Decoherence of a quantum gyroscope

TL;DR

This paper models a quantum gyroscope's decoherence through repeated interactions with spin-1/2 particles, revealing distinct relaxation and dephasing timescales and providing insights into quantum measurement stability.

Contribution

It introduces a simple model of decoherence for a quantum gyroscope using Heisenberg interactions, analyzing relaxation and dephasing in the semiclassical limit.

Findings

Coherent states evolve over classical timescales.

Dephasing occurs on a shorter, state-dependent timescale.

The model captures key decoherence mechanisms in quantum directional measurements.

Abstract

We study the behavior of a quantum gyroscope, that is, a quantum system which singles out a direction in space in order to measure certain properties of incoming particles such as the orientation of their spins. We show that repeated Heisenberg interactions of the gyroscope with several incoming spin-1/2 particles provides a simple model of decoherence which exhibits both relaxation and dephasing. Focusing on the semiclassical limit, we derive equations of motion for the evolution of a coherent state and investigate the evolution of a superposition of such states. While a coherent state evolves on a timescale given by the classical ratio of the angular momentum of the gyroscope to that of the incoming particles, dephasing acts on a much shorter timescale that depends only on the angular difference of the states in the superposition.