Nakazato Hiromichi, Sergi Alessandro, Migliore Agostino, Messina Antonino
Department of Physics, Waseda University, Tokyo 169-8555, Japan.
Dipartimento di Scienze Matematiche e Informatiche, Scienze Fisiche e Scienze della Terra, Università degli Studi di Messina, Viale F. Stagno d'Alcontres 31, 98166 Messina, Italy.
Entropy (Basel). 2023 Jan 3;25(1):96. doi: 10.3390/e25010096.
We report the step-by-step construction of the exact, closed and explicit expression for the evolution operator U(t) of a localized and isolated qubit in an arbitrary time-dependent field, which for concreteness we assume to be a magnetic field. Our approach is based on the existence of two independent dynamical invariants that enter the expression of SU(2) by means of two strictly related time-dependent, real or complex, parameters. The usefulness of our approach is demonstrated by exactly solving the quantum dynamics of a qubit subject to a controllable time-dependent field that can be realized in the laboratory. We further discuss possible applications to any SU(2) model, as well as the applicability of our method to realistic physical scenarios with different symmetry properties.
我们报告了在任意随时间变化的场中，一个局域且孤立的量子比特的演化算符U(t)的精确、封闭且显式表达式的逐步构建过程，为具体起见，我们假定该场为磁场。我们的方法基于两个独立动力学不变量的存在，它们通过两个严格相关的随时间变化的实参数或复参数进入SU(2)的表达式。通过精确求解一个处于可控随时间变化场中的量子比特的量子动力学（该场可在实验室中实现），证明了我们方法的实用性。我们进一步讨论了其在任何SU(2)模型中的可能应用，以及我们的方法在具有不同对称性质的现实物理场景中的适用性。
