On the interpretation of single stochastic trajectories of the Wigner distribution
Year: 2015
Type: preprint
Abstract: individual stochastic realisations of squared mode amplit udes |�| 2 of the sampled Wigner distribution W(�), which we denote via ˜ Pn. We provide an operational definition of ˜ Pn in terms of the underlying Wigner function, which allows us to explicitly calculate the overlap between the two number distributions and hence quantify the statistical distance between them. We find that there is inde ed a close quantitative correspondence between Pn and ˜ Pn for a wide range of states, justifying the broadly accepted v iew that, for highly occupied modes, individual stochastic realisations of Wigner trajectorie s should approximately correspond to outcomes of single experiments. However, we also find counterexamples for whic h high mode occupation may not be sufficient for such an interpretation; we find instead that a more releva nt and sufficient requirement is the smoothness and broadness of the Wigner function W(�) for the state of interest relative to the scale of oscillatio ns of the Wigner function for a Fock state, W|ni(�).
Source: arXiv (Cornell University)
Language: English
Subfield: Atomic and Molecular Physics, and Optics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W1597020522