Combining Floquet and Lyapunov techniques for time-dependent problems in optomechanics and electromechanics

Result code in IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F61989592%3A15310%2F20%3A73601594" target="_blank" >RIV/61989592:15310/20:73601594 - isvavai.cz</a>

Result on the web

<a href="https://iopscience.iop.org/article/10.1088/1367-2630/ab8cab/pdf" target="_blank" >https://iopscience.iop.org/article/10.1088/1367-2630/ab8cab/pdf</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1088/1367-2630/ab8cab" target="_blank" >10.1088/1367-2630/ab8cab</a>

Result language

angličtina

Original language name

Combining Floquet and Lyapunov techniques for time-dependent problems in optomechanics and electromechanics

Original language description

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.

Czech name

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Czech description

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Type

J_imp - Article in a specialist periodical, which is included in the Web of Science database

CEP classification

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OECD FORD branch

10306 - Optics (including laser optics and quantum optics)

Project

Result was created during the realization of more than one project. More information in the Projects tab.

Continuities

P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)

Publication year

2020

Confidentiality

S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Name of the periodical

New Journal of Physics

ISSN

1367-2630

e-ISSN

—

Volume of the periodical

22

Issue of the periodical within the volume

6

Country of publishing house

GB - UNITED KINGDOM

Number of pages

17

Pages from-to

"063019-1"-"063019-17"

UT code for WoS article

000543092500001

EID of the result in the Scopus database

2-s2.0-85088873737