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

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

2008-07-22

arxiv.org/abs/0807.3500v1

Physics

Quantum Physics

23 pages, 2 figures

Scientific paper

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.

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