论文标题
反驳提出的公理以定义确切的旋转波近似
Refuting a Proposed Axiom for Defining the Exact Rotating Wave Approximation
论文作者
论文摘要
对于线性驱动的量子两级系统或量子系统，可以使用Arxiv中引入的精确旋转波近似：1807.02858在旋转框架中沿着旋转框架中的旋转框架轨迹的一组频点。这项工作引入了有效的哈密顿系列$ \ mathcal h _ {\ text {eff}} $生成平滑的量子轨迹；该系列是使用Magnus膨胀和泰勒系列（Magnus-Taylor扩展）的组合获得的。然而，由于不能保证该哈密顿系列的任意脉冲形状会融合，因此相同的工作假设有效的哈密顿量的公理定义。提出的公理的前两个定义$ \ Mathcal H _ {\ text {eff}} $ to（i）进行分析，并且（ii）生成频镜的时间演变。在这项工作中，我们探究了第三个公理---由上面提到的平滑轨迹的动机---即（iii）变异原理，表明在整个脉冲持续时间内采取的汉密尔顿积极特征值的整体是由此$ \ nathcal h _ _ _ {\ feff text {\ feff}} $最小化的。我们通过上述积分的各种最小化来反驳第三个公理的有效性。
For a linearly driven quantum two-level system, or qubit, sets of stroboscropic points along the cycloidal-like trajectory in the rotating frame can be approximated using the exact rotating wave approximation introduced in arXiv:1807.02858. That work introduces an effective Hamiltonian series $\mathcal H_{\text{eff}}$ generating smoothed qubit trajectories; this series has been obtained using a combination of a Magnus expansion and a Taylor series, a Magnus-Taylor expansion. Since, however, this Hamiltonian series is not guaranteed to converge for arbitrary pulse shapes, the same work hypothesizes an axiomatic definition of the effective Hamiltonian. The first two of the proposed axioms define $\mathcal H_{\text{eff}}$ to (i) be analytic and (ii) generate a stroboscopic time evolution. In this work we probe a third axiom---motivated by the smoothed trajectories mentioned above---namely, (iii) a variational principle stating that the integral of the Hamiltonian's positive eigenvalue taken over the full pulse duration is minimized by this $\mathcal H_{\text{eff}}$. We numerically refute the validity of this third axiom via a variational minimization of the said integral.
