Noise driven escape times in trapped ion systems

Trapped atomic ions are a promising platform for large scale quantum computation. To date, one of their biggest drawbacks has been the effects of 'anomalous motional heating' caused by electric field noise associated with trap surfaces. Precise understanding of the underlying mechanisms remains elusive, and this is a problem of considerable interest since motional heating impacts the fidelity of coherent operations and the length of time during which they can be performed. In order to shed light on these processes, we carry out simulations of first passage time distributions (FPTDs) associated with ion heating in the highly underdamped limit. These FPTDs make it possible to distinguish between correlated 'multiplicative' or 'parametric forcing' noise, and uncorrelated 'additive' noise. At long times, we find that the first passage time distribution (i.e., the distribution of times taken for the ion to gain a certain kinetic energy starting from the same initial condition) displays exponential decay for additive noise, while the decay for multiplicative noise appears to have a more complex form. In this talk, the focus is mostly on a classical model, but connections to quantum models and experimental realizations are also touched upon.