Quantum parameter estimation with the Landau-Zener transition

Abstract

We investigate the fundamental limits in precision allowed by quantum mechanics from Landau-Zener transitions, concerning Hamiltonian parameters. While the Landau-Zener transition probabilities depend sensitively on the system parameters, much more precision may be obtained using the acquired phase, quantified by the quantum Fisher information. This information scales with a power of the elapsed time for the quantum case, whereas it is time independent if the transition probabilities alone are used. We add coherent control to the system and increase the permitted maximum precision in this time-dependent quantum system. The case of multiple passes before measurement, Landau-Zener-Stueckelberg interferometry, is considered, and we demonstrate that proper quantum control can cause the quantum Fisher information about the oscillation frequency to scale as ${T}^{4}$, where $T$ is the elapsed time. These results are foundational for frequency standards and quantum clocks.