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arXiv:1907.06808 · Physical Review A

Generalized Bloch oscillations of ultracold lattice atoms subject to higher-order gradients

Qian-Ru Zhu, Shou-Long Chen, Shao-Jun Li, Xue-Ting Fang, Lushuai Cao, Zhong-Kun Hu

Published Nov 5, 2019• 3 citations

Abstract

The standard Bloch oscillation normally refers to the oscillatory tunneling dynamics of quantum particles in a periodic lattice plus a linear gradient. In this paper we theoretically investigate the generalized form of the Bloch oscillation in the presence of additional higher-order gradients and demonstrate that the higher-order gradients can significantly modify the tunneling dynamics, particularly in the spectrum of the density oscillation. The spectrum of the standard Bloch oscillation is composed of a single prime frequency and its higher harmonics, while the higher-order gradients in the external potential give rise to fine structures in the spectrum around each of these Bloch frequencies, which are composed of series of frequency peaks. Our investigation leads to a twofold consequence to the applications of Bloch oscillations for measuring external forces. For one thing, under a limited resolution of the measured spectrum, the fine structures would manifest as a blur to the spectrum and lead to intrinsic errors to the measurement. For another, given that the fine structures could be experimentally resolved, they can supply more information on the external force than the strength of the linear gradient, and be used to measure more complicated forces.

DOI: 10.1103/physreva.100.053603

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g

.

Bloch oscillations of quantum particles manifest themselves as periodic spreading and relocalization of the associated wave functions when traversing lattice potentials subject to external gradient forces. Albeit this phenomenon is deeply rooted into the very foundations of quantum mechanics, all experimental observations so far have only contemplated dynamics of one and two particles initially prepared in separable local states. Evidently, a more general description of genuinely quantum Bloch oscillations will be achieved on excitation of a Bloch oscillator by nonlocal states. Here we report the observation of Bloch oscillations of two-particle N00N states, and discuss the nonlocality on the ground of Bell-like inequalities. The time evolution of two-photon N00N states in Bloch oscillators, whether symmetric, antisymmetric or partially symmetric, reveals transitions from particle antibunching to bunching. Consequently, the initial states can be tailored to produce spatial correlations akin to those of bosons, fermions and anyons, presenting potential applications in photonic quantum simulation.