Efficient algebraic solution for a time-dependent quantum harmonic oscillator

Abstract

Using operator ordering techniques based on BCH-like 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 literature in order to prove the usefulness of the method and, based on these references, we discuss efficiency in squeezing, when comparing the parametric resonance modulation and the Janszky-Adam scheme.

arXiv comment15 pages, 5 figures

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• New BCH-like relations of the su(1, 1), su(2) and so(2, 1) Lie algebras
• Exact solution of a time-dependent quantum harmonic oscillator with two frequency jumps via the Lewis-Riesenfeld dynamical invariant method
• Quasienergy operators and generalized squeezed states for systems of trapped ions
• Algebraic approach to a two-qubit quantum thermal machine
• The time-dependent harmonic oscillator revisited
• Quantum-based solution of time-dependent complex Riccati equations
• Time-dependent quantum harmonic oscillator: a continuous route from adiabatic to sudden changes
• The time-dependent quantum harmonic oscillator: a pedagogical approach via the Lewis-Riesenfeld dynamical invariant method
• Non-Classicality and Non-adiabaticity in a Single Trapped Ion
• $\text{Symdyn}$: an automated algebraic solution for high-order quantum systems