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Quantum Science and Technology

Maximising optomechanical entanglement with optimal control

Dionisis Stefanatos

Published Feb 23, 2017• 30 citations
Publisher

Abstract

Abstract In this article, we formulate the generation of optomechanical entanglement between the linearly coupled cavity field and the mechanical resonator as an optimal control problem in hyperbolic space H 3 , with control input the effective coupling rate (optomechanical coupling strength) of the two oscillators. Next, we use optimal control theory to find the allowed optimal values of the coupling which maximise the amount of generated entanglement for a fixed duration of the interaction. Finally, we employ a numerical optimisation method to obtain the exact optimal pulse sequences for several illustrative examples. When the effective coupling rate is comparable or larger than the frequency of the mechanical resonator, a substantial amount of entanglement can be generated within a fraction of a single oscillator period.

DOI
10.1088/2058-9565/aa629c

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Abstract In this article, we formulate the generation of optomechanical entanglement between the linearly coupled cavity field and the mechanical resonator as an optimal control problem in hyperbolic space H 3 , with control input the effective coupling rate (optomechanical coupling strength) of the two oscillators. Next, we use optimal control theory to find the allowed optimal values of the coupling which maximise the amount of generated entanglement for a fixed duration of the interaction. Finally, we employ a numerical optimisation method to obtain the exact optimal pulse sequences for several illustrative examples. When the effective coupling rate is comparable or larger than the frequency of the mechanical resonator, a substantial amount of entanglement can be generated within a fraction of a single oscillator period.
In this article, we formulate the generation of optomechanical entanglement between the linearly coupled cavity field and the mechanical resonator as an optimal control problem in hyperbolic space H3H^3H3, with control input the coupling rate of the two oscillators. Next, we use optimal control theory to find the allowed optimal values of the coupling which maximize the amount of generated entanglement for a fixed duration of the interaction. Finally, we employ a numerical optimization method to obtain the exact optimal pulse sequences for several illustrative examples. In the strong coupling regime, where the coupling rate is comparable or larger than the frequency of the mechanical resonator, a substantial amount of entanglement can be generated within a fraction of a single oscillator period.
Abstract Cavity optomechanical systems are one of the leading experimental platforms for controlling mechanical motion in the quantum regime. We exemplify that the control over cavity optomechanical systems greatly increases by coupling the cavity also to a two-level system, thereby creating a hybrid optomechanical system. If the two-level system can be driven largely independently of the cavity, we show that the nonlinearity thus introduced enables us to steer the extended system to non-classical target states of the mechanical oscillator with Wigner functions exhibiting significant negative regions. We illustrate how to use optimal control techniques beyond the linear regime to drive the hybrid system from the near ground state into a Fock target state of the mechanical oscillator. We base our numerical optimization on realistic experimental parameters for exemplifying how optimal control enables the preparation of decidedly non-classical target states, where naive control schemes fail. Our results thus pave the way for applying the toolbox of optimal control in hybrid optomechanical systems for generating non-classical mechanical states.
Abstract We study theoretically a two-mode optomechanical system where two cavity modes are coupled to a single mechanical mode. It is shown that the whole system can yield good squeezing, which is comparable to that produced by dispersive coupling, the numerical results which we obtained showed periodic oscillations with a maximum peaks in one of the two quadrature component with a value less than 0.5. We also showed that entanglement can be achieved by calculating the variance in quadrature component of the field operators. Our results are useful in non- degenerate parametric oscillation.
Abstract We study theoretically the generation of strong entanglement of two mechanical oscillators in an unresolved-sideband optomechanical cavity, using a reservoir engineering approach. In our proposal, the effect of unwanted counter-rotating terms is suppressed via destructive quantum interference by the optical field of two auxiliary cavities. For arbitrary values of the optomechanical interaction, the entanglement is obtained numerically. In the weak-coupling regime, we derive an analytical expression for the entanglement of the two mechanical oscillators based on an effective master equation, and obtain the optimal parameters to achieve strong entanglement. Our analytical results are in accord with numerical simulations.
We present a scheme for realizing phase-controlled entanglement in a microwave optomechanical system comprising two microwave cavities and two mechanical oscillators. Under specific driving conditions, we show that this optomechanical interface can be exploited to generate simultaneously the stationary cavity–cavity entanglement, mechanical–mechanical entanglement, and cavity–mechanical entanglement. Due to the closed loop interaction, we find that the entanglement can be controlled flexibly by tuning the phase difference between the optomechanical coupling strengths. The dependence of the entanglement on the amplitudes of the optomechanical coupling strengths is also explored in detail. Moreover, the bipartite entanglements are robust against temperature, and it is shown that the mechanical oscillators are cooled to the ground state in the parameter regimes for observing entanglement.
We study theoretically a two-mode optomechanical system where two cavity modes are coupled to a single mechanical mode. It is shown that the whole system can yield good squeezing, which is comparable to that produced by dispersive coupling, the numerical results which we obtained showed periodic oscillations with a maximum peaks in one of the two quadrature component with a value less than 0.5. We also showed that entanglement can be achieved by calculating the variance in quadrature component of the field operators. Our results are useful in non- degenerate parametric oscillation.