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The European Physical Journal D

A trapped ion in an optomechanical system: entanglement dynamics

Marziyeh Hassani Nadiki, Mohammad Kazem Tavassoly, Navid Yazdanpanah

Published Jun 1, 2018• 11 citations
Publisher
DOI
10.1140/epjd/e2018-80778-6

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It is presented a scheme for generating entanglement between a moving mirror and the vibrational degree of freedom of a single trapped ion. The system consists of an interferometer with an optomechanical cavity at one arm and a cavity with a single trapped ion at another arm. Because of the radiation pressure, it is possible to entangle the cavity field with the moving mirror at the optomechanical arm and by tuning the cavity field with the internal levels of the ion, it is possible to generate an entangled state comprising the cavity and the ion arm. The cavity fields may be coupled via a beam splitter, making possible to generate entanglement between the moving mirror and the vibrational state of motion of a single trapped ion.
We theoretically show how two impurity defects in a crystalline structure can be entangled through coupling with the crystal. We demonstrate this with a harmonic chain of trapped ions in which two ions of a different species are embedded. Entanglement is found for sufficiently cold chains and for a certain class of initial, separable states of the defects. It results from the interplay between localized modes which involve the defects and the interposed ions, it is independent of the chain size, and it decays slowly with the distance between the impurities. These dynamics can be observed in systems exhibiting spatial order; viable realizations are optical lattices, optomechanical systems, or cavity arrays in circuit QED.
We consider an optomechanical system composed of a trapped ion dispersively coupled to a single mode of a pumped optical cavity. We focus on a parameter range for which the semiclassical description predicts two clearly distinct equilibrium configurations in the limits of small and large photon pumping, while a bistable regime is found for intermediate pumping. This semiclassical description, however, is not valid in close proximity to the system transitions or when the mean photon number is low. Here, we provide a numerical analysis of the fully quantum state in the few-photon regime, exploring the features of the asymptotic state across the transition and analyzing possible markers of semiclassical bistability. We find an increase in the entropy of the system and of the entanglement in the transition region but no clear signatures of metastability in the spectrum of the evolution.