Maximizing optomechanical entanglement with optimal control
This work provides a method to maximize entanglement in optomechanical systems, which is relevant for quantum information processing, though the results are specific to the strong coupling regime.
The authors formulate optomechanical entanglement generation as an optimal control problem and use optimal control theory to maximize entanglement for fixed interaction duration, achieving substantial entanglement in the strong coupling regime within a fraction of an 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 $H^3$, 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.