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Physica Scripta

Conventional photon blockade in a four-wave mixing system with Kerr nonlinearity

Zhu-Xin Wang, Hui Min Yang, Xiaoqian Wang, Hongyu Lin, Zhihai Yao

Published Nov 15, 2022• 11 citations
Publisher

Abstract

Abstract 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.

DOI
10.1088/1402-4896/aca2fc

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Abstract 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.
The conventional photon blockade is studied in a three-wave-mixing system. The analytic conditions for realizing the photon blockade are obtained by analyzing the eigenvalues of the system Hamiltonian, which is expanded by an effective single excited space for the high-frequency mode. The numerical results are calculated by solving the master equation in a truncated Fock space, which agrees well with the analytic conditions. Different from the other schemes of the conventional photon blockade, photon antibunching can be realized in the three modes of the three-wave-mixing system simultaneously due to the nature of the system.
The conventional photon blockade (CPB) for high-frequency mode is investigated in a second-order nonlinear system with Kerr nonlinearity. By solving the master equation and calculating the zero-delay-time second-order correlation function g(2)(0), we obtain that strong photon antibunching can be achieved in this scheme. The optimal condition for strong antibunching is also calculated analytically and discussed in detail. We find that the Kerr nonlinearity can largely enhance the CPB effect in the high-frequency mode, and this scheme is not sensitive to the reservoir temperature. In addition, when compared with the linear coupled system, the system has obvious advantages in CPB implementation.
Based on the four wave mixing, a three mode nonlinear system is proposed. The single photon blockade is discussed through analytical analysis and numerical calculation. The analytical analysis shows that the conventional photon blockade and unconventional photon blockade can be realized at the same time, and the analytical conditions of the two kinds of blockade are the same. The numerical results show that the system not only has the maximum average photon number in the blockade region, but also can have strong photon anti-bunching in the region with small nonlinear coupling coefficient, which greatly reduces the experimental difficulty of the system. This optical system which can realize the compound photon blockade effect is helpful to realize the high-purity single photon source.
A high-quality single-photon blockade system can effectively enhance the quality of single-photon sources. Conventional photon blockade(CPB) suffers from low single-photon purity and high requirements for system nonlinearity, while unconventional photon blockade(UPB) has the disadvantage of low brightness. Recent research by [Laser Photon.Rev 14,1900279,2020] demonstrates that UPB can be used to enhance the strength of CPB, thereby improving the purity of single-photon sources. Research by [Opt. Express 30(12),21787,2022] shows that there is an intersection point between CPB and UPB in certain nonlinear systems, where the performance of single photons is better. In this study, we investigated the phenomenon of photon blockade in a non-degenerate four-wave mixing system, where CPB and UPB can occur simultaneously within the same parameter range. We refer to this phenomenon as composite photon blockade. Particularly, when the system achieves composite photon blockade, the value of g(2)(0) is smaller, and there are more single photons. We conducted analytical analysis and numerical calculations to study the conditions for the realization of CPB, UPB, and 2PB in the system, and discussed in detail the influence of system parameters on various blockade effects.
In this paper, the photon blockade effect in a nondegenerate four-wave-mixing system embedded with a two-level atom has been studied. By using an analytical calculation and numerical analysis, we find that both one-photon and two-photon blockade effects could be realized in this system by adjusting the parameters of the system. That is, (i) when the four-wave-mixing interaction and the atom-cavity coupling strength are not equal, the system can realize a one-photon blockade; (ii) when they are consistent with each other, the system can realize a two-photon blockade. In addition, we also discuss the influence of different parameters on the photon blockade effect in detail. The results show that the system constructed in this paper not only could enhance the one-photon blockade effect decisively, but also could implement a two-photon blockade easily with a well-designed energy-level structure, and evidently the blockade effect depends on the parameters of the system. All the results may provide theoretical references for single-photon and multiphoton sources or devices in designing future experiments and practical applications.
In this paper, the photon-pair blockade effect in a three-wave mixing system with Kerr nonlinearity has been studied. By analytical calculation and numerical analysis, we find that the conventional photon blockade and unconventional photon blockade of the photon pair could be realized simultaneously in the strong-coupling regime in this system, and the photon-pair blockade effect could be enhanced strongly by the combination of them. The combination could also lead to a much stronger photon-pair blockade effect in this hybrid system than in a three-wave mixing system, which may contribute to construction of single photon-pair sources with much higher purity without the loss of brightness. In addition, both the same-frequency and different-frequency photon-pair blockades could be realized in this scheme, which may contribute to construction of the same-frequency or different-frequency photon-pair sources or devices. All the results may provide useful theoretical references for the design of correlated photon-pair sources or devices in future experiments and applications.