Quantum Dynamics of Time-Dependent Optomechanical Systems!

Sofia Qvarfort, Plato, ADK, Bruschi, DE +4 more

We study the fundamental sensitivity that can be achieved with an ideal optomechanical system in the nonlinear regime for measurements of time-dependent gravitational fields. Using recently developed methods to solve the dynamics of a nonlinear optomechanical system with a time-dependent Hamiltonian, we compute the quantum Fisher information for linear displacements of the mechanical element due to gravity. We demonstrate that the sensitivity can not only be further enhanced by injecting squeezed states of the cavity field, but also by modulating the light--matter coupling of the optomechanical system. We specifically apply our results to the measurement of gravitational fields from small oscillating masses, where we show that, in principle, the gravitational field of an oscillating nano-gram mass can be detected based on experimental parameters that will likely be accessible in the near-term future. Finally, we identify the experimental parameter regime necessary for gravitational wave detection with a quantum optomechanical sensor.

Max Ludwig, Georg Heinrich, Florian Marquardt

Max Ludwig

Sofia Qvarfort, A. D. K. Plato, David Edward Bruschi +4 more

We study the fundamental sensitivity that can be achieved with an ideal optomechanical system in the nonlinear regime for measurements of time-dependent gravitational fields. The optomechanical system consists of a cavity mode and a mechanical oscillator coupled to it via (non-linear) radiation pressure coupling. Using recently developed methods to solve the dynamics of a nonlinear optomechanical system with a time-dependent Hamiltonian, we compute the quantum Fisher information for linear displacements of the mechanical element due to gravity. We demonstrate that the sensitivity can be further enhanced by injecting squeezed states of the cavity field or by modulating the light–matter coupling of the optomechanical system. We specifically apply our results to the measurement of gravitational fields from small oscillating masses, where we show that, in principle, the gravitational field of an oscillating nanogram mass can be detected based on experimental parameters that will likely be accessible in the near-term future. Finally, we identify the experimental parameter regime necessary for gravitational wave detection with a quantum optomechanical sensor.

S. Höfer, Klemens Hammerer

Iivari Pietikäinen, Ondřej Černotík, Radim Filip

Abstract Cavity optomechanics and electromechanics form an established field of research investigating the interactions between electromagnetic fields and the motion of quantum mechanical resonators. In many applications, linearised form of the interaction is used, which allows for the system dynamics to be fully described using a Lyapunov equation for the covariance matrix of the Wigner function. This approach, however, is problematic in situations where the Hamiltonian becomes time dependent as is the case for systems driven at multiple frequencies simultaneously. This scenario is highly relevant as it leads to dissipative preparation of mechanical states or backaction-evading measurements of mechanical motion. The time-dependent dynamics can be solved with Floquet techniques whose application is, nevertheless, not straightforward. Here, we describe a general method for combining the Lyapunov approach with Floquet techniques that enables us to transform the initial time-dependent problem into a time-independent one, at the acceptable cost of enlarging the drift and diffusion matrix. We show how the lengthy process of applying the Floquet formalism to the original equations of motion and deriving a Lyapunov equation from their time-independent form can be simplified with the use of properly defined Fourier components of the drift matrix of the original time-dependent system. We then use our formalism to comprehensively analyse dissipative generation of mechanical squeezing beyond the rotating wave approximation. Our method is applicable to various problems with multitone driving schemes in cavity optomechanics, electromechanics, and related disciplines.