Noise Driven Quantum First Passage Time Distributions in Ion Traps

A Quantum First-Passage Time Distribution (QFPTD) is the distribution of times at which an identically prepared quantum system is first observed to have escaped some neighborhood. Here, we use these distributions to study the noise-driven heating of trapped ion motion after ground state cooling. We demonstrate a novel single-shot measurement scheme whose binary outcome tells us whether or not the motional energy of the harmonically-trapped ion has exceeded a given energy threshold, thereby enabling us to measure this distribution. These FPTDs make it possible to distinguish between correlated 'multiplicative' or 'parametric forcing' noise, and uncorrelated 'additive' noise. We present analytic solutions to this problem and show good agreement with the known classical limit. We also discuss some of the subtleties related to quantum measurement that distinguish Quantum First Passage Time Distributions from their classical counterparts.