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arXiv:quant-ph/0202113 · Physical Review A

Simulation of chaos-assisted tunneling in a semiclassical regime on existing quantum computers

Alexei D. Chepelianskii, Dima L. Shepelyansky

Published Nov 13, 2002• 8 citations
arXivHTMLPDF

Abstract

We present a quantum algorithm that allows one to simulate chaos-assisted tunneling in deep semiclassical regime on existing quantum computers. This opens additional possibilities for investigation of macroscopic quantum tunneling and realization of semiclassical Schr\"odinger cat oscillations [E. Schr\"odinger, Naturwissenschaften 32, 807 (1935)]. Our numerical studies determine the decoherence rate induced by noisy gates for these oscillations and propose a suitable parameter regime for their experimental implementation.

DOI
10.1103/physreva.66.054301

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We present a quantum algorithm that allows one to simulate chaos-assisted tunneling in deep semiclassical regime on existing quantum computers. This opens additional possibilities for investigation of macroscopic quantum tunneling and realization of semiclassical Schr"odinger cat oscillations [E. Schr"odinger, Naturwissenschaften 32, 807 (1935)]. Our numerical studies determine the decoherence rate induced by noisy gates for these oscillations and propose a suitable parameter regime for their experimental implementation.
We present an extension of the chaos-assisted tunneling mechanism to spatially periodic lattice systems. We demonstrate that driving such lattice systems in an intermediate regime of modulation maps them onto tight-binding Hamiltonians with chaos-induced long-range hoppings t_{n}∝1/n between sites at a distance n. We provide a numerical demonstration of the robustness of the results and derive an analytical prediction for the hopping term law. Such systems can thus be used to enlarge the scope of quantum simulations to experimentally realize long-range models of condensed matter.
We study the interplay of chaos and tunneling between two weakly coupled Bose-Josephson junctions. The classical phase space of the composite system has a mixed structure including quasi-integrable self-trapping islands for particles and excitations, separated by a chaotic sea. We show that the many-body dynamical tunneling gap between macroscopic Schrödinger cat states supported by these islands is chaos-enhanced. The many-body tunneling rate fluctuates over several orders of magnitude with small variations of the system parameters or the particle number.
We study the time evolution of mean values of quantum operators in a regime plagued by two difficulties: the smallness of ℏ and the presence of strong and ubiquitous classical chaos. While numerics become too computationally expensive for purely quantum calculations as ℏ→0, methods that take advantage of the smallness of ℏ-that is, semiclassical methods-suffer from both conceptual and practical difficulties in the deep chaotic regime. We implement an approach which addresses these conceptual problems, leading to a deeper understanding of the origin of the interference contributions to the operator's mean value. We show that in the deep chaotic regime our approach is capable of unprecedented accuracy, while a standard semiclassical method (the Herman-Kluk propagator) produces only numerical noise. Our work paves the way to the development and employment of more efficient and accurate methods for quantum simulations of systems with strongly chaotic classical limits.
The field of quantum simulation, which aims at using a tunable quantum system to simulate another, has been developing fast in the past years as an alternative to the all-purpose quantum computer. So far, most efforts in this domain have been directed to either fully regular or fully chaotic systems. Here, we focus on the intermediate regime, where regular orbits are surrounded by a large sea of chaotic trajectories. We observe a quantum chaos transport mechanism, called chaos-assisted tunneling, that translates in sharp resonances of the tunneling rate and provides previously unexplored possibilities for quantum simulation. More specifically, using Bose-Einstein condensates in a driven optical lattice, we experimentally demonstrate and characterize these resonances. Our work paves the way for quantum simulations with long-range transport and quantum control through complexity.
The study of quantum tunneling dates back to the early days of quantum mechanics, and has been a major topic of investigation in both theory and experiment. In recent years, there has been significant effort to understand tunneling phenomena for systems that exhibit chaos in their classical counterpart [13,15,18,29,42]. In particular, tunneling was predicted for mixed systems where chaotic and stable regions are intermingled [14]. The tunneling in this case is between two stable regions (referred to as nonlinear resonances, or islands of stability) in the classical phase space. The classical transport between these islands is forbidden by “dynamical barriers” in phase space. In contrast, quantum tunneling can couple the two islands so that a wave packet oscillates coherently between the two symmetry-related regions. This phenomenon is called dynamical tunneling because it occurs in phase space, without a fixed potential barrier. In the case of a mixed phase space, the presence of the chaotic region can enhance the rate of dynamical tunneling, a phenomenon known as chaos-assisted tunneling [53]. In this chapter, we review our experimental observation of chaosassisted tunneling with ultracold cesium atoms [48-51]. We first give a brief overview of some basic concepts and of earlier work in order to provide a context for our results.