Quantum Optimal Control for Mixed State Squeezing in Cavity Optomechanics

Abstract

The performance of key tasks in quantum technology, such as accurate state preparation, can be maximized by utilizing external controls and deriving their shape with optimal control theory. For non-pure target states, the performance measure needs to match both the angle and the length of the generalized Bloch vector. A measure based on this simple geometric picture that separates angle and length mismatch into individual terms is introduced and the ensuing optimization framework is applied to maximize squeezing of an optomechanical oscillator at finite temperature. The results herein show that shaping the cavity drives can speed up squeezed state preparation by more than two orders of magnitude. Cooperativities and pulse shapes required to this end are fully compatible with the current experimental technology.

Optimally controlled quantum discrimination and estimation

“…Unlike the trace distance discussed above, D bures cannot be related to D HS , not even in the case of qubits. Nevertheless, the increase of D HS is expected to increase D bures as well [73]. For the maximization of D HS , shown in Fig.…”

“…Note that the relation D 2 tr = D HS only holds for qubits in which case maximization of D tr and maximization of D HS are equivalent. Since both distances are appropriate measures of state distinguishability, we choose D HS for maximization in optimal control, since it is more suitable for that purpose [72,73] because it allows us to build analytical gradients with respect to the states ρ 1 and ρ 2 .…”

Optimal control for feedback cooling in cavityless levitated optomechanics

“…Optimal control theory has been applied to other experimental systems [41], including for manipulation of Bose-Einstein condensates to prepare complex quantum states [42], designing excitation pulses in NMR [43] and tailoring robustness in solid-state spin magnetometry [44]. Additionally, it has been proposed for mixed state squeezing in cavity optomechanics [45], feedback cooling and squeezing of levitated nanopshperes in cavities [46] and recently for feedback cooling in low frequency magnetic traps [27]. To compare optimal cooling with typical feedback cooling, we numerically emulate the system, by solving its equations of motion, and we estimate its motion by numerically solving a second set of equations (section 4).…”

Engineering fast high-fidelity quantum operations with constrained interactions

“…The ability to generate squeezed states with quantum oscillators is of particular interest since it allows one, among others, to enhance sensing capabilities 52 or to reach the single-photon strong coupling regime with optomechanical systems using only linear resources 53 . Recently, optimal control techniques have been used to achieve squeezing of an optomechanical oscillator at finite temperature 54 .…”

“…Following the general procedure (see also "Methods") and parametrizing Δ (n) , g ðnÞ x ðtÞ and g ðnÞ y ðtÞ like we did for the qubit problem (Eqs. (54) and (55)), we can easily find the correction Hamiltonian (64). We stress that in this example we correct the unitary evolution generated by Eq.…”