Quantum Dynamics of Nonlinear Oscillators

W. Leoński

Alexey Dmitrievich Alliluev, Денис В. Макаров

Andrey G. Grozin

Chaitanya S. Joshi, M. Jonson, Erika Andersson +1 more

We investigate the quantum entanglement dynamics of undriven anharmonic (nonlinear) oscillators with quartic potentials. We first consider the indirect interaction between two such nonlinear oscillators mediated by a third, linear oscillator and show that this leads to a time-varying entanglement of the oscillators, the entanglement being strongly influenced by the nonlinear oscillator dynamics. In the presence of dissipation, the role of nonlinearity is strongly manifested in the steady-state dynamics of the indirectly coupled anharmonic oscillators. We further illustrate the effect of nonlinearities by studying the coupling between an electromagnetic field in a cavity and one movable mirror which is modelled as a nonlinear oscillator. For this case, we present a full analytical treatment, which is valid in a regime where both the nonlinearity and the coupling due to radiation pressure are weak. We show that, without the need of any conditional measurements on the cavity field, the state of the movable mirror is non-classical as a result of the combined effect of the intrinsic nonlinearity and the radiation-pressure coupling. This interaction is also shown to be responsible for squeezing the movable mirror's position quadrature beyond the minimum uncertainty state even when the mirror is initially prepared in its ground state.

K. J. McNeil

The quantum dynamics of a coherently driven nonlinear oscillator are studied by solving the Schrödinger equation numerically. The results are used to examine the effect of increasingly strong driving on the mean number, squeezing, the second-order correlation function and the general behaviour of the Q function. For comparison, the corresponding quantities for the classical Liouville dynamics are also computed. It is found that while the dynamics do maintain some quantum aspects as the strength of the driving is increased, the spectacular quantum features of the undriven nonlinear oscillator are in fact progressively lost.

Jakob Wagner, Jeff Maki, Oded Zilberberg +1 more

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.