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arXiv:1701.07581 · Physical Review A

Interaction-induced Bloch oscillation in a harmonically trapped and fermionized quantum gas in one dimension

Lijun Yang, Lihong Zhou, Wei Yi, Xiaoling Cui

Published May 17, 2017• 3 citations
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Abstract

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.

DOI
10.1103/physreva.95.053617

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\n Motivated by a recent experiment (Catani J.\net al., Phys. Rev. A, 85 (2012) 023623) we study breathing oscillations in the width of a harmonically trapped impurity interacting with a separately trapped Bose gas. We provide an intuitive physical picture of such dynamics at zero temperature, using a time-dependent variational approach. The amplitudes of breathing oscillations are suppressed by self-trapping, due to interactions with the Bose gas. Further, exciting phonons in the Bose gas leads to damped oscillations and non-Markovian dynamics of the width of the impurity, the degree of which can be engineered through controllable parameters. Our results, supported by simulations, reproduce the main features of the dynamics observed by Catani et al. despite the temperature of that experiment. Moreover, we predict novel effects at lower temperatures due to self-trapping and the inhomogeneity of the trapped Bose gas.\n

•Apr 26, 2012•15 citations
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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∼FαV_d\sim {F}^αVd​∼Fα with a positive exponent ααα smaller than unity. The drift velocity monotonically increases with force, though the scaling behavior varies considerably across different regimes of FFF. 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.
We investigate the tunneling dynamics of an ultracold bosonic impurity species which interacts repulsively with a second, larger Bose gas. Both species are held in a finite-sized quasi-one-dimensional box potential. In addition, the impurity bosons experience a periodic potential generated by an optical lattice. We initially prepare our binary mixture in its ground state, such that the impurities and Bose gas are phase separated and the impurities localize pairwise in adjacent sites of the periodic potential, by tuning the interaction strengths and the lattice depth correspondingly. The dynamics is initiated by suddenly lowering the repulsive interspecies interaction strength, thereby entering a different regime in the crossover diagram. For specific postquench interspecies interaction strengths we find that a single impurity tunnels first to the neighboring empty site and depending on the quench strength can further tunnel to the next-neighboring site. Interestingly, this effect is highly sensitive to the presence of the Bose gas and does not occur when the Bose gas does not interact with the impurity species throughout the dynamics. Moreover, we find that the tunneling process is accompanied by strong entanglement between the Bose gas and the impurity species as well as correlations among the impurities.
We investigate the behavior of a harmonically trapped system consisting of an impurity in a dilute ideal Bose gas after the boson-impurity interaction is suddenly switched on. As a theoretical framework, we use a field-theory approach in the space-time domain within the TTT-matrix approximation. We establish the form of the corresponding TTT matrix and address the dynamical properties of the system. As a numerical application, we consider a simple system of a weakly interacting impurity in one dimension where the interaction leads to oscillations of the impurity density. Moreover, we show that the amplitude of the oscillations can be driven by periodically switching the interaction on and off.
Motivated by a recent experiment (Catani J. et al. , Phys. Rev. A , 85 (2012) 023623 ) we study breathing oscillations in the width of a harmonically trapped impurity interacting with a separately trapped Bose gas. We provide an intuitive physical picture of such dynamics at zero temperature, using a time-dependent variational approach. The amplitudes of breathing oscillations are suppressed by self-trapping, due to interactions with the Bose gas. Further, exciting phonons in the Bose gas leads to damped oscillations and non-Markovian dynamics of the width of the impurity, the degree of which can be engineered through controllable parameters. Our results, supported by simulations, reproduce the main features of the dynamics observed by Catani et al. despite the temperature of that experiment. Moreover, we predict novel effects at lower temperatures due to self-trapping and the inhomogeneity of the trapped Bose gas.
\n Motivated by a recent experiment (Catani J.\net al., Phys. Rev. A, 85 (2012) 023623) we study breathing oscillations in the width of a harmonically trapped impurity interacting with a separately trapped Bose gas. We provide an intuitive physical picture of such dynamics at zero temperature, using a time-dependent variational approach. The amplitudes of breathing oscillations are suppressed by self-trapping, due to interactions with the Bose gas. Further, exciting phonons in the Bose gas leads to damped oscillations and non-Markovian dynamics of the width of the impurity, the degree of which can be engineered through controllable parameters. Our results, supported by simulations, reproduce the main features of the dynamics observed by Catani et al. despite the temperature of that experiment. Moreover, we predict novel effects at lower temperatures due to self-trapping and the inhomogeneity of the trapped Bose gas.\n