Driven nonlinear quantum oscillators are a central platform for quantum technologies, yet their dissipative dynamics are typically described using Lindblad or Caldeira-Leggett master equations derived under assumptions that exclude nonlinearities and driving. Here, we derive a generalized Caldeira-Leggett master equation for driven nonlinear oscillators by retaining the full nonlinear and time-dependent system dynamics in the construction of the dissipator. For position- and momentum-dependent system-bath coupling, the dissipator itself becomes dynamically dressed, generating nonlinear and drive-dependent dissipative channels beyond conventional fixed-dissipator approaches. This produces nonlinear damping together with dissipation-induced corrections to the effective drive. The resulting dissipative dynamics suppress large-amplitude excitations and reduce phase-space fluctuations. For a driven Kerr oscillator, this leads to the suppression of bistability, asymmetric resonance responses, and strongly modified fluctuation distributions. More broadly, our results establish a microscopic framework in which nonlinear dynamics and driving directly reshape the dissipative sector of driven open quantum systems.Driven nonlinear quantum oscillators are a central platform for quantum technologies, yet their dissipative dynamics are typically described using Lindblad or Caldeira-Leggett master equations derived under assumptions that exclude nonlinearities and driving. Here, we derive a generalized Caldeira-Leggett master equation for driven nonlinear oscillators by retaining the full nonlinear and time-dependent system dynamics in the construction of the dissipator. For position- and momentum-dependent system-bath coupling, the dissipator itself becomes dynamically dressed, generating nonlinear and drive-dependent dissipative channels beyond conventional fixed-dissipator approaches. This produces nonlinear damping together with dissipation-induced corrections to the effective drive. The resulting dissipative dynamics suppress large-amplitude excitations and reduce phase-space fluctuations. For a driven Kerr oscillator, this leads to the suppression of bistability, asymmetric resonance responses, and strongly modified fluctuation distributions. More broadly, our results establish a microscopic framework in which nonlinear dynamics and driving directly reshape the dissipative sector of driven open quantum systems.

quant-pharXiv:2605.08021May 11, 20260 citations

Quantum Nonlinear Effect in Dissipatively Coupled Optomechanical System

Wen-Quan Yang, Wei Niu, Yonghong Ma +1 more

A full-quantum approach is used to study quantum nonlinear properties of a compound Michelson-Sagnac interferometer optomechanical system. The effective Hamiltonian shows that both dissipative and dispersive couplings possess imaginary- and real-Kerr nonlinearities. And unexpectedly, the nonlinearities caused by the dissipative coupling have non-Hermitian Hamiltonian-like properties. It can protect the quantum nature of the dispersive coupling beyond the traditional dissipation of the system. This protection mechanism allows the system to exhibit strong quantum nonlinear effects in the parameter region of the hyperbolic function $J^2 = Δ_c Δ_e$ . Moreover, we can obtain strong anti-bunching effects whether in strong or weak coupling regimes with the help of the dispersive and dissipative couplings jointly. It may provide a new perspective to experimentally realize and study the strong quantum nonlinear effects.A full-quantum approach is used to study quantum nonlinear properties of a compound Michelson-Sagnac interferometer optomechanical system. The effective Hamiltonian shows that both dissipative and dispersive couplings possess imaginary- and real-Kerr nonlinearities. And unexpectedly, the nonlinearities caused by the dissipative coupling have non-Hermitian Hamiltonian-like properties. It can protect the quantum nature of the dispersive coupling beyond the traditional dissipation of the system. This protection mechanism allows the system to exhibit strong quantum nonlinear effects in the parameter region of the hyperbolic function $J^2 = Δ_c Δ_e$. Moreover, we can obtain strong anti-bunching effects whether in strong or weak coupling regimes with the help of the dispersive and dissipative couplings jointly. It may provide a new perspective to experimentally realize and study the strong quantum nonlinear effects.

arXiv:2309.03719Sep 7, 20230 citations

Quantum Dissipative Systems

Ulrich Weiß

WORLD SCIENTIFIC eBooksNov 20, 2011693 citations

J^2 = Δ_c Δ_e

. Moreover, we can obtain strong anti-bunching effects whether in strong or weak coupling regimes with the help of the dispersive and dissipative couplings jointly. It may provide a new perspective to experimentally realize and study the strong quantum nonlinear effects.