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理论物理通讯：英文版

Quantum Signatures of Chaos in Adiabatic Interaction Between a Trapped Ion and a Laser Standing Wave

Li, Hui Hui, Hai Hai, Wenhua, Xu, Jun

Published Jan 1, 2008• 0 citations
OpenAlex

Abstract

我们在与承受波浪的强壮的激光交往的一个单个套住的离子的一个古典异种诊所点附近学习量运动。我们构造量系统的一套准确协调状态并且从准确解决方案表明混乱的量签名能被在承受波浪的套住的离子和激光之间的断热的相互作用导致，在位置和动量的量期望值对应于古典主义地混乱的轨道的地方。在阶段空间的混乱区域被说明。及时，进化和指数地增加的海森堡不确定性被发现的精力十字路口和量回声。结果为控制不稳定的常规、混乱的运动建议一个理论计划。

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我们在与承受波浪的强壮的激光交往的一个单个套住的离子的一个古典异种诊所点附近学习量运动。我们构造量系统的一套准确协调状态并且从准确解决方案表明混乱的量签名能被在承受波浪的套住的离子和激光之间的断热的相互作用导致，在位置和动量的量期望值对应于古典主义地混乱的轨道的地方。在阶段空间的混乱区域被说明。及时，进化和指数地增加的海森堡不确定性被发现的精力十字路口和量回声。结果为控制不稳定的常规、混乱的运动建议一个理论计划。
We study quantum motion around a classical heteroclinic point of a single trapped ion interacting with a strong laser standing wave. We construct a set of exact coherent states of the quantum system and from the exact solutions reveal that quantum signatures of chaos can be induced by the adiabatic interaction between the trapped ion and the laser standing wave, where the quantum expectation values of position and momentum correspond to the classically chaotic orbit. The chaotic region on the phase space is illustrated. The energy crossing and quantum resonance in time evolution and the exponentially increased Heisenberg uncertainty are found. The results suggest a theoretical scheme for controlling the unstable regular and chaotic motions.
We show how a nonlinear chaotic system, the parametrically kicked nonlinear oscillator, may be realized in the dynamics of a trapped, laser-cooled ion, interacting with a sequence of standing-wave pulses. Unlike the original optical scheme [G. J. Milburn and C. A. Holmes, Phys. Rev. A 44, 4704 (1991)], the trapped ion enables strongly quantum dynamics with minimal dissipation. This should permit an experimental test of one of the quantum signatures of chaos: irregular collapse and revival dynamics of the average vibrational energy.
We unitarily transform the Hamiltonian of a trapped ion, situated at any position of a standing-wave laser field, to that for the normal Jaynes-Cummings model in the bare ionic basis, and we obtain the general evolution operator of the trapped ion system. We show the existence of super-revivals of the ionic inversion if the trapped ion is not located at a node of the standing wave, and we examine the degree of entanglement between the vibrational phonons and the trapped ion. For some parameter values, we find chaotic behavior.