Higher-Order Interactions in Quantum Optomechanics: Analysis of Quadratic Terms

Sina Khorasani

doi:10.1038/s41598-018-35055-6

Abstract

This article presents a full operator analytical method for studying the quadratic nonlinear interactions in quantum optomechanics. The method is based on the application of higher-order operators, using a six-dimensional basis of second order operators which constitute an exactly closed commutators. We consider both types of standard position-field and the recently predicted non-standard momentum-field quadratic interactions, which is significant when the ratio of mechanical frequency to optical frequency is not negligible. This unexplored regime of large mechanical frequency can be investigated in few platforms including the superconducting electromechanics and simulating quantum cavity electrodynamic circuits. It has been shown that the existence of non-standard quadratic interaction could be observable under appropriate conditions.

Highlights

The field of quantum optomechanics1–3 is flourishing as one of the modern applications of quantum physics, where interactions of optical field and mechanical motion inside a confined cavity is being studied
Many of the studies in this field utilize linearization of photonic aand phononic bladder operators around their mean values as a → a + aand b → b + b, where the substituted ladder operators represent field fluctuations around their respective mean values. This way of linearization is insufficient for quadratic18–25 and higher-order interactions where the resulting Langevin equations26–29 are expected to be strongly nonlinear
We base the simulation on the parameters mostly taken from a recent study on superconducting electromechanics33 where radio-and mechanical frequencies are accurately tuned and set to equal values

Summary

Introduction

The field of quantum optomechanics is flourishing as one of the modern applications of quantum physics, where interactions of optical field and mechanical motion inside a confined cavity is being studied. Many of the studies in this field utilize linearization of photonic aand phononic bladder operators around their mean values as a → a + aand b → b + b, where the substituted ladder operators represent field fluctuations around their respective mean values This way of linearization is insufficient for quadratic and higher-order interactions where the resulting Langevin equations are expected to be strongly nonlinear. It has been shown that a non-standard quadratic term could exist due to momentum-field interaction and relativistic effects, the strength of which is proportional to (Ω/ω) with Ω and ω respectively being the mechanical and optical frequencies30 Such momentum-field interactions are not expected to survive under the regular operating conditions of large optical frequencies ω Ω. Using the membrane-in-the-middle setup in optomechanical experiments could altogether eliminate the standard optomechanical interaction, leaving only the quadratic terms and higher

Results

Discussion

Conclusion