Efficient algebraic solution for a time-dependent quantum harmonic oscillator

Using operator ordering techniques based on Baker-Campbell-Hausdorff (BCH) relations of the su(1,1) Lie algebra and a time-splitting approach, we present an alternative method of solving the dynamics of a time-dependent quantum harmonic oscillator for any initial state. We find an iterative analytical solution given by simple recurrence relations that are very well suited for numerical calculations. We use our solution to reproduce and analyse some results from the literature to prove the usefulness of our method. We also discuss the efficiency in squeezing by comparing the parametric resonance modulation with the so-called Janszky-Adam scheme.