Higher-order interactions in quantum optomechanics: Analytical solution of nonlinearity
arXiv:1702.04982 · doi:10.3390/photonics4040048
Abstract
A method is described to solve the nonlinear Langevin equations arising from quadratic interactions in quantum mechanics. While, the zeroth order linearization approximation to the operators is normally used, here first and second order truncation perturbation schemes are proposed. These schemes employ higher-order system operators, and then approximate number operators with their corresponding mean boson numbers, only where needed. Spectral densities of higher-order operators are derived, and an expression for the second-order correlation function at zero time-delay has been found, which reveals that the cavity photon occupation of an ideal laser at threshold reaches , in good agreement with extensive numerical calculations. As further applications, analysis of the quantum anharmonic oscillator, calculation of functions, analysis of quantum limited amplifiers, and nondemoliton measurements.
References in corpus (33)
- Strong dispersive coupling of a high finesse cavity to a micromechanical membrane
- Single-photon Optomechanics
- Microwave Quantum Illumination
- Quantum Illumination at the Microwave Wavelengths
- Large Quantum Superpositions and Interference of Massive Nanometer-Sized Objects
- Nonreciprocity and magnetic-free isolation based on optomechanical interactions
- Squeezed Optomechanics with Phase-matched Amplification and Dissipation
- Dispersive optomechanics: a membrane inside a cavity
- Nonreciprocal reconfigurable microwave optomechanical circuit
- Cooling and squeezing via quadratic optomechanical coupling
- Hanbury Brown and Twiss interferometry of single phonons from an optomechanical resonator
- Quantum-limited directional amplifiers with optomechanics
- Optomechanical trapping and cooling of partially transparent mirrors
- The optomechanical instability in the quantum regime
- Nonlinear cavity optomechanics with nanomechanical thermal fluctuations
- Quantum bits with Josephson junctions
- Optomechanical-like coupling between superconducting resonators
- Amplified opto-mechanical transduction of virtual radiation pressure
- Enhancement of mechanical effects of single photons in modulated two-mode optomechanics
- Macroscopic tunneling of a membrane in an optomechanical double-well potential
- Circuit analog of quadratic optomechanics
- Radiation Pressure Cooling as a Quantum Dynamical Process
- Proposal for an Optomechanical Microwave Sensor at the Subphoton Level
- Cross-Kerr nonlinearity in optomechanical systems
- Phonon number quantum jumps in an optomechanical system
- Antibunching in an optomechanical oscillator
- Stochastic resonance in a tristable optomechanical system
- Optomechanics with a position-modulated Kerr-type nonlinear coupling
- Quantum reservoir engineering through quadratic optomechanical interaction in the reversed dissipation regime
- Optomechanical oscillator controlled by variation in its heat bath temperature
- Dynamic stabilization of an optomechanical oscillator
- Symmetry Operators for the Fokker-Plank-Kolmogorov Equation with Nonlocal Quadratic Nonlinearity
- Spatio-Temporal Forecasting by Coupled Stochastic Differential Equations: Applications to Solar Power