Precision gravimetry is key to a number of scientific and industrial applications, including climate change research, space exploration, geological surveys and fundamental investigations into the nature of gravity. A variety of quantum systems, such as atom interferometry and on-chip-Bose–Einstein condensates have thus far been investigated to this aim. Here, we propose a new method which involves using a quantum optomechanical system for measurements of gravitational acceleration. As a proof-of-concept, we investigate the fundamental sensitivity for gravitational accelerometry of a cavity optomechanical system with a trilinear radiation pressure light-matter interaction. The phase of the optical output encodes the gravitational acceleration g and is the only component which needs to be measured. We prove analytically that homodyne detection is the optimal readout method and we predict an ideal fundamental sensitivity of Δg = 10−15 ms−2 for state-of-the-art parameters of optomechanical systems, showing that they could, in principle, surpass the best atomic interferometers even for low optical intensities. Further, we show that the scheme is strikingly robust to the initial thermal state of the oscillator.
We analytically solve the time evolution of a nonlinear optomechanical Hamiltonian with arbitrary time-dependent mechanical squeezing and optomechanical coupling. The solution is based on techniques which provide a new set of analytical tools to study the unitary evolution of optomechanical systems in full generality. To demonstrate the applicability of our method, we compute the degree of non-Gaussianity of the time-evolved state of the system by means of a measure based on the relative entropy of the state. We find that the addition of a constant mechanical squeezing term generally decreases the overall non-Gaussian character of the state. For squeezing modulated at resonance, we recover the Mathieu equations, which we solve pertubatively. We find that the non-Gaussianity increases with both time and the squeezing parameter in this specific regime. ‡ Current address: § We note here that non-Gaussianity for the case D 1 = D 2 = 0 has been already studied [9].
We study the fundamental bounds on precision measurements of parameters contained in a timedependent nonlinear optomechanical Hamiltonian, which includes the nonlinear light-matter coupling, a mechanical displacement term, and a single-mode mechanical squeezing term. By using a recently developed method to solve the dynamics of this system, we derive a general expression for the quantum Fisher information and demonstrate its applicability through three concrete examples: estimation of the strength of a nonlinear light-matter coupling, the strength of a time-modulated mechanical displacement, and a single-mode mechanical squeezing parameter, all of which are modulated at resonance. Our results can be used to compute the sensitivity of a nonlinear optomechanical system to a number of external and internal effects, such as forces acting on the system or modulations of the light-matter coupling.arXiv:1910.04485v1 [quant-ph]
We study the non-Gaussian character of quantum optomechanical systems evolving under the fully nonlinear optomechanical Hamiltonian. By using a measure of non-Gaussianity based on the relative entropy of an initially Gaussian state, we quantify the amount of non-Gaussianity induced by both a constant and time-dependent cubic light-matter coupling and study its general and asymptotic behaviour. We find analytical approximate expressions for the measure of non-Gaussianity and show that initial thermal phonon occupation of the mechanical element does not significantly impact the non-Gaussianity. More importantly, we also show that it is possible to continuously increase the amount of non-Gassuianity of the state by driving the light-matter coupling at the frequency of mechanical resonance, suggesting a viable mechanism for increasing the non-Gaussianity of optomechanical systems even in the presence of noise. Figure 1. An optomechanical system consisting of a moving end mirror. The operators â and â † denote the creation and annihilation operators for the light field, and b and b † denote the motional degree of freedom of the mirror. Other examples of optomechanical systems include levitated nanobeads and cold-atom ensembles. 7 We should note here that, since uncertainties in quantum Gaussian systems are fundamentally bounded by the Heisenberg uncertainty relation, which in principle does not hold for classical systems, Gaussian operations are in fact sufficient to run some protocols requiring genuine quantum features, such as continuous variable quantum key distribution.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.
hi@scite.ai
10624 S. Eastern Ave., Ste. A-614
Henderson, NV 89052, USA
Copyright © 2024 scite LLC. All rights reserved.
Made with 💙 for researchers
Part of the Research Solutions Family.