Unconventional photon blockade in two coupled Kerr nonlinear cavities at resonance

Photon blockades are traditionally classified into conventional and unconventional types, depending on distinct physical mechanisms. Regarding the cavity decay rate κ, the conventional photon blockade takes place under strong nonlinearity condition (g>κ), whereas the unconventional photon blockade occurs in the regime of weak nonlinearity (g<κ). We here propose how to derive an optimal condition for photon blockade utilizing a two-photon Jaynes-Cummings model. Under this condition, the equal-time second-order correlation function reaches its minimum, leading to photon antibunching in both conventional and unconventional photon blockade regimes (g>κ and g<κ), even in g∼κ. This characteristic is termed universal photon blockade. By comparing it with the conventional and the unconventional photon blockades in the weak-driving limit, the advantages of universal photon blockade are revealed. Our proposal paves an avenue towards the future study of photon blockades and has potential applications in generating antibunched photons.

Traditionally, photon blockades (PB) are classified into two distinct categories—conventional and unconventional—based on their unique physical mechanisms. In relation to the cavity decay rate κ, conventional photon blockade occurs under conditions of strong nonlinearity (J&amp;gt;κ), while unconventional photon blockade is observed in situations of weak nonlinearity (J&amp;lt;κ). In this study, we examine a two-mode cavity optomechanical system (Jâ†â†b+Jââb̂†) and a two-photon parametric drive εp(â†â†+ââ). When the detunings significantly exceed the dissipation rates of the cavity (|Δa|,|Δb|≫κ), the optimal condition for PB becomes independent of the coupling strength. This implies that photon antibunching effects can occur in both strong and weak regimes (J&amp;gt;κ and J&amp;lt;κ), even when J∼κ, and we could achieve PB solely through the adjustment of detunings. Furthermore, we generalize the approach to the conversion between single photon and three photons (Jâ†3b+Jâ3b̂†) with a three-photon parametric drive εp(â†3+â3) and arrive at nearly identical conclusions. This work presents a method for implementing a single-photon source, which holds significant potential for practical engineering applications due to its independence from coupling strength.

We propose a hybrid cavity-magnon system scheme that integrates a yttrium iron garnet sphere with a microwave cavity filled with Kerr medium, aiming to achieve both conventional and unconventional photon blockade simultaneously. Our research demonstrates that by tuning the strength of the Kerr nonlinearity and adjusting the two-photon driving intensity, we can realize quantum effects associated with both types of photon blockade. Furthermore, through careful selection of system parameters, we have obtained optimal results for photon blockade under ideal conditions. This scheme fully exploits the advantages offered by both conventional and unconventional photon blockade mechanisms, effectively reducing the equal-time second-order photon correlation function while also achieving a higher mean photon number. It provides an alternative and experimentally feasible platform for preparing single-photon sources characterized by enhanced purity and brightness.

We study the interaction between a quantum-dot and a bi-mode\nmicro/nano-optical cavity composed of second-order nonlinear materials.\nCompared with the Jaynes-Cummings (J-C) model, except for a coherent weak\ndriving field, a strong pump light illuminates the two-mode optical cavity.\nAnalytical results indicate that the model exhibits abundant non-classical\noptical phenomena, such as conventional photon blockade induced by the\nnonlinear interaction between polaritons. It constitutes unconventional photon\nblockade induced by quantum interference due to parametric driving. We compare\nthe photon statistical properties and average photon number of the proposed\nmodel, J-C model, and double-mode driven optical cavity under the same\nparameters and the proposed model can obtain stronger antibunching photons and\nhigher average photon number.\n

&lt;sec&gt;The photon blockade effects in a system consisting of an artificial giant atom coupled with three cavities are investigated. By solving the Schrödinger equation, we obtain the steady-state probability amplitudes of the system and derive the analytical expressions for the equal-time second-order correlation function. Based on these analytical expressions, the optimal conditions for achieving the photon blockade under different driving conditions are derived in detail.&lt;/sec&gt;&lt;sec&gt;We first examine the energy spectra and transition pathways for the single-photon and two-photon excitations in weakly driven cavity mode, and then investigate the statistical properties of photons. It is demonstrated that the optimal conventional photon blockade can be achieved by selecting appropriate driving detuning as characterized by the equal-time second-order correlation function of &lt;inline-formula&gt;&lt;tex-math id="M3"&gt;\begin{document}$g^{\left(2\right)}\left(0\right)\approx{10}^{-3.4} $\end{document}&lt;/tex-math&gt;&lt;/inline-formula&gt;. Remarkably, we observe that both cavities of the system exhibit robust photon blockade effects against the weak driving. It is also found that with the increase of the coupling strength between the artificial giant atom and cavities, the photon blockade phenomenon becomes more pronounced while maintaining its robustness to the weak driving. Furthermore, we consider the case of simultaneously driving both the artificial giant atom and cavity modes. The unique multi-point coupling characteristics of the artificial giant atom provide additional transition pathways for photons, thereby allowing us to use the resulting quantum interference to further enhance photon blockade. When the system satisfies the optimal parametric conditions for both the conventional and unconventional photon blockade effects, one cavity exhibits exceptional photon blockade with &lt;inline-formula&gt;&lt;tex-math id="M4"&gt;\begin{document}$g^{\left(2\right)}\left(0\right)\approx{10}^{-6.5} $\end{document}&lt;/tex-math&gt;&lt;/inline-formula&gt;.&lt;/sec&gt;&lt;sec&gt;This research greatly relaxes the stringent parameter requirements for the experimental realization of single-photon sources and provides a theoretical support for improving their quality, which is crucial for achieving high-performance single-photon sources.&lt;/sec&gt;

&lt;sec&gt;By combining analytical solutions and numerical simulations, we investigate the control mechanism of photon blockade effects in a hybrid quantum system consisting of a Kerr-medium single-mode cavity coupled with an optical parametric amplifier (OPA).&lt;/sec&gt;&lt;sec&gt;To study photon blockade in the system, the dynamics are described by a master equation derived from the effective Hamiltonian, which considers single-mode cavity decay. In order to obtain analytical solutions under optimal photon blockade conditions, the quantum state of the system is expanded to the two-photon level based on the Fock state, and the steady-state probability amplitudes are derived by solving the Schrödinger equation, thereby yielding analytical expressions for the optimal photon blockade regime. The results demonstrate that photon blockade can be achieved in the system at appropriate parameters. Comparative analysis shows excellent agreement between the analytical results and numerical simulations of the equal-time second-order correlation function, validating both the correctness of the analytical solutions and the effectiveness of photon blockade in the system.&lt;/sec&gt;&lt;sec&gt;The numerical results show that the average photon number significantly increases under resonant conditions, providing theoretical support for optimizing single-photon source brightness, which is essential for achieving high-brightness single-photon sources.&lt;/sec&gt;&lt;sec&gt;Furthermore, variations in the driving phase can cause the optimal photon blockade region to shift in the two-dimensional parameter space of driving strength and OPA nonlinear coefficient, and even reverse the opening direction of the parabolic-shaped optimal blockade region. Both numerical and theoretical results confirm the regulatory effect of the driving phase on photon blockade.&lt;/sec&gt;&lt;sec&gt;Additionally, the influence of Kerr nonlinearity is examined. The results show that photon blockade persists robustly over a broad range of Kerr nonlinear strengths, exhibiting universal characteristics.&lt;/sec&gt;&lt;sec&gt;Physical mechanism analysis indicates that the photon blockade effect originates from destructive quantum interference between two photon transition pathways in the system under specific parameters, effectively suppressing two-photon excitation. Although Kerr nonlinearity modulates the energy levels of the system, it does not affect the quantum interference pathways, thus keeping the photon blocking effect stable over a wide parameter range.&lt;/sec&gt;

The photon blockade based on weak nonlinearities is called the unconventional photon blockade. The study of the unconventional photon blockade in recent decades has mainly focused on the ${\ensuremath{\chi}}^{(3)}$ Kerr nonlinearity. In this paper, we study the photon blockade in two weakly coupled nonlinear cavities via ${\ensuremath{\chi}}^{(2)}$ nonlinearity, where ${\ensuremath{\chi}}^{(2)}$ mediates the conversion of a single photon in the cavity with high frequency into two photons with low frequency in another cavity. When the two cavity modes are driven simultaneously, our calculations show that the strong photon antibunching can be obtained in the cavity. The optimal condition for strong antibunching is found by analytic calculations and numerical simulations, and discussions of the optimal condition are presented. The differences between the present scheme and that with ${\ensuremath{\chi}}^{(3)}$ nonlinearity are discussed. This scheme is not sensitive to the change of decay rates, which makes the experimental realization easy.

In this paper, the unconventional photon blockade is studied in a three-wave-mixing system with a non-degenerate parametric amplification. A method of only retaining the Fock-state basis in the interference path is used to calculate the optimal analytic conditions of unconventional photon blockade. The numerical results agree well with the analytic conditions, which verifies the validity of this method. Our calculations indicate that the strong photon antibunching can be obtained in the high-frequency mode of the three-wave mixing. And the influence of system parameters on photon blockade is also discussed.

In this paper, we show that photon blockade can be observed in a system with weak Kerr nonlinearities. The system consists of two spatially overlapping single-mode semiconductor cavities with tunable one- and two-photon tunneling. We find that both conventional and unconventional single-photon blockades are controllable by manipulating the phase in the hopping regardless of the weakness of nonlinearity. We refer to the photon blockade with weak nonlinearities as an unconventional photon blockade. The unconventional photon blockade effect originates from the destructive interference between different paths from the ground state to two-photon states. We analytically derive the exact optimal conditions for strong antibunching, which are in good agreement with those obtained by numerical simulations. The optimal parameters for photon blockade are derived. Based on these parameters, the semiconductor cavity systems can be used as a single-photon source in regimes of both weak and strong nonlinearities.

We propose how to achieve strong photon antibunching effect in a cavity-QED system coupled with two Rydberg–Rydberg interaction atoms. Via calculating the equal time second-order correlation function $$g^{(2)}(0)$$ , we find that the unconventional photon blockade and the conventional photon blockade appear in the atom-driven scheme, and they are both significantly affected by the Rydberg–Rydberg interaction. We also find that under appropriate parameters, one obtains the extremely strong photon antibunching by combining the conventional photon blockade and the unconventional photon blockade, and the mean photon number in the cavity can be improved significantly. In the cavity-driven scheme, the existence of the Rydberg–Rydberg interaction severely destroys the photon antibunching under the unconventional photon blockade mechanism. These results will help to guide the implementation of the single photon emitter in the Rydberg atoms-cavity system.

The unconventional photon blockade with weak χ (2) nonlinearity in a system consists of two single-mode cavities driving by two external fields is studied in this paper. The photon statistical properties, described by the second-order correlation function, are discussed, and the exact optimal conditions for strong photon anti-bunching is analytically derived. The optimal frequency detuning and nonlinear interaction strength for the strong photon anti-bunching are also obtained, which are in good agreement with numerical simulations. We find that the unconventional photon blockade effect can be controlled by tuning the relative phase between two complex driving fields when the two cavity modes are driven simultaneously. Our results provide a promising scheme for the coherent manipulation of photon blockade through tuning the relative phase between the two driving fields, which makes the experimental realization more flexible.

We explore a method for achieving photon blockade (PB) through a two-photon Jaynes-Cummings (JC) model that includes both cavity and atom drivings. Analytical expressions for the steady state are derived to calculate photon-number distribution and correlation functions. Based on this analysis, we establish the theoretical conditions required for generating PB by controlling both drivings and propose a scheme to identify conventional photon blockade (CPB) and unconventional photon blockade (UPB) by analyzing the second- and third-order correlation functions. We validate our findings through numerical simulations conducted in an artificial atom system. We discuss two cases, one in which the transition frequency of the two-level atom is in two-photon resonance with the cavity frequency and the other in which it is off-resonance. We observe a significant interplay between CPB and UPB effects in the resonant case. In the off-resonance case, we demonstrate that UPB can be achieved by manipulating the strengths of atom driving and cavity driving to satisfy a specific relationship while meeting the requirements for optimal detuning relations. This work provides essential insights into controlling the PB effect using the two-photon JC model with both the atom and cavity drivings.

We explore the photon blockade in optomechanical systems with a position-modulated Kerr-type nonlinear coupling, i.e. . We find that the Kerr-type nonlinear coupling can enhance the photon blockade greatly. We evaluate the equal-time second-order correlation function of the cavity photons and find that the optimal photon blockade does not happen at the single photon resonance. By working within the few-photon subspace, we get an approximate analytical expression for the correlation function and the condition for the optimal photon blockade. We also find that the photon blockade effect is not always enhanced as the Kerr-type nonlinear coupling strength g2 increases. At some values of g2, the photon blockade is even weakened. For the system we considered here, the second-order correlation function can be smaller than 1 even in the unresolved sideband regime. By numerically simulating the master equation of the system, we also find that the thermal noise of the mechanical environment can enhance the photon blockade. We give out an explanation for this counter-intuitive phenomenon qualitatively.

The unconventional photon blockade, which relies on the physical mechanism of quantum interference, is primarily investigated using a general master equation, where a weak nonlinearity must be presented in the system to achieve photon antibunching. In this study, we explore the unconventional photon blockade using an alternative master equation known as the two-photon absorption master equation, which is derived from the system and environment interaction via two-photon absorption. Specifically, we find that the unconventional photon blockade can be triggered in two-coupled cavities, where each cavity interacts with a two-photon absorption environment. Different from unconventional photon blockade via the general master equation, we show that the two-photon absorption acts as the weak nonlinearity, and this photon blockade corresponds to a large average photon number. To derive optimal conditions for achieving this blockade, we propose a non-Hermitian Hamiltonian method to describe the mode loss caused by the two-photon absorption. In addition, we highlight the distinctions between our proposal and other approaches for generating single-photon states based on two-photon absorption.

We propose a scheme of photon blockade in a system comprising of coupled cavities embedded in Kerr nonlinear material, where two cavities are driven and dissipated. We analytically derive the exact optimal conditions for strong photon antibunching, which are in good agreement with those obtained by numerical simulations. We find that conventional and unconventional photon blockades have controllable flexibilities by tuning the strength ratio and relative phase between two complex driving fields. Such unconventional photon-blockade effects are ascribed to the quantum interference effect to avoid two-photon excitation of the coupled cavities. We also discuss the statistical properties of the photons under given optimal conditions. Our results provide a promising platform for the coherent manipulation of photon blockade, which has potential applications for quantum information processing and quantum optical devices.