Non-Markovian master equation for a damped oscillator with time-varying parameters

TL;DR

This paper derives an exact non-Markovian master equation for a damped harmonic oscillator with time-varying parameters, enabling analysis of external modulation effects on quantum coherence and decoherence.

Contribution

It generalizes previous non-Markovian master equations to include time-dependent parameters and applies this to parity kick decoupling, revealing significant effects of external driving on dissipation.

Findings

Time-dependent dissipative coefficients are significantly altered by external pulses.

Kicking period must be shorter than bath memory time for effective coherence protection.

Soft pulses in an ohmic bath have notable effects on system dynamics.

Abstract

We derive an exact non-Markovian master equation that generalizes the previous work [Hu, Paz and Zhang, Phys. Rev. D {\bf 45}, 2843 (1992)] to damped harmonic oscillators with time-varying parameters. This is achieved by exploiting the linearity of the system and operator solution in Heisenberg picture. Our equation governs the non-Markovian quantum dynamics when the system is modulated by external devices. As an application, we apply our equation to parity kick decoupling problems. The time-dependent dissipative coefficients in the master equation are shown to be modified drastically when the system is driven by $\pi$ pulses. For coherence protection to be effective, our numerical results indicate that kicking period should be shorter than memory time of the bath. The effects of using soft pulses in an ohmic bath are also discussed.