论文标题
在快速测量下的量子系统的非热和zeno极限
Non-Hermitian and Zeno limit of quantum systems under rapid measurements
论文作者
论文摘要
我们深入研究了隔离量子系统的第一个检测时间之间的关系，该系统被强固定频率$ 1/τ$反复扰动，确定它是否在某些给定状态$ |中。 ψ_\ text {d} \ rangle $，以及带有附加想象潜力$ 2I \ hbar |的同一系统的吸收时间| ψ_\ text {d} \ rangle \langleψ_\ text {d} | /τ$。与以前的工作相反，我们直接比较了小$τ$（即Zeno，limit）中这两个问题的解决方案。我们发现相对于$τ$，在$ f（t）$中发现了缩放崩溃，并计算了zeno限制中第一个检测时间概率密度$ f（t）$的总检测概率以及矩的矩。我们表明，只要初始状态$ | ψ_\ text {in} \ rangle $不平行于检测状态，即只有$ | \langleψ_\ text {d} | ψ_\ text {in} \ rangle | <1 $。但是，当违反这种情况时，按时间尺度检测状态的较小概率密度大于$τ$，这在所有这种情况下都是四个不同的因素。我们以静电类比形式表达了两个问题的ZENO极限的解决方案。我们的结果通过数值模拟证实。
We investigate in depth the relation between the first detection time of an isolated quantum system that is repeatedly perturbed by strong local measurements with a large fixed frequency $1/τ$, determining whether it is in some given state $| ψ_\text{d} \rangle$, and the time of absorption to the same state of the same system with the added imaginary potential $2i\hbar | ψ_\text{d} \rangle \langle ψ_\text{d} | / τ$. As opposed to previous works, we compare directly the solutions of both problems in the small $τ$, i.e., Zeno, limit. We find a scaling collapse in $F(t)$ with respect to $τ$ and compute the total detection probability as well as the moments of the first detection time probability density $F(t)$ in the Zeno limit. We show that both solutions approach the same result in this small $τ$ limit, as long as the initial state $| ψ_\text{in} \rangle$ is not parallel to the detection state, i.e. as long as $| \langle ψ_\text{d} | ψ_\text{in} \rangle | < 1$. However, when this condition is violated, the small probability density to detect the state on time scales much larger than $τ$ is precisely a factor of four different for all such times. We express the solution of the Zeno limit of both problems formally in terms of an electrostatic analogy. Our results are corroborated with numerical simulations.
