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arXiv:1003.5479 · Physical Review A

Interaction-induced fractional Bloch and tunneling oscillations

Рамаз Хомерики, Dmitry O. Krimer, Masudul Haque, Sergej Flach A

Published Jun 28, 2010• 53 citations
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Abstract

We study the dynamics of few interacting bosons in a one-dimensional lattice with dc bias. In the absence of interactions the system displays single-particle Bloch oscillations. For strong interaction the Bloch oscillation regime re-emerges with fractional Bloch periods which are inversely proportional to the number of bosons clustered into a bound state. The interaction strength affects the oscillation amplitude. Excellent agreement is found between numerical data and a composite particle dynamics approach. For specific values of the interaction strength, a particle will tunnel from the interacting cloud to a well-defined distant lattice location.

DOI
10.1103/physreva.81.065601

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We study the dynamics of few interacting bosons in a one-dimensional lattice with dc bias. In the absence of interactions the system displays single-particle Bloch oscillations. For strong interaction the Bloch oscillation regime re-emerges with fractional Bloch periods which are inversely proportional to the number of bosons clustered into a bound state. The interaction strength affects the oscillation amplitude. Excellent agreement is found between numerical data and a composite particle dynamics approach. For specific values of the interaction strength, a particle will tunnel from the interacting cloud to a well-defined distant lattice location.
We study the dynamics of interacting superfluid bosons in a one-dimensional vertical optical lattice after a sudden increase of the lattice potential depth. We show that this system can be exploited to investigate the effects of strong interactions on Bloch oscillations. We perform theoretical modeling of this system, identify experimental challenges, and explore a regime of Bloch oscillations characterized by interaction-induced matter-wave collapse and revivals which modify the Bloch oscillations dynamics. In addition, we study three dephasing mechanisms: finite value of tunneling, effective three-body interactions, and a background harmonic potential. We also find that the center-of-mass motion in the presence of finite tunneling goes through collapse and revivals, giving an example of quantum transport where interaction-induced revivals are important. We quantify the effects of residual harmonic trapping on the momentum distribution dynamics and show the occurrence of an interaction-modified temporal Talbot effect. Finally, we analyze the prospects and challenges of exploiting Bloch oscillations of cold atoms in the strongly interacting regime for precision measurement of the gravitational acceleration ggg.
We investigate the dynamics of two bosons in a tilted one-dimensional optical lattice with both standard and density-assisted tunnelling. The relative sign of the two tunnelling processes strongly affects the Bloch dynamics, leading to distinct reinforcing and competing regimes. We examine how the tunnelling processes generate correlations and find that, in the absence of onsite interactions, the early-time entanglement growth follows the same scaling with the density-assisted tunnelling amplitude. Finite onsite interaction changes this picture by breaking the symmetry between the reinforcing and competing regimes and enhancing the correlation differently in two regimes. This shows how the interplay between the two tunnelling mechanisms can change dyanmics and entanglement in a controlled few-body setting. Particularly, at equal tunnelling amplitudes, the doublon and singlon sectors decouple completely for arbitrary onsite interaction, lattice tilting, and initial state.
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.
Quantum tunneling is one of the most fundamental processes in nature. Single particle hopping of ultracold atoms in optical lattices changes its character dramatically when the ensemble is prepared in strongly correlated quantum phases due to atom-atom interactions. Correlated hopping in a Mott-insulating chain of bosons that is tilted to the Mott gap has recently been employed to study long-range order in the 1D transvers Ising model [1,2]. We study correlated tunneling dynamics for an ensemble of tilted 1D Mott chains after a sudden quench to the vicinity of the Ising paramagnetic to antiferromagnetic phase transition point [3]. The quench results in coherent oscillations for the orientation of effective Ising spins, detected via oscillations in the number of doubly occupied lattice sites. We characterize the quench by varying the system parameters. We report significant modification of the tunneling rate induced by interactions and show clear evidence for collective effects in the oscillatory response. We observe higher-order many-body tunneling processes over up to five lattice sites when the tilt per site is tuned to integer fractions of the Mott gap. Secondand third-order tunneling shows up in the transient response after the quench, from which we extract the characteristic scaling in accordance with perturbation theory and numerical simulations. In a second set of experiments we study the response of an ensemble of 1D superfluids in the Bose-Hubbard regime when subject to a tilt [4]. For large values of the tilt, we observe interaction-induced coherent decay and matter-wave quantum phase revivals of the Bloch oscillating ensemble. We analyze the revival period dependence on interactions by means of a Feshbach resonance. When reducing the value of the tilt, we observe the disappearance of the quasi-periodic phase revival signature towards an irreversible decay of Bloch oscillations, indicating the transition from regular to quantum chaotic dynamics.
It is well known that an electron in a single-band tight-binding lattice coherently driven by an external dc electric field undergoes Bloch oscillations. In the framework of the extended Hubbard model, here it is shown theoretically that two strongly interacting electrons with on-site and nearest-neighbor site repulsion undergo a sequence of Bloch oscillations and Zener tunneling, the so-called Bloch-Zener oscillations (BZOs), among different narrow bands formed by bound particle states. Such a kind of BZOs arise because of nearest-neighbor site particle interaction and are thus rather distinct than BZOs observed for a single electron in biperiodic lattices supporting two single-particle minibands.
The coherent dynamics of two strongly interacting electrons hopping on a one-dimensional lattice and driven by combined dc-ac fields is theoretically investigated in the framework of the Hubbard model. It is shown that, under appropriate forcing conditions in the strong-field regime, super-Bloch oscillations (SBOs) can be observed for the bound particle state, but not for unpaired electrons that remain frozen in the lattice. As compared to single-particle SBOs, SBOs of correlated particles are generally quasiperiodic.