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.

We propose an innovative design for quantum batteries (QBs) that involves coupling two-level systems to a topological photonic waveguide. Employing the resolvent method, we analytically explore the thermodynamic performance of QBs. First, we demonstrate that in the long-time limit, only bound states significantly contribute to the stored energy of QBs. We observe that near-perfect energy transfer can occur in the topologically nontrivial phase. Moreover, the maximum stored energy exhibits singular behavior at the phase boundaries, where the number of bound states undergoes a transition. Second, when a quantum charger and a quantum battery are coupled at the same sublattice within a unit cell, the ergotropy becomes immune to dissipation at that location, facilitated by a dark state and a topologically robust dressed bound state. Third, we show that as dissipation intensifies along with the emergence of the quantum Zeno effect, the charging power of QBs experiences a temporary boost. Our findings offer valuable guidance for improving quantum battery performance in realistic conditions through structured reservoir engineering.

In this work, we propose a scheme in three-mode optical systems to simulate a strongly coupled optomechanical system. The nonreciprocity observed in such a three-mode optomechanical circulatory system (OMCS) is explored. To be specific, we first derive a quantum Langevin equation (QLE) for the strongly coupled OMCS by suitably choosing the laser field, then we give a condition for the frequency of the laser and the mechanical decay rate, beyond which the optomechanical system has a unidirectional transmission regardless of how strong the optomechanical coupling is. The optomechanically induced transparency is also studied. The present results can be extended to a more general two-dimensional optomechanical system and a planar quantum network, and the prediction is possible to be observed in an optomechanical crystal or integrated quantum superconducting circuit. This scheme paves a way for the construction of various quantum devices that are necessary for quantum information processing.

Motivated by entanglement protection, our work utilizes a resonance effect to enhance optomechanical entanglement in the coherent-state representation. We propose a filtering model to filter out the significant detuning components between a thermal-mechanical mode and its surrounding heat baths in the weak-coupling limit. We reveal that protecting continuous-variable entanglement involves the elimination of degrees of freedom associated with significant detuning components, thereby resisting decoherence. We construct a nonlinear Langevin equation of the filtering model and numerically show that the filtering model doubles the robustness of the stationary maximum optomechanical entanglement to the thermal fluctuation noise and mechanical damping. Furthermore, we generalize these results to an optical cavity array with one oscillating end mirror to investigate the long-distance optimal optomechanical-entanglement transfer. Our study breaks new ground for applying the resonance effect to protect quantum systems from decoherence and advancing the possibilities of large-scale quantum information processing and quantum network construction.

We derive a compact analytical solution of the $n\mathrm{th}$-order equal-time correlation functions by using scattering matrix ($S$ matrix) under a weak coherent state input. Our solution applies to any dissipative quantum system that respects the U(1) symmetry. We further extend our analytical solution into two categories depending on whether the input and output channels are identical. The first category provides a different path for studying cross-correlation and multiple-drive cases, while the second category is instrumental in studying waveguide quantum electrodynamics systems. Our analytical solution allows for easy investigation of the statistical properties of multiple photons even in complex systems. Furthermore, we have developed a user-friendly open-source library in Python known as the quantum correlation solver, and this tool provides a convenient means to study various dissipative quantum systems that satisfy the above-mentioned criteria. Our study enables using $S$ matrix to study the photonic correlation and advance the possibilities for exploring complex systems.