Nonclassical photon statistics

Some nonclassical properties of a particular state of light are demonstrated by computing the Wigner function. A quantum model of generating this state is proposed. A criterion called the distance variation difference is introduced to measure how far any state is from its corresponding coherent state.

Figure 1

Scheme for generating an Erlang process of order 2 from the initial Poisson process and notations for multicounting.

Figure 2

Diagram for enumerating the terms of the twofold PDF.

Figure 3

$Q\left(\alpha \right)$ functions versus $\alpha ∊\mathrm{Re}$ in dimensionless units for Erlang process of order $2$ with density $\lambda =4$. The function $Q_d\left(\alpha \right)$ is obtained taking into account only diagonal elements of the density operator.

Figure 4

Erlang process of order $2$. The Wigner function $W\left(\alpha \right)$ is plotted versus $\alpha$ in dimensionless units with $\phi =0$ for the average value of the photon number $\lambda =4$. The function $W_d\left(\alpha \right)$ is obtained when taking into account only diagonal elements of the density operator.

Figure 5

Erlang processes of order $2$. The Wigner function $W\left(\alpha \right)$ is plotted versus $\alpha$ in dimensionless units with $\phi =0$ for various average values of the photon number $\lambda =3,6,9$.

Figure 6

Erlang processes of order $r$. $W_d\left(\alpha \right)$ functions versus $\alpha$ in dimensionless units where $\phi =0$, the average value of the photon number $\lambda =9$, and for various values of $r=1,\dots ,5$. The function $W_d\left(\alpha \right)$ is obtained taking into account only diagonal elements of the density operator.

Figure 7

Variation distance function $D$ versus $\lambda$, the average value of the photon number, in dimensionless units for various states which are denoted T for thermal, M for mixture of coherent and thermal $(\varrho =0.1)$, C for coherent, Sq for squeezed, E for Erlang of order $2$, and S for superposition of two coherent states.