Unitary dynamics and finite-time measurements: a case study

TL;DR

This paper investigates how finite-time measurements influence quantum decay processes, revealing that measurement parameters can either hinder or accelerate decay, with implications for quantum control.

Contribution

It provides an analytical and numerical analysis of the interplay between unitary dynamics and measurement coupling in a quantum chain, extending beyond ideal projective measurements.

Findings

Decay can be slowed or sped up depending on measurement parameters.

Energy shifts of the measured site affect decay dynamics.

Finite-time measurement effects are significant in quantum decay control.

Abstract

The inhibition of the decay of a quantum system by frequent measurements is known as quantum Zeno effect. Beyond the limit of projective measurements, the interplay between the unitary dynamics of the system and the coupling to a measurement apparatus becomes relevant. We explore this interplay by considering a quantum particle moving on a one-dimensional chain. A local measurement by coupling to an apparatus with a two-dimensional Hilbert space detects the presence of the particle on a specific chain site. The decay of the population is studied analytically for a two-site chain and numerically for a larger system as a function of the measurement time and the time between subsequent measurements. Particular attention is given to the shift of the energy of the measured site due to the coupling to the apparatus. The decay of the initial population can be hindered or accelerated, depending on the chosen system and the coupling parameters.