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Role of dissipation in the stability of a parametrically driven quantum harmonic oscillator
Chaki Subhasish,Bhattacherjee Aranyabhuti 한국물리학회 2021 THE JOURNAL OF THE KOREAN PHYSICAL SOCIETY Vol.79 No.7
We study the dissipative dynamics of a single quantum harmonic oscillator subjected to parametric driving within an effective Hamiltonian approach. Using the Liouville–von Neumann approach, we show that the time evolution of a parametrically driven dissipative quantum oscillator has a strong connection with the classical, damped Mathieu equation. Based on the numerical analysis of the Monodromy matrix, we demonstrate that the dynamical instability generated by the parametric driving is reduced by the effect of dissipation. Furthermore, we obtain a closed relationship between the localization of the Wigner function and the stability of the damped Mathieu equation.