initial velocity. We find these results to be independent of whether the system is integrable or not, and robust to changes in the microscopics of the model, suggesting that they are universal.
The early quantum theory of electrical conductivity in crystal lattices by Bloch and Zener [1,2] led to the striking prediction that a homogeneous static electric field induces an oscillatory rather than uniform motion of the electrons. These so-called Bloch oscillations have never been observed in natural crystals because the scattering time of the electrons by the lattice defects is much shorter than the Bloch period. In semiconductor superlattices the larger spatial period leads to a much shorter Bloch period (,600 fs) and Bloch oscillations have recently been observed through the emission of THz radiation by the electrons [3]. Here we present Bloch oscillations of atoms in the fundamental energy band of a periodic optical potential. We directly measure the atomic momentum distribution evolving in time under the influence of a constant inertial force for various potential depths. We experimentally observe oscillation periods in the millisecond range as well as positive and negative effective masses. Bloch oscillations are a pure quantum effect which can be explained in a simple one-dimensional model. The periodicity of the lattice (period d) leads to a band structure (Fig. 1) of the energy spectrum of the particle and the corresponding eigenenergies Ensqd and eigenstates jn, ql (Bloch states) are labeled by the discrete band index n and the continuous quasimomentum q; Ensqd and jn, ql are periodic functions of q with period 2pyd and q is conventionally restricted to the first Brillouin zone g2pyd, pydg [4]. Under the influence of a constant external force F, weak enough not to induce interband transitions, a given Bloch state jn, qs0dl evolves (up to a phase factor) into the state jn, qstdl according to qstd qs0d 1 Ftyh . (1) This evolution is periodic with a period tB hyjFjd corresponding to the time required for the quasimomentum to scan a full Brillouin zone. The mean velocity in jn, qstdl