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arXiv:1710.10318 · Physical Review A

Reservoir engineering of bosonic lattices using chiral symmetry and localized dissipation

Yariv Yanay, Aashish A. Clerk

Published Oct 12, 2018• 26 citations
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Abstract

We show how a generalized kind of chiral symmetry can be used to construct highly efficient reservoir engineering protocols for bosonic lattices. These protocols exploit only a single squeezed reservoir coupled to a single lattice site; this is enough to stabilize the entire system in a pure, entangled steady state. Our approach is applicable to lattices in any dimension and does not rely on translational invariance. We show how the relevant symmetry operation directly determines the real-space correlation structure in the steady state and give several examples that are within reach in several one- and two-dimensional quantum photonic platforms.

DOI
10.1103/physreva.98.043615

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We show how a generalized kind of chiral symmetry can be used to construct highly efficient reservoir engineering protocols for bosonic lattices. These protocols exploit only a single squeezed reservoir coupled to a single lattice site; this is enough to stabilize the entire system in a pure, entangled steady state. Our approach is applicable to lattices in any dimension and does not rely on translational invariance. We show how the relevant symmetry operation directly determines the real-space correlation structure in the steady state and give several examples that are within reach in several one- and two-dimensional quantum photonic platforms.
We demonstrate an approach to the generation of custom entangled many-body states through reservoir engineering, using the symmetry properties of bosonic lattice systems coupled to a local squeezed reservoir [Yanay and Clerk, Phys. Rev. A 98, 043615 (2018)]. We outline an algorithm where, beginning with a desired set of squeezing correlations, one uses the symmetry to constrain the Hamiltonian and find a lattice configuration which stabilizes a pure steady state realizing these correlations. We demonstrate how to use this process to stabilize two unique pure states with nonlocal correlations that could be useful for quantum information applications. First, we show how to drive a square lattice into a product state of entangled quadruplets of sites. Second, using a bisected system, we generate a steady state where local measurements in one half of the lattice herald a pure delocalized state in the second half.
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 analyze a general method for the dissipative preparation and stabilization of volume-law entangled states of fermionic and qubit lattice systems in one dimension (and higher dimensions for fermions). Our approach requires minimal resources: nearest-neighbor Hamiltonian interactions that obey a suitable chiral symmetry, and the realization of just a single, spatially localized dissipative pairing interaction. In the case of a qubit array, the dissipative model we study maps to an interacting fermionic problem. Nonetheless, we analytically show the existence of a unique pure entangled steady state (a so-called rainbow state). Our ideas are compatible with a number of experimental platforms, including superconducting circuits and trapped ions.
This paper analyzes the dynamics of a large quantum lattice of non-interacting bosons when it is locally coupled to a reservoir of squeezed light. The authors find that the medium term evolution of the lattice shows ballistic behavior, with a quasi-stationary state on the inside of an expanding light-cone. In the long term, the system's approach to a final steady state is dictated by a dissipative spectrum that shows complex, non-monotonous dependence on the strength of the coupling to the reservoir.
Abstract We study the dissipative stabilization of entangled states in arrays of quantum systems. Specifically, we are interested in the states of qubits (spin- 1 / 2 ) which may or may not interact with one or more cavities (bosonic modes). In all cases only one element, either a cavity or a qubit, is lossy and irreversibly coupled to a reservoir. When the lossy element is a cavity, we consider a squeezed reservoir and only interactions which conserve the number of cavity excitations. Instead, when the lossy element is a qubit, pure decay and a properly selected structure of XY-interactions are taken into account. We show that in all cases, in the steady state, many pairs of distant, non-directly interacting qubits, which cover the whole array, can get entangled in a stationary way, by means of the interplay of dissipation and local interactions.
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.