A study of decoherence effects in the Stern-Gerlach experiment using matrix Wigner functions

TL;DR

This paper uses matrix Wigner functions to analyze decoherence effects in the Stern-Gerlach experiment, providing insights into quantum dynamics and decoherence timescales with environmental interactions.

Contribution

It introduces a phase space analysis of the Stern-Gerlach experiment with decoherence, offering analytical formulas and a new decoherence timescale based on matrix Wigner functions.

Findings

Decoherence causes diffusive behavior in position and momentum distributions.

Non-diagonal terms decay over time, quantifying decoherence.

Derived a new decoherence timescale differing from previous models.

Abstract

We analyze the Stern-Gerlach experiment in phase space with the help of the matrix Wigner function, which includes the spin degree of freedom. Such analysis allows for an intuitive visualization of the quantum dynamics of the apparatus. We include the interaction with the environment, as described by the Caldeira-Leggett model. The diagonal terms of the matrix provide us with information about the two components of the state, that arise from interaction with the magnetic field gradient. In particular, from the marginals of these components, we obtain an analytical formula for the position and momentum probability distributions in presence of decoherence, that show a diffusive behavior for large values of the decoherence parameter. These features limit the dynamics of the present model. We also observe the decay of the non-diagonal terms with time, and use this fact to quantify the amount of decoherence, from the norm of those terms in phase space. From here, we can define a decoherence time scale, which differs from previous results that make use of the same model.