Nonclassical characteristic functions for highly sensitive measurements

Characteristic functions are shown to be useful for highly sensitive measurements. Redistributions of motional Fock states of a trapped atom can be directly monitored via the most fragile nonclassical part of the characteristic function. The method can also be used for decoherence measurements in optical quantum-information systems.

Figure 1

Characteristic functions $G_m\left(k\right)$ versus $k$ for number states $m=10$ (full line), 9 (dashed-dotted line), and 11 (dotted line), together with the classical limit $G_{\text{gr}}\left(k\right)=e^{-k^2∕2}$ (dashed line).

Figure 2

The time evolution is shown for the occupation probability $p_{10}\left(t\right)$ of the state $|m=10⟩$, the normalized mean excitation number $n\left(t\right)$, the Mandel parameter $Q\left(t\right)$, and the normalized characteristic function $g_{10}\left(k_{\text{max}},t\right)$ for $\overline{n}=1$.

Figure 3

Time evolution of the normalized mean photon number $n\left(t\right)$, the quadrature variance $s\left(t\right)$, and the characteristic function $g_{\text{sv}}\left(k_{\text{max}},t\right)$ of an initial squeezed vacuum state with $r=1.32$ for $\overline{n}=1$.