论文标题
二次依赖时间量子谐波振荡器
Quadratic Time-dependent Quantum Harmonic Oscillator
论文作者
论文摘要
我们为哈密顿级级别提供了一种谎言代数方法，涵盖了驱动的参数量子谐波振荡器，其中参数集（质量，频率，驱动强度和参数泵）是时间依赖性的。我们基于统一的转化方法为我们的一般二次二级量子谐波模型提供了解决方案。例如，我们向周期驱动的量子谐波振荡器展示了一个分析解决方案，而无需旋转波近似。它适用于任何给定的失沟和耦合力量制度。为了进行验证，我们为历史的Caldirola-Kanai Quantum谐波振荡器提供了分析解决方案，并表明我们框架中存在一个单一的转换，将其广义版本带入了Paul Trap Hamiltonian。此外，我们还展示了我们的方法如何提供广义模型的动力学，其在实验室框架中数字上的schrödinger方程变得不稳定。
We present a Lie algebraic approach to a Hamiltonian class covering driven, parametric quantum harmonic oscillators where the parameter set -- mass, frequency, driving strength, and parametric pumping -- is time-dependent. Our unitary-transformation-based approach provides a solution to our general quadratic time-dependent quantum harmonic model. As an example, we show an analytic solution to the periodically driven quantum harmonic oscillator without the rotating wave approximation; it works for any given detuning and coupling strength regime. For the sake of validation, we provide an analytic solution to the historical Caldirola--Kanai quantum harmonic oscillator and show that there exists a unitary transformation within our framework that takes a generalized version of it onto the Paul trap Hamiltonian. In addition, we show how our approach provides the dynamics of generalized models whose Schrödinger equation becomes numerically unstable in the laboratory frame.
