Higher‐Order Interactions in Quantum Optomechanics: Revisiting Theoretical Foundations
Abstract
:1. Introduction
2. Classical Hamiltonian
2.1. The Equations of Motion
2.2. Lagrangian
2.3. Hamiltonian
2.4. Single Optical Mode
3. Field Quantization
3.1. Conditions for Observation of Momentum-Field Quadratic Interactions
- The mechanical frequency must be of the same order of magnitude or exceeding the electromagnetic frequency . This is also possible and at least one experiment using superconducting optomechanics [79] has accessed this regime. Other possibilities are molecular optomechanics [78] as well as a rotating cylinder [80].
3.2. Linearized Quantization
3.2.1. Optical Field
3.2.2. Mechanical Field
3.2.3. Squeezing Hamiltonian
3.2.4. Special Case
4. Relativistic Considerations
5. Conclusions and Future Work
Acknowledgments
Conflicts of Interest
Appendix A. Equations of Motion
Appendix B. Special Case
Appendix C. Squared Annihilator
Appendix D. Relativistic Correction
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Khorasani, S. Higher‐Order Interactions in Quantum Optomechanics: Revisiting Theoretical Foundations. Appl. Sci. 2017, 7, 656. https://doi.org/10.3390/app7070656
Khorasani S. Higher‐Order Interactions in Quantum Optomechanics: Revisiting Theoretical Foundations. Applied Sciences. 2017; 7(7):656. https://doi.org/10.3390/app7070656
Chicago/Turabian StyleKhorasani, Sina. 2017. "Higher‐Order Interactions in Quantum Optomechanics: Revisiting Theoretical Foundations" Applied Sciences 7, no. 7: 656. https://doi.org/10.3390/app7070656