Abstract
We demonstrate application of the method of higher-order operators to nonlinear standard optomechanics. It is shown that a symmetry breaking in frequency shifts exists, corresponding to inequivalency of red and blue side-bands. This arises from nonlinear higher-order processes leading to inequal detunings. Similarly, a higher-order resonance shift exists appearing as changes in both of the optical and mechanical resonances. We provide the first known method to explicitly estimate the population of coherent phonons. We also calculate corrections to spring effect due to higher-order interactions and coherent phonons, and show that these corrections can be quite significant in measurement of single-photon optomechanical interaction rate. It is shown that there exists non-unique and various choices for the higher-order operators to solve the optomechanical interaction with different multiplicative noise terms, among which a minimal basis offers exactly linear Langevin equations, while decoupling one Langevin equation and thus leaving the whole standard optomechanical problem exactly solvable by explicit expressions. We finally present a detailed treatment of multiplicative noise as well as nonlinear dynamic stability phases by the method of higher-order operators. Similar approach can be used outside the domain of standard optomechanics to quadratic and all other types of nonlinear interactions in quantum physics.
Highlights
Nonlinear quantum interactions with stochastic noise input stand among the most difficult analytical challenges to solve in the context of stochastic differential equations
We present a full mathematical treatment of multiplicative noise terms, which turn out to play a crucial rule in higher-order quantum optomechanics
We show for the first time that the introduced method of higher-order operators can be used to estimate the coherent population of phonons in the optomechanical cavity, here referred to as the coherent phonon number
Summary
Nonlinear quantum interactions with stochastic noise input stand among the most difficult analytical challenges to solve in the context of stochastic differential equations. While linearized interactions remain accurate for description of many experiments, a certain class of quadratic and higher-order physical phenomena cannot be normally understood under linearized approximations. While in classical problems the resulting Langevin equations are scalar functions, in quantum problems one has to deal with nonlinear operator differential equations. If expanded unto base kets, bosonic operators can assume infinite-dimensional matrix forms, rendering the solution entirely intractable
Sign-in/Register to view highlights & summary 
Published Version (
Free)
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call