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arXiv:quant-ph/0002091 · Journal of Optics B Quantum and Semiclassical Optics

Prospects for photon blockade in four-level systems in the N configuration with more than one atom

Andrew D. Greentree, John A. Vaccaro, S.R. de Echaniz, Alan V. Durrant, J. P. Marangos

Published May 24, 2000• 38 citations
arXivHTMLPDF

Abstract

We show that for appropriate choices of parameters it is possible to achieve photon blockade in idealized one-, two- and three-atom systems. We also include realistic parameter ranges for rubidium as the atomic species. Our results circumvent the doubts cast by recent discussion in the literature (Grangier et al 1998 Phys. Rev. Lett. 81 2833, Imamoglu et al 1998 Phys. Rev. Lett. 81 2836) on the possibility of photon blockade in multi-atom systems.

DOI
10.1088/1464-4266/2/3/306

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We show that for appropriate choices of parameters it is possible to achieve photon blockade in idealized one-, two- and three-atom systems. We also include realistic parameter ranges for rubidium as the atomic species. Our results circumvent the doubts cast by recent discussion in the literature (Grangier et al 1998 Phys. Rev. Lett. 81 2833, Imamoglu et al 1998 Phys. Rev. Lett. 81 2836) on the possibility of photon blockade in multi-atom systems.
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.
We have achieved a conventional photon blockade and two-photon blockade in a second-order nonlinear system with a two-level atom embedded in a high-frequency cavity. The physical mechanisms behind the implementation of both types of photon blockade are explained, and analytical conditions for achieving a conventional photon blockade are derived, which are consistent with the numerical solutions of the master equation in the steady-state limit. By appropriately setting the system parameters, we can achieve simultaneous conventional photon blockade in the high-frequency cavity and two-photon blockade in the low-frequency cavity. The effects of driving factors and environmental temperature on photon blockade are analyzed. The adjustability of the coupling coefficient between the high-frequency cavity and the atom, as well as the nonlinear coupling coefficient between different nanocavities, is discussed in the context of implementing conventional photon blockades. The tunability of these coupling coefficients may significantly reduce the experimental complexity of implementing the system.
This paper discusses conventional photon blockade (CPB) and two-photon blockade (2PB) in a three-wave mixing system embedded with a two-level atom in the high-frequency cavity. Analytical conditions for achieving CPB and 2PB are obtained by analyzing the eigenvalues of the system Hamiltonian. Numerical solutions, derived by solving the master equation in a truncated Fock space, are consistent with the analytical conditions. Detailed analysis of system parameters reveals the influence of the embedded atom on achieving different types of photon blockade. Unlike previous schemes, this system can achieve single-photon blockade simultaneously in three photon modes. Additionally, by adjusting the coupling coefficient between the atom and high-frequency mode photons, the system can switch between single-photon blockade and two-photon blockade in the high-frequency mode.
The most simple and seemingly straightforward application of the photon blockade effect, in which the transport of one photon prevents the transport of others, would be to separate two incoming indistinguishable photons to different output ports. We show that time-energy uncertainty relations inherently prevent this ideal situation when the blockade is implemented by a two-level system. The fundamental nature of this limit is revealed in the fact that photon blockade in the strong coupling regime of cavity QED, resulting from the nonlinearity of the Jaynes-Cummings energy level structure, exhibits efficiency and temporal behavior identical to those of photon blockade in the bad cavity regime, where the underlying nonlinearity is that of the atom itself. We demonstrate that this limit can be exceeded, yet not avoided, by exploiting time-energy entanglement between the incident photons. Finally, we show how this limit can be circumvented completely by using a three-level atom coupled to a single-sided cavity, enabling an ideal and robust photon routing mechanism.
We study the photon blockade phenomenon in a nanocavity containing a single four-level quantum emitter. By numerically simulating the second-order autocorrelation function of the intra-cavity field with realistic parameters achievable in a state-of-the-art photonic-crystal nanocavity, we show that significant photon blockade effects appear even outside the strong coupling regime. We introduce an intuitive picture of the photon blockade that explains the performance difference between the two-level and the four-level emitter schemes reported in previous works, as well as why—in contrast to a cavity containing a two-level atom—signatures of photon blockade appear and should be experimentally observable outside the strong coupling regime when a four-level emitter is used. Finally, we show that thanks to the emitter–cavity coupling achievable in a nanocavity, photon blockade can be realized despite the large frequency difference between the relevant optical transitions in realistic four-level emitters, which has so far prevented the experimental realization of this photon blockade scheme.