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Quantum Science and Technology

Discrete-time reservoir engineering with entangled bath and stabilising squeezed states

Zibo Miao, Alain Sarlette

Published Jul 31, 2017• 7 citations
Publisher

Abstract

Abstract This theoretical proposal investigates how resonant interactions occurring when a harmonic oscillator is fed with a stream of entangled qubits allow us to stabilise squeezed states of the harmonic oscillator. We show that the properties of the squeezed state stabilised by this engineered reservoir, including the squeezing strength, can be tuned at will through the parameters of the ‘input’ qubits, albeit in tradeoff with the convergence rate. We also discuss the influence of the type of entanglement in the input from a pairwise case to a more widely distributed case. This paper can be read either as a proposal to stabilise squeezed states or as a step toward treating quantum systems with time-entangled reservoir inputs.

DOI
10.1088/2058-9565/aa7ce8

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Abstract This theoretical proposal investigates how resonant interactions occurring when a harmonic oscillator is fed with a stream of entangled qubits allow us to stabilise squeezed states of the harmonic oscillator. We show that the properties of the squeezed state stabilised by this engineered reservoir, including the squeezing strength, can be tuned at will through the parameters of the ‘input’ qubits, albeit in tradeoff with the convergence rate. We also discuss the influence of the type of entanglement in the input from a pairwise case to a more widely distributed case. This paper can be read either as a proposal to stabilise squeezed states or as a step toward treating quantum systems with time-entangled reservoir inputs.
This theoretical proposal investigates how resonant interactions occurring when a harmonic oscillator is fed with a stream of entangled qubits allow us to stabilize squeezed states of the harmonic oscillator. We show that the properties of the squeezed state stabilized by this engineered reservoir, including the squeezing strength, can be tuned at will through the parameters of the "input" qubits, albeit in tradeoff with the convergence rate. We also discuss the influence of the type of entanglement in the input, from a pairwise case to a more widely distributed case. This paper can be read in two ways: either as a proposal to stabilize squeezed states, or as a step towards treating quantum systems with time-entangled reservoir inputs.
In this paper, we continue our investigation on controlling the state of a quantum harmonic oscillator, by coupling it to a reservoir composed of a sequence of qubits. Specifically, we show that sending qubits separable from each other but initialised at different states in pairs can stabilise the oscillator at squeezed states. However, only if entanglement is allowed in the reservoir qubit can we stabilise the oscillator at a wider set of squeezed states. This thus provides a proof for the necessity of involving entanglement in the reservoir qubits input to the oscillator, as regard to the stabilisation of quantum states in the proposed system setting. On the other hand, this system setup can be in turn used to estimate the coupling strength between the oscillator and reservoir qubits. We further demonstrate that entanglement in the reservoir input qubits contributes to the corresponding quantum Fisher information. From this point of view, entanglement is proved to play an indispensable role in the improvement of estimation precision in quantum metrology.
This paper is concerned with a discrete-time reservoir engineering consisting of a sequence of qubits which are used to manipulate the quantum state of a harmonic oscillator. We consider the controllability problem regarding such a system both in the finite time and infinite time scenarios, with detailed proofs. In more concrete terms, we discuss how the quantum state of the harmonic oscillator evolves step by step, and provide the final state afterkkksteps. The role of entanglement involved in the reservoir is also discussed by demonstrating photon numbers. In terms of infinite time controllability analysis, we take advantage of the approximated Lindblad master equation, to explore under what circumstances can we stabilize coherent states, squeezed states and Schrödinger cat states. Stabilization of certain quantum states as well as the corresponding convergence rates are proved by means of Lyapunov functions. These results shed light on a systematic framework towards controllability analysis in quantum reservoir engineering.
Reservoir engineering makes it possible to adjust the dissipation of quantum systems by driving the reservoir. This inspires investigations on how to slow a system's damping via squeezing reservoirs. In this paper we characterize damping by the quantum reliability of quantum states. We analyze the reliability loss of the harmonic oscillators in a squeezed thermal reservoir, where the quantum states under consideration have garnered significant interest in recent experiments, such as the coherent state, the squeezed coherent state, and the cat state. We explore the optimal protocol to extend the lifetime of these quantum states by adjusting the squeezed parameters of the squeezed thermal reservoir in both the high-damping and low-damping regimes. In the low-damping regime, our findings suggest that the unique optimal protocol follows the phase-matching condition and is insensitive to the reservoir's temperature. We also evaluate the optimal condition for the large damping regime. Furthermore, we show that when the state parameters satisfy a specific condition, there exists an interval for the damping rate, within which a bifurcation of the optimal protocol occurs.
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 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.