Gaussian approximation and its corrections for driven dissipative Kerr model
arXiv:2410.09547 · doi:10.1103/5649-9p4j
Abstract
We develop a systematic projection-operator technique for constructing Gaussian approximations and their perturbative corrections in bosonic nonlinear models. As a case study, we apply it to the driven dissipative Kerr oscillator. In the absence of external driving, the model can be solved exactly within a low-dimensional Fock subspace, leading to strongly non-Gaussian states. Nevertheless, we demonstrate that the evolution of first- and second-order moments is captured by our Gaussian scheme with high accuracy even in this regime, providing a natural benchmark. For the general case with external driving, our approach reduces the equations of motion to a closed system for means and covariances and allows one to compute systematic corrections beyond the Gaussian level in closed form. We also calculate the dynamics of linear and quadratic combinations of creation and annihilation operators in both weak- and strong-drive regimes.
References in corpus (32)
- Gaussian Quantum Information
- High-yield wafer-scale fabrication of ultralow-loss, dispersion-engineered silicon nitride photonic circuits
- Non-Gaussian Quantum States and Where to Find Them
- Exact steady state of a Kerr resonator with one- and two-photon driving and dissipation: Controllable Wigner-function multimodality and dissipative phase transitions
- Procedures for Converting among Lindblad, Kraus and Matrix Representations of Quantum Dynamical Semigroups
- Driven-dissipative quantum Kerr resonators: new exact solutions, photon blockade and quantum bistability
- Irreversible quantum evolution with quadratic generator: Review
- Joint quantum estimation of loss and nonlinearity in driven-dissipative Kerr resonators
- Observation of first- and second-order dissipative phase transitions in a two-photon driven Kerr resonator
- Quantum non-Gaussianity of light and atoms
- Gaussian Quantum Trajectories for the Variational Simulation of Open Quantum-Optical Systems
- Enhancement of parameter estimation by Kerr interaction
- Non-perturbative effects in corrections to quantum master equation arising in Bogolubov-van Hove limit
- Randomness in Classical Mechanics and Quantum Mechanics
- Non-Gaussian pure states and positive Wigner functions
- Functional Classical Mechanics and Rational Numbers
- Thouless pumping in a driven-dissipative Kerr resonator array
- Lindblad dynamics of Gaussian states and their superpositions in the semiclassical limit
- Differential Parametric Formalism for the Evolution of Gaussian States: Nonunitary Evolution and Invariant States
- Parametric oscillator in a Kerr medium: evolution of coherent states
- Kerr Nonlinearity Induced Nonreciprocity in dissipatively coupled resonators
- Learning quantum states of continuous variable systems
- Photon-number tomography of multimode states and positivity of the density matrix
- Photon number and optical tomograms for Gaussian states
- Time-convolutionless master equations for composite open quantum systems
- Gaussian-state Ansatz for the non-equilibrium dynamics of quantum spin lattices
- Dispersive effects in ultrafast non-linear phenomena
- Higher order moments dynamics for some multimode quantum master equations
- Parametric approximation as open quantum systems problem
- Lindblad dynamics of open multi-mode bosonic systems: Algebra of bilinear superoperators, exceptional points and speed of evolution
- On time-dependent projectors and on generalization of thermodynamical approach to open quantum systems
- Sub-Poissonian Light in a Waveguide Kerr-medium