Test of Causal Non-Linear Quantum Mechanics by Ramsey Interferometry on the Vibrational Mode of a Trapped Ion

TL;DR

This paper tests a causal non-linear extension of quantum mechanics using Ramsey interferometry on a trapped ion's vibrational mode, setting a new upper limit on the non-linear perturbation's magnitude.

Contribution

It provides an experimental test of causal non-linear quantum theories using a well-controlled trapped ion system, establishing a stringent upper limit on non-linear effects.

Findings

Set a limit of 5.4×10⁻¹² on the non-linear perturbation magnitude

Demonstrated Ramsey interferometry as a sensitive probe for non-linear quantum effects

Provided experimental constraints on causal non-linear quantum theories

Abstract

Kaplan and Rajendran have recently demonstrated that non-linear and state-dependent terms can be consistently added to quantum field theory to yield causal non-linear time evolution in quantum mechanics. Causal non-linear theories have the unavoidable feature that their quantum effects are dramatically sensitive to the full physical spread of the quantum state of the system. As a result, such theories are not well tested by conventional atomic and nuclear spectroscopy. By using a well-controlled superposition of vibrational modes of a $^{40}$Ca$^+$ ion trapped in a harmonic potential, we set a stringent limit of $5.4\times 10^{-12}$ on the magnitude of the unitless scaling factor $\tilde{\epsilon}_{\gamma}$ for the predicted causal, non-linear perturbation.