Department of Physics and Astronomy, University of Rochester, Rochester, New York 14627, USA.
Center for Coherence and Quantum Optics, University of Rochester, Rochester, New York 14627, USA.
Nat Commun. 2017 Mar 9;8:14695. doi: 10.1038/ncomms14695.
Quantum metrology has been studied for a wide range of systems with time-independent Hamiltonians. For systems with time-dependent Hamiltonians, however, due to the complexity of dynamics, little has been known about quantum metrology. Here we investigate quantum metrology with time-dependent Hamiltonians to bridge this gap. We obtain the optimal quantum Fisher information for parameters in time-dependent Hamiltonians, and show proper Hamiltonian control is generally necessary to optimize the Fisher information. We derive the optimal Hamiltonian control, which is generally adaptive, and the measurement scheme to attain the optimal Fisher information. In a minimal example of a qubit in a rotating magnetic field, we find a surprising result that the fundamental limit of T time scaling of quantum Fisher information can be broken with time-dependent Hamiltonians, which reaches T in estimating the rotation frequency of the field. We conclude by considering level crossings in the derivatives of the Hamiltonians, and point out additional control is necessary for that case.
量子计量学已经在具有时不变哈密顿量的各种系统中进行了研究。然而，对于具有时变哈密顿量的系统，由于动力学的复杂性，对量子计量学知之甚少。在这里，我们研究了具有时变哈密顿量的量子计量学，以弥补这一差距。我们获得了时变哈密顿量中参数的最优量子 Fisher 信息，并表明通常需要适当的哈密顿量控制来优化 Fisher 信息。我们推导出了最优的哈密顿量控制，通常是自适应的，以及达到最优 Fisher 信息的测量方案。在一个旋转磁场中qubit 的最小示例中，我们发现了一个令人惊讶的结果，即具有时变哈密顿量的量子 Fisher 信息的 T 时间标度的基本限制可以被打破，在估计磁场的旋转频率时，可以达到 T。最后，我们考虑了哈密顿量导数的能级交叉，并指出在这种情况下需要额外的控制。
