Phase uncertainties of a squeezed state
Matthias Freyberger, W. P. Schleich · Physical Review A · 1994
We investigate various measures of phase uncertainty in their dependence on the average number of photons for the case of a phase squeezed state. We use the following three measures: (i) the geometrical uncertainty (\ensuremath{\delta}${\mathit{cphi}}_{\mathit{g}}$${)}^{2}$, (ii) the dispersion (\ensuremath{\delta}${\mathit{cphi}}_{\mathit{d}}$${)}^{2}$, and (iii) the rotational width (\ensuremath{\delta}${\mathit{cphi}}_{\mathit{r}}$${)}^{2}$. Whereas (\ensuremath{\delta}${\mathit{cphi}}_{\mathit{g}}$${)}^{2}$ and (\ensuremath{\delta}${\mathit{cphi}}_{\mathit{r}}$${)}^{2}$ decay quadratically with the average number of photons 〈n〉, the dependence of (\ensuremath{\delta}${\mathit{cphi}}_{\mathit{d}}$${)}^{2}$ is only of the form ln〈n〉/〈n${\mathrm{〉}}^{2}$. We give physical pictures for these scaling laws.