发表机构
Università di Napoli Federico II; SPIN-CNR; INFN, Sezione di Napoli（那不勒斯费德里科二世大学; 意大利国家研究委员会自旋物理研究所; 意大利国家核物理研究院那不勒斯分部）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文研究自旋-玻色子模型中量子Fisher信息的动力学交叉，通过解析与数值模拟揭示浴谱结构、温度及能量弛豫对量子比特能隙估计精度的影响。
AI 中文摘要
我们研究了一个与玻色子环境耦合的二能级系统的动力学量子Fisher信息，重点关注量子比特能隙的估计。我们将解析计算与数值控制的矩阵乘积态模拟相结合。在零温度下精确可解的纯退相欧姆区域中，长时间量子Fisher信息表现出依赖于耦合的代数行为，从而导致动力学交叉：在弱耦合下它无界增长，在交叉耦合处趋近于有限的渐近值，在强耦合下则消失。在有限温度下，热涨落抑制了长时间增长并产生有限时间最大值，其对方差耦合的依赖性保留了零温交叉的清晰特征。我们证明，在非欧姆浴中，这种交叉在零温度下不存在：长时间量子Fisher信息在亚欧姆区域消失，在超欧姆区域发散。相反，在非零温度下，对于超欧姆二次浴，交叉出现且交叉耦合变得依赖于温度。此外，在零温欧姆区域，我们引入了额外的振幅阻尼系统-浴耦合，该耦合诱导能量弛豫。这种弛豫通道将无界的长时间增长替换为与约化相互作用基态相关的有限渐近量子Fisher信息，而纯退相交叉的特征在早期动力学中持续存在。这些结果建立了浴的低频结构与动力学间隙传感的渐近计量学行为之间的直接联系，并展示了热涨落和能量弛豫如何正则化量子Fisher信息的理想纯退相动力学交叉。
英文摘要
We investigate the dynamical quantum Fisher information of a two-level system coupled to a bosonic environment, focusing on the estimation of the qubit gap. We combine analytical calculations with numerically controlled matrix-product-state simulations. In the exactly solvable pure-dephasing Ohmic regime at zero temperature, the long-time quantum Fisher information displays a coupling-dependent algebraic behavior, leading to a dynamical crossover: it grows without bound at weak coupling, approaches a finite asymptotic value at the crossover coupling, and vanishes at strong coupling. At finite temperature, thermal fluctuations suppress the long-time growth and generate a finite-time maximum, whose dependence on the dephasing coupling retains a clear signa- ture of the zero-temperature crossover. We show that this crossover is absent at zero temperature in non-Ohmic baths: the long-time quantum Fisher information vanishes in the sub-Ohmic and diverges in the super-Ohmic regimes. At non-zero temperature instead, the crossover appears for a super-Ohmic quadratic bath and the crossover coupling becomes temperature-dependent. Moreover, in the zero-temperature Ohmic regime, we introduce an additional amplitude-damping system-bath coupling that induces energy relaxation. This relaxation channel replaces the unbounded long-time growth with a finite asymptotic quantum Fisher information associated with the reduced interacting ground state, while a signature of the pure-dephasing crossover persists in the early-time dynamics. These results establish a direct connection between the low-frequency structure of the bath and the asymptotic metrological behavior of dynamical gap sensing, and show how thermal fluctuations and energy relaxation regularize the ideal pure-dephasing dynamical crossover of the quantum Fisher information.
Comments12 pages, 9 figures
