Quantum Dynamical Simulation of a Transversal Stern--Gerlach Interferometer

TL;DR

This paper uses numerical simulations to investigate whether a transversal Stern--Gerlach interferometer can achieve partial-beam recombination, ultimately confirming its fundamental irreversibility in quantum dynamics despite ideal conditions.

Contribution

It provides the first detailed numerical simulation demonstrating the irreversibility of a transversal Stern--Gerlach interferometer's quantum evolution under ideal conditions.

Findings

Quantum dynamics are fundamentally irreversible in the interferometer.

Numerical simulation confirms theoretical predictions.

Perfect control does not enable reversibility.

Abstract

Originally conceived as a gedankenexperiment, an apparatus consisting of two Stern--Gerlach apparatuses joined in an inverted manner touched on the fundamental question of the reversibility of evolution in quantum mechanics. Theoretical analysis showed that uniting the two partial beams requires an extreme level of experimental control, making the proposal in its original form unrealizable in practice. In this work we revisit the above question in a numerical study concerning the possibility of partial-beam recombination in a spin-coherent manner. Using the Suzuki--Trotter numerical method of wave propagation and a configurable, approximation-free magnetic field, a simulation of a transversal Stern--Gerlach interferometer under ideal conditions is performed. The result confirms what has long been hinted at by theoretical analyses: the transversal Stern--Gerlach interferometer quantum dynamics is fundamentally irreversible even when perfect control of the associated magnetic fields and beams is assumed.