Dynamics and control of two coupled quantum oscillators: An analytical approach

We analyze two coupled quantum oscillators in a common Lorentzian environment and control them by detuning (temporarily shifting) their frequencies. The reduced dynamics are solved exactly, without Born or Markov approximations, by propagating each detuning segment in closed form. We study two control schedules: detuning, with perfectly periodic on and off pulses of fixed period, width, and amplitude; and detuning, with the same on/off structure but cycle-to-cycle jitter in period, width, and/or amplitude. Our main observable is the average excitation number (AEN) of each mode. Detuning moves the system away from the bath’s spectral peak, suppressing decoherence and damping non-Markovian revivals; in effectively Markovian baths the benefit is small. We quantify performance with a simple time-domain suppression factor. Larger detuning amplitudes and higher duty cycles yield stronger protection. \textcolor{blue}{In addition, we evaluate the quantum mutual information between the oscillator pair and the pseudomode bath, showing that detuning control significantly reduces system-bath correlations and information backflow. These results give practical design rules linking detuning, duty cycle, and bath width, and provide an exact benchmark for controlled non-Markovian dynamics.