Bulletin of the American Physical Society
APS March Meeting 2020
Volume 65, Number 1
Monday–Friday, March 2–6, 2020; Denver, Colorado
Session M02: Optomechanics
11:15 AM–2:15 PM,
Wednesday, March 4, 2020
Sponsoring Unit: DAMOP
Chair: Srivatsan Chakram, University of Chicago
Abstract: M02.00008 : Floquet–Lyapunov approach to optomechanical systems
View Presentation Abstract
We introduce a method to solve the dynamics of a time-periodic system, by using the Floquet approach to write the dynamics in the form of a Lyapunov equation. With the Floquet method, we can transform a periodic linear differential equation into a time-independent linear system. After which, for the time-independent Hamiltonian that is quadratic in the
canonical operators, the time development can be expressed in the form of a Lyapunov equation, which can be solved efficiently.
We demonstrate this method in an optomechanical system with dissipative generation of squeezing. We show that we can include the counter-rotating terms ignored in the rotating-wave approximation. The method is also useful with levitating particles in an amplitude modulated trapping field.
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