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 ${\chi }^{\left(3\right)}$ Kerr nonlinearity. In this paper, we study the photon blockade in two weakly coupled nonlinear cavities via ${\chi }^{\left(2\right)}$ nonlinearity, where ${\chi }^{\left(2\right)}$ 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 ${\chi }^{\left(3\right)}$ nonlinearity are discussed. This scheme is not sensitive to the change of decay rates, which makes the experimental realization easy.

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.

In this paper, we show that nonreciprocal unconventional photon blockade can be observed in a spinning cavity immersed in a degenerate optical parametric amplifier (OPA) driven by the laser driving with weak Kerr nonlinearities through the Fizeau drag. We analytically derive the optimal conditions for strong antibunching, which are in good agreement with those obtained by numerical simulations. Under the weak driving condition, we discuss the physical origins of the nonreciprocal unconventional photon blockade, which originates from the destructive interference between different paths from the ground state to two-photon states by driving the device from the left side. While the quantum interference paths are broken when the device is driven from the right side, which leads to the occurring of the photon bunching. Moreover, we extend the above results to the general non-Markovian regimes, in which the cavity couples with a thermal reservoir consisting of collection of infinite oscillators (bosonic photonic modes). We show nonreciprocal unconventional photon blockade exhibits a transition from the non-Markovian to Markovian regimes by controlling environmental spectral width regardless of the weakness of OPA gain and driving field.

The semiconductor diode, which acts as an electrical rectifier and allows unidirectional electronic transports, is the key to information processing in integrated circuits. Analogously, an optical rectifier (or diode) working at specific target wavelengths has recently become a highly sought-after device in optical communication and signal processing. In this paper, we propose a scheme to realize an optical diode for photonic transport at the level of few photons. The system consists of two spatially overlapping single-mode semiconductor microcavities coupled via ${\chi }^{\left(2\right)}$ nonlinearities. The photon blockade is predicted to take place in this system. These photon blockade effects can be achieved by tuning the frequency of the input laser field (driving field). Based on those blockades, we analytically derive the one- and two-photon current in terms of a zero and a finite time-delayed two-order correlation function. The results suggest that the system can serve as a one- and two-photon quantum optical diode which allows transmission of photons in one direction much more efficiently than in the other.

The photon blockade based on weak nonlinearities is called unconventional photon blockade. The studies of the unconventional photon blockade in recent decades are all limited to Markovian approximation. In this paper, we propose a scheme to achieve a strong photon antibunching in non-Markovian reservoir. An exact non-Markovian master equation for the optical cavity coupled with a degenerate optical parametric amplifier (DOPA) is derived. We show that this unconventional photon blockade originates from the destructive interference between two paths which are formed by the DOPA pump and a driving field. Unconventional single-photon blockades that exhibit a transition from the non-Markovian to Markovian regime by controlling environmental spectral width regardless of the weakness of DOPA gain and driving field are found. We analytically derive an optimal condition for strong antibunching, which is in good agreement with that obtained by the full numerical simulation. The presented results then are compared with that given by Markovian approximation in the weak-coupling limit. Our scheme might have paved an avenue towards the investigations of unconventional photon blockades in many other non-Markovian quantum systems in quantum optics.

The photon blockade based on destructive quantum interference is called the unconventional photon blockade (UPB), which has been intensively studied in Markovian systems but barely explored in the non-Markovian ones. In this paper, we construct a coupled-cavities system to achieve UPB with the non-Markovian effect, where the dissipationless left cavity and Markovian dissipative right cavity are respectively mediated by two-photon pump and single-photon driving field. Through the equivalence between the Markovian master equation and Heisenberg-Langevin equation for the environment initialization in the vacuum state, we can derive the exact non-Markovian Heisenberg-Langevin equation and reduced master equation for the left cavity, which contains the two-photon pump and effective single-photon driving field. In the non-Markovian regime (the dissipation falling below a threshold), the effective single-photon driving field holds nonzero, which can lead to UPB occurring due to a closed quantum interference path forming. When the dissipation exceeds the threshold, the system enters the Markovian regime, where UPB weakens. Especially, if the dissipation approaches infinity, UPB for the left cavity disappears due to the effective single-photon driving field tending to zero. We analytically derive an optimal condition for UPB, which is in good agreement with that obtained by the numerical simulation. We also discuss the situation where both cavities have dissipations. Finally, the above model is extended to a general system involving a dissipationless left cavity (mediated by two-photon pump) coupling with noninteracting dissipative right cavities (driven by single-photon driving fields). Our scheme might pave an avenue towards applications on photon statistics and quantum optics with the non-Markovian effect.