Clocking the Quantum Sojourn Time: Spurious Scatterings and Correction to the Larmor Clock

TL;DR

This paper examines the quantum sojourn time measurement using Larmor clocks, identifies spurious scattering effects, and proposes corrections to ensure physically meaningful, positive-definite sojourn times across energy regimes.

Contribution

It introduces a correction method for the Larmor clock to eliminate unphysical scattering effects, ensuring positive sojourn times in quantum systems.

Findings

Corrected sojourn times are positive for arbitrary potentials.

The method applies to both unitary and non-unitary quantum clocks.

High- and low-energy limits of the corrected times are physically consistent.

Abstract

We revisit the notions of the quantum-mechanical sojourn time in the context of the quantum clocks to enquire whether the sojourn time be clocked without the clock affecting the dynamics of the wave motion. Upon recognizing that the positivity of conditional sojourn time is not ensured even in the case of physically co-evolving clock mechanisms, we trace its origins to the non-trivial inadvertent scattering arising from the disparity, however weak, engendered by the very clock potential. Specifically, our investigations focus on the Larmor spin rotation-based unitary clock where the alleviation of these unphysical contributions has been achieved by correcting the mathematical apparatus of extracting the sojourn times. The corrections have been obtained for both the spin precession-based and spin alignment-based scenarios. The sojourn times so obtained are found to have proper high- and low-energy limits and turn out to be positive definite for an arbitrary potential. The regimen provided here is general and appeals equivalently for unitary as well as non-unitary clocks where the clock-induced perturbations couple to the system Hamiltonian.