论文标题
时间依赖性量子谐波振荡器：从绝热到突然变化的连续途径
Time-dependent quantum harmonic oscillator: a continuous route from adiabatic to sudden changes
论文作者
论文摘要
在这项工作中，我们为问题提供了一个答案：量子谐波振荡器（HO）频率的突然或绝热是多么突然或绝热？为此，我们通过进行频率过渡来控制它的发生速度，从而调查了HO的行为，最初是处于其基本状态。该系统的结果状态显示为通过Bogoliubov转换相关的两个基础上的真空挤压状态。我们表征了两个碱基中挤压参数的时间演变，并通过改变从突然到绝热的频率过渡的速率来讨论其与绝热性的关系。最后，我们获得了一个分析近似表达，将挤压与过渡速率以及初始频率和最终频率有关。我们的结果阐明了与该系统的绝热定理有关的文献中的微妙和常见不准确性。
In this work, we provide an answer to the question: how sudden or adiabatic is a change in the frequency of a quantum harmonic oscillator (HO)? To do this, we investigate the behavior of a HO, initially in its fundamental state, by making a frequency transition that we can control how fast it occurs. The resulting state of the system is shown to be a vacuum squeezed state in two bases related by Bogoliubov transformations. We characterize the time evolution of the squeezing parameter in both bases and discuss its relation with adiabaticity by changing the rate of the frequency transition from sudden to adiabatic. Finally, we obtain an analytical approximate expression that relates squeezing to the transition rate as well as the initial and final frequencies. Our results shed some light on subtleties and common inaccuracies in the literature related to the interpretation of the adiabatic theorem for this system.
