[Paper Review] Zero-dimensional models for gravitational and scalar QED decoherence

Qidong Xu, M. P. Blencowe|arXiv (Cornell University)|May 6, 2020

Cosmology and Gravitation Theories3 references4 citations

TL;DR

This paper develops zero-dimensional toy models for gravitational and scalar QED decoherence by mapping linearized gravity and scalar QED interactions onto harmonic oscillator system-bath models. It demonstrates that the scalar-gravity model maps to phase damping, while scalar QED maps approximately to two-photon damping, and uses an operational visibility measure to quantify decoherence in a gauge-invariant way, offering insights for probing quantum gravity effects in tabletop experiments.

ABSTRACT

We investigate the dynamics of two quantum mechanical oscillator system-bath toy models obtained by truncating to zero spatial dimensions linearized gravity coupled to a massive scalar field and scalar QED. The scalar-gravity toy model maps onto the phase damped oscillator, while the scalar QED toy model approximately maps onto an oscillator system subject to two-photon damping. The toy models provide potentially useful insights into solving for open system quantum dynamics relevant to the full scalar QED and weak gravitational field systems, in particular operational probes of the decoherence for initial scalar field system superposition states.

Motivation & Objective

• To develop simplified 0d system-bath models that capture essential features of scalar field systems weakly coupled to linearized gravity and scalar QED.
• To investigate decoherence dynamics in these models using standard open quantum systems techniques, avoiding reliance on non-gauge-invariant density matrix elements.
• To test an operational, interferometric visibility measure as a gauge-invariant probe of decoherence for superposition states.
• To assess the viability of standard approximation methods—such as the rotating wave approximation and perturbative Langevin equations—for analyzing full quantum field systems with non-quadratic interactions.
• To guide future analysis of full scalar matter–weak gravity systems by validating methods on tractable toy models before extending to realistic, low-energy experiments.

Proposed method

• Truncate the full scalar field–gravity and scalar QED actions to zero spatial dimensions, reducing the system to a single harmonic oscillator coupled to a bath of harmonic oscillators.
• Model the scalar-gravity interaction via a non-quadratic coupling resembling the energy-momentum tensor coupling in linearized gravity, leading to phase damping dynamics.
• Model the scalar QED interaction via a non-quadratic coupling resembling the minimal coupling of a scalar field to the electromagnetic potential, leading to two-photon damping dynamics.
• Apply the rotating wave approximation (RWA) to derive effective quantum Langevin equations for the system oscillator under both models.
• Use the Wigner function and position probability density to visualize time evolution of superposition states and interference fringes.
• Define and compute fringe visibility ν as an operational, gauge-invariant measure of decoherence, tracking the decay of interference patterns over time.

Experimental results

Research questions

• RQ1 How do zero-dimensional system-bath models of linearized gravity and scalar QED reproduce known decoherence mechanisms such as phase damping and two-photon damping?
• RQ2 Can an operational, interferometric visibility measure serve as a gauge-invariant alternative to analyzing off-diagonal density matrix elements in gravitational decoherence?
• RQ3 To what extent do standard open quantum systems approximations—such as RWA and Markovian assumptions—remain valid and useful in the context of weakly coupled quantum field theories?
• RQ4 How does the initial preparation of the system-environment state affect the initial decoherence burst, particularly in the presence of unknown UV cutoffs?
• RQ5 Can insights from these 0d models be reliably extended to analyze full scalar field systems coupled to weak gravitational or electromagnetic fields?

Key findings

• The scalar-gravity toy model maps exactly onto the phase-damped oscillator, confirming that linearized gravity induces decoherence via a coupling analogous to standard phase damping.
• The scalar QED toy model approximately maps onto a two-photon damped oscillator, indicating that scalar QED interactions lead to a distinct, non-phase-damping decoherence channel.
• Interference fringes in the position probability density survive significantly longer in the scalar QED model than in the scalar-gravity model, with measurable visibility persisting after 190 cycles despite decay of the initial coherent state peaks.
• Visibility reduction rates increase with higher damping strength and bath temperature, but unlike single-photon damping, the rate decreases with larger initial coherent state amplitude in the two-photon model.
• The operational visibility measure ν provides a gauge-invariant, measurable proxy for decoherence that avoids the pitfalls of non-gauge-invariant density matrix elements.
• Finite initial state preparation times can mitigate spurious cut-off dependence in early decoherence dynamics, suggesting that initial state preparation is critical for reliable decoherence rate extraction.