Higher‐Order Interactions in Quantum Optomechanics: Revisiting Theoretical Foundations

Khorasani, Sina

doi:10.3390/app7070656

Cited by 12 publications

(44 citation statements)

References 94 publications

(161 reference statements)

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“…Recently, the author has reconsidered the theoretical description of optomechanics [65] and shown that quadratic interactions are subject to two corrections resulting from momentum conservation and relativistic effects. Such types of quadratic corrections become significant when the mechanical frequency is within the same order of or exceeds electromagnetic frequency.…”

Section: Introductionmentioning

confidence: 99%

Method of Higher-order Operators for Quantum Optomechanics

Khorasani

2018

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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.

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Section: Introductionmentioning

confidence: 99%

Method of Higher-order Operators for Quantum Optomechanics

Khorasani

2018

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“…Recently, theory of optomechanics has been revisited by the author [30] as well as others for nonlinear [31] and quadratic [32] interactions. 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) 2 with Ω and ω respectively being the mechanical and optical frequencies [30]. Normally, such momentum-field interactions are not expected to survive under the regular operating conditions of large optical frequencies ω >> Ω.…”

Section: Introductionmentioning

confidence: 99%

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

Khorasani

2018

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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.

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“…When combined with a parametric amplification term, then the total interaction Hamiltonian could be a lot more difficult to solve. So far, no exact solution to this problem has been reported to the best knowledge of the authors.Here, we demonstrate that the cross-Kerr interaction with parametric amplification could be exactly solvable using the method of higher-order operators [11][12][13][14][15][16], which has evolved out of the rich domain of quadratic optomechanics [17][18][19][20][21][22][23]. This method employs a different basis than the simple bath ladder operators, and quite recently has been independently also reported elsewhere [18].…”

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confidence: 88%