Accessing the non-equal-time commutators of a trapped ion

TL;DR

This paper presents a method to measure non-equal-time commutators in a trapped ion system, providing insights into time-ordering effects in quantum dynamics through electronic-state measurements.

Contribution

It introduces a procedure to extract non-equal-time commutators from experimental data in a trapped ion setup, linking measurable quantities to fundamental quantum time-ordering effects.

Findings

Successful demonstration of the extraction method using generated data.

Direct measurement of the expectation value of the interaction Hamiltonian.

Insights into the role of time-ordering in quantum evolution.

Abstract

The vibronic dynamics of a trapped ion in the resolved-sideband regime can be described by the explicitly time-dependent nonlinear Jaynes-Cummings model. It is shown that the expectation value of the interaction Hamiltonian and its non-equal-time commutator can be determined by measuring the electronic-state evolution. This yields direct insight into the time-ordering contributions to the unitary time evolution. In order to prove extraction of the quantities of interest works for possibly real data, we demonstrate the procedure by means of generated data.