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arXiv:quant-ph/0206177 · Physical Review A

Dynamics of entanglement between two trapped atoms

Holger Mack, Matthias Freyberger

Published Oct 21, 2002• 29 citations
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Abstract

We investigate the dynamics of entanglement between two continuous variable quantum systems. The model system consists of two atoms in a harmonic trap which are interacting by a simplified s-wave scattering. We show, that the dynamically created entanglement changes in a steplike manner. Moreover, we introduce local operators which allow us to violate a Bell-Clauser-Horne-Shimony-Holt inequality adapted to the continuous variable case. The correlations show nonclassical behavior and almost reach the maximal quantum-mechanical value. This is interesting since the states prepared by this interaction are very different from any Einstein-Podolsky-Rosen--like state.

DOI
10.1103/physreva.66.042113

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We investigate the dynamics of entanglement between two continuous variable quantum systems. The model system consists of two atoms in a harmonic trap which are interacting by a simplified s-wave scattering. We show, that the dynamically created entanglement changes in a steplike manner. Moreover, we introduce local operators which allow us to violate a Bell-Clauser-Horne-Shimony-Holt inequality adapted to the continuous variable case. The correlations show nonclassical behavior and almost reach the maximal quantum-mechanical value. This is interesting since the states prepared by this interaction are very different from any Einstein-Podolsky-Rosen--like state.
We undertake a detailed analysis of the non-local properties of the fundamental problem of two trapped, distinguishable neutral atoms that interact with a short-range potential characterized by an s-wave scattering length. We show that this interaction generates continuous variable (CV) entanglement between the external degrees of freedom of the atoms and consider its behaviour as a function of both, the distance between the traps and the magnitude of the inter-particle scattering length. We first quantify the entanglement in the ground state of the system at zero temperature and then, adopting a phase-space approach, test the violation of the Clauser–Horn–Shimony–Holt inequality at zero and non-zero temperature and under the effects of general dissipative local environments.
We demonstrate an optimal quantum control strategy for the deterministic preparation of entangled harmonic oscillator states in trapped ions. The protocol employs dynamical phase modulation of laser-driven Jaynes-Cummings and anti-Jaynes-Cummings interactions. We prepare two-mode squeezed vacuum states in the motions of a trapped ion and characterize the states with phase-space tomography. We verify continuous-variable entanglement by measuring an Einstein-Podolsky-Rosen entanglement parameter of 0.0132(7), which surpasses the threshold of 0.25 for Reid's Einstein-Podolsky-Rosen criterion. We also perform a continuous-variable Bell test and find a violation of the Clauser-Horne-Shimony-Holt inequality, measuring 2.26(3), exceeding the entanglement threshold of 2. We also demonstrate the flexibility of our method by preparing a non-Gaussian entangled oscillator state-a superposition of two-mode squeezed vacuum states.
We generalize Bell's inequalities to biparticle systems with continuous quantum variables. This is achieved by introducing the Bell operator in perfect analogy to the usual spin-1/2 systems. It is then demonstrated that two-mode squeezed vacuum states display quantum nonlocality by using the generalized Bell operator. In particular, the original Einstein-Podolsky-Rosen entangled states, which are the limiting case of the two-mode squeezed vacuum states, can maximally violate Bell's inequality due to Clauser, Horne, Shimony and Holt. The experimental aspect of our scheme and nonlocality of arbitrary biparticle entangled pure states of continuous variables are briefly considered.
We analyze the quantum entanglement between two interacting atoms trapped in a spherical harmonic potential. At ultracold temperature, ground-state entanglement is generated by the dominated sss-wave interaction. Based on a regularized pseudopotential Hamiltonian, we examine the quantum entanglement by performing the Schmidt decomposition of low-energy eigenfunctions. We indicate how the atoms are paired and quantify the entanglement as a function of a modified sss-wave scattering length inside the trap.
We generalize Bell's inequalities to biparty systems with continuous quantum variables. This is achieved by introducing the Bell operator in perfect analogy to the usual spin- 1/2 systems. It is then demonstrated that two-mode squeezed vacuum states display quantum nonlocality by using the generalized Bell operator. In particular, the original Einstein-Podolsky-Rosen states, which are the limiting case of the two-mode squeezed vacuum states, can maximally violate Bell's inequality due to Clauser, Horne, Shimony, and Holt. The experimental aspect of our scheme is briefly considered.