We studied the second-order correlation function of computational ghost imaging, and we gave the expressions of second-order correlation function in the signal and background region. We found the total intensity of the modulated source influences the visibility of the reconstructed image. We discussed the positive-negative correlation phenomenon in a computational ghost imaging (CGI) system, and a protocol was given to distinguish the positive and negative correlations. This protocol allows us to determine the dividing line of positive and negative correlations before sampling, and it was verified by our simulations and experiments; the imaging quality of computational ghost imaging can be greatly improved by using this protocol.

The experimental implementation of computational ghost imaging based on orthogonalized patterns usually consists of two steps, corresponding to the illumination of the positive and negative elements. Here, we put forward a novel technique which avoids "negative illumination" and involves a single round of measurements. Our method is based on the properties of the second-order correlation function in Hadamard-based computational ghost imaging. Experimental results show that object information may be effectively recovered with half of the measurements compared to the conventional differential scheme. As a matter of fact, the application of our scheme is not limited to the Hadamard pattern, but it may be applied also to other orthogonal matrices. As such, it may be relevant for the general development of computational ghost imaging.

The Duffing Chaos System can detect weak signals that are obscured by Gaussian noise because it is sensitive to specific signal functions and can withstand noise. In this paper, we investigate the use of intermittent chaotic phenomena in fractional-order incommensurate Duffing chaotic systems for weak signal detection. This new intermittent chaotic state has not appeared in integer-order Duffing systems before, so this phenomenon reflects the superiority of fractional-order Duffing systems. We start by giving the incommensurate fractional-order Duffing system’s weak signal detection model. Then design a time series-based judgment method that successfully separates chaotic, intermittent chaotic, and limit cycle states. Finally, the intermittent chaotic of fractional-order detection system is used to determine the amplitude and frequency of the weak signals to calculate the detection performance. The results show that the weak signal can be detected at a maximum signal-to-noise ratio of $$-$$ - 13.26 dB for single-detection oscillator amplitude detection. When detecting the frequency, a single-detection oscillator can detect the frequency range of 1050 rad/s, proving that the fractional-order chaos detection system is better than the integer-order chaos detection system.

We investigate conventional photon blockade in a non-degenerate four wave mixing system with Kerr non-linearity. By analyzing the Hamiltonian of the system, we have acquired the corresponding condition to implement photon anti-bunching effect. And we solve the master equation with the purpose of obtaining solutions numerically. We find that the analytic conditions could be consistent with numerical results, and photon blockade could be realized in this system. Furthermore, we discuss the effect of several parameters on the realization of conventional photon blockade in detail. The results show that four wave mixing interaction and Kerr non-linearity could significantly enhance the conventional photon blockade effect, whereas the dissipation rate has a negative effect on implementing photon blockade.