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arXiv:1707.01593 · Physical Review A

Hybrid phase-space–Fock-space approach to evolution of a driven nonlinear resonator

Mostafa Khezri, Alexander N. Korotkov

Published Oct 16, 2017• 5 citations
arXivHTMLPDF

Abstract

We analyze the quantum evolution of a weakly nonlinear resonator due to a classical near-resonant drive and damping. The resonator nonlinearity leads to squeezing and heating of the resonator state. Using a hybrid phase-space--Fock-space representation for the resonator state within the Gaussian approximation, we derive evolution equations for the four parameters characterizing the Gaussian state. Numerical solution of these four ordinary differential equations is much simpler and faster than simulation of the full density matrix evolution, while providing good accuracy for the system analysis during transients and in the steady state. We show that steady-state squeezing of the resonator state is limited by 3 dB; however, this limit can be exceeded during transients.

DOI
10.1103/physreva.96.043839

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We present a new approach for deriving exact closed-form solutions for the steady state of a wide class of driven-dissipative nonlinear resonators that is distinct from more common complex-P-function methods. Our method generalizes the coherent quantum-absorber approach of Stannigel et al. [New J. Phys. 14, 063014 (2012)] to include nonlinear driving and dissipation and relies crucially on exploiting the Segal-Bargmann representation of Fock space. Our solutions and method reveal a wealth of previously unexplored observable phenomena in these systems, including new generalized photon-blockade and antiblockade effects and an infinite number of new parameter choices that yield quantum bistability.
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.