2017
DOI: 10.3390/app7070656
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Higher‐Order Interactions in Quantum Optomechanics: Revisiting Theoretical Foundations

Abstract: Abstract:The theory of quantum optomechanics is reconstructed from first principles by finding a Lagrangian from light's equation of motion and then proceeding to the Hamiltonian. The nonlinear terms, including the quadratic and higher-order interactions, do not vanish under any possible choice of canonical parameters, and lead to coupling of momentum and field. The existence of quadratic mechanical parametric interaction is then demonstrated rigorously, which has been so far assumed phenomenologically in prev… Show more

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Cited by 12 publications
(44 citation 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%
“…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%
“…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%
“…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].…”
mentioning
confidence: 88%