Noncommutative $q$-photon-added coherent states

We construct the photon-added coherent states of a noncommutative harmonic oscillator associated to a $q$-deformed oscillator algebra. Various nonclassical properties of the corresponding system are explored, first, by studying two different types of higher-order quadrature squeezing, namely, the Hillery type and the Hong-Mandel type, and second, by testing the sub-Poissonian nature of photon statistics in higher order with the help of the correlation function and the Mandel parameter. Also, we compare the behavior of different types of quadrature and photon number squeezing of our system with those of the ordinary harmonic oscillator by considering the same set of parameters.

Figure 1

Comparison of Hillery-type higher-order squeezing coefficient of a harmonic oscillator (scattered dots) versus a NCHO (for $q=0.9$) (solid and dotted lines) as a function of (a) $\varphi$ for different values of $m$, with $N=1,\alpha =2.1$, and (b) $\left|\alpha \right|$ for different values of $N$, with $\varphi =0.1,m=1$.

Figure 2

Comparison of Hong-Mandel–type higher-order squeezing coefficient of a harmonic oscillator (scattered dots) versus a NCHO (for $q=0.9$) (solid and dotted lines) as a function of (a) $\varphi$ for different values of $m$, with $N=4,\alpha =1.0+1.2i$, and (b) $\left|\alpha \right|$ for different values of $N$, with $\varphi =0.1,m=3$.

Figure 3

Comparison of higher-order correlation function of a harmonic oscillator (scattered dots) versus a NCHO (for $q=0.9$) (solid and dotted lines) as a function of $\left|\alpha \right|$ (a) for different values of $m$, with $N=2$ and (b) for different values of $N$, with $m=1$.

Figure 4

Comparison of higher-order Mandel parameter of a harmonic oscillator (scattered dots) versus a NCHO (for $q=0.9$) (solid and dotted lines) as a function of $\left|\alpha \right|$ (a) for different values of $m$, with $N=2$ and (b) for different values of $N$, with $m=1$.

Figure 5

Higher-order Mandel parameter of a NCHO as a function of $q$ for different values of $\alpha$, with $m=1$ and $N=2$.