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arXiv:1611.00726 · Journal of Physics A Mathematical and Theoretical

Pure Gaussian states from quantum harmonic oscillator chains with a single local dissipative process

Shan Ma, Matthew J. Woolley, Ian R. Petersen, Naoki Yamamoto

Published Feb 10, 2017• 22 citations
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Abstract

Abstract We study the preparation of entangled pure Gaussian states via reservoir engineering. In particular, we consider a chain consisting of ( 2 ℵ + 1 ) quantum harmonic oscillators where the central oscillator of the chain is coupled to a single reservoir. We then completely parametrize the class of ( 2 ℵ + 1 ) -mode pure Gaussian states that can be prepared by this type of quantum harmonic oscillator chain. This parametrization allows us to determine the steady-state entanglement properties of such quantum harmonic oscillator chains.

DOI
10.1088/1751-8121/aa5fbe

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Abstract We study the preparation of entangled pure Gaussian states via reservoir engineering. In particular, we consider a chain consisting of ( 2 ℵ + 1 ) quantum harmonic oscillators where the central oscillator of the chain is coupled to a single reservoir. We then completely parametrize the class of ( 2 ℵ + 1 ) -mode pure Gaussian states that can be prepared by this type of quantum harmonic oscillator chain. This parametrization allows us to determine the steady-state entanglement properties of such quantum harmonic oscillator chains.
Abstract We study theoretically a finite harmonic chain where the two central oscillators are damped into a two-mode squeezed reservoir. By suitably choosing the Hamiltonian of the chain, the entire chain can be stabilized into a pure entangled steady state, even if it starts in a mixed state. We identify a condition on the system parameters such that the corresponding chain evolves into a pure steady state. We then proceed to parametrize a class of stabilizable pure states. Our approach is based on reservoir engineering and is particularly applicable to optomechanical systems and superconducting quantum circuits.
We study the dissipative preparation of many-body entangled Gaussian states in bosonic lattice models which could be relevant for quantum technology applications. We assume minimal resources, represented by systems described by particle-conserving quadratic Hamiltonians, with a single localized squeezed reservoir. We show that in this way it is possible to prepare, in the steady state, the wide class of pure states which can be generated by applying a generic passive Gaussian transformation on a set of equally squeezed modes. This includes nontrivial multipartite entangled states such as cluster states suitable for measurement-based quantum computation.
We investigate a simple arrangement of coupled harmonic oscillators which brings out some interesting effects concerning creation of entanglement. It is well known that if each member in a linear chain of coupled harmonic oscillators is prepared in a ``classical state,'' such as a pure coherent state or a mixed thermal state, no entanglement is created in the rotating wave approximation. On the other hand, if one of the oscillators is prepared in a nonclassical state (pure squeezed state, for instance), entanglement may be created between members of the chain. In the setup considered here, we found that a great family of nonclassical (squeezed) states can localize entanglement in such a way that distant oscillators never become entangled. We present a detailed study of this particular localization phenomenon. Our results may find application in future solid state implementations of quantum computers, and we suggest an electromechanical system consisting of an array of coupled micromechanical oscillators as a possible implementation.
We show that a squeezed bath, that acts on the central element of a harmonic chain, can drive the whole system to a steady state featuring a series of nested entangled pairs of oscillators that, ideally, covers the whole chain regardless of its size. We study how to realize this effect in various physical implementations, including optomechanical and superconducting devices, using currently available technologies. In these cases no squeezed fields are actually needed, and the squeezed bath is, instead, simulated by quantum reservoir engineering with bichromatic drives.