Spatial correlation functions for the collective degrees of freedom of many trapped ions

TL;DR

This paper explores how spatial correlation functions in trapped ion systems reveal quantum correlations, analyzing their behavior for different states and detection regimes to deepen understanding of collective quantum phenomena.

Contribution

It introduces a method to connect electronic state measurements with quantum correlations in the ions' vibrational modes, focusing on Gaussian, thermal, and squeezed states.

Findings

Correlation functions reflect quantum correlations in ion vibrational states.

Long detection-time limit simplifies the correlation analysis.

Differences between thermal and squeezed states are characterized.

Abstract

Spatial correlation functions provide a glimpse into the quantum correlations within a quantum system. Ions in a linear trap collectively form a nonuniform, discretized background on which a scalar field of phonons propagates. Trapped ions have the experimental advantage of each having their own "built-in" motional detector: electronic states that can be coupled, via an external laser, to the ion's vibrational motion. The post-interaction electronic state can be read out with high efficiency, giving a stochastic measurement record whose classical correlations reflect the quantum correlations of the ions' collective vibrational state. Here we calculate this general result, then we discuss the long detection-time limit and specialize to Gaussian states, and finally we compare the results for thermal versus squeezed states.