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Physical Review A

Unconventional photon blockade with non-Markovian effects in driven dissipative coupled cavities

H. Z. Shen, Ji-Feng Yang, X. X. Yi

Published Apr 29, 2024• 62 citations
Publisher

Abstract

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.

DOI
10.1103/physreva.109.043714

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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.
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.
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.
Abstract We have investigated the unconventional photon blockade (UPB) in a hybrid system consisting of a Jaynes–Cummings model nonlinearly coupled with two other modes via a three-wave mixing interaction, operating in the weak coupling regime (compared with the decay rates of the system). We present both analytical and numerical results, obtained by solving the Schrödinger equation and the quantum master equation, respectively. The results show that the numerical simulations agree well with the analytical predictions and that the UPB effect would occur in this hybrid system both in the cavity-driven and atom-driven conditions. Under both driving conditions, the hybrid system could exhibit superior performance over the Jaynes–Cummings model under the same driving condition, i.e. achieve a stronger photon blockade effect. The influences of driving strength and coupling coefficient on photon blockade effect have also been discussed. Our finding may have potential applications in single-photon sources design.
In this paper, we show that the photon blockade (PB) can be observed in a nonreciprocal way with a driven spinning atom-cavity coupled filled with [Formula: see text] nonlinear medium. We analytically derive the optimal conditions for strong photon 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 (UPB), which originates from the destructive quantum 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 occurrence of the photon bunching. Moreover in the opposite direction of driving the device, we also observe another nonreciprocal UPB effect, which can occur by generating bunching and antibunching effects via driving the device from the left and right sides under the derived optimal conditions, respectively. Finally, we cannot observe the nonreciprocal UPB phenomenon with the large cavity decay compared to the atomic spontaneous emission rate (or the bad cavity limit), and give the physical reason behind it. Possible experimental implementation for this scheme is presented.
Abstract Quantum information processing, a key component of quantum information science, has attracted considerable attention. Its realization requires physical platforms and resources, among which optical systems and single-photon sources based on photon blockade (PB) have been widely employed. Here we investigate PB behaviors in a coupled optical cavity system driven by both single- and two-photon fields. The optimal conditions for PB are obtained with respect to the two-photon driving strength and cavity-laser detuning via analytical calculations. Using these optimal solutions, we show that a significant PB effect is achievable even with weak Kerr nonlinearity, and confirm that this behavior corresponds to unconventional PB (UPB) through a comparison of the second- and third-order correlation functions. Furthermore, our analysis reveals that UPB can be enhanced by two-photon dissipation. These results provide theoretical strategies for enhancing UPB, and offer insight into its fundamental mechanism.
We theoretically study the photon blockade (PB) effect in a double-cavity optomechanical system with the two-photon driving. By analytical calculations and numerical simulations, the physical mechanisms of conventional photon blockade (CPB) and unconventional photon blockade (UPB) are discussed in detail. And then we obtain the optimal parameter conditions for PB. In our work, there exist both the CPB induced by strong nonlinear interaction and the UPB caused by quantum interference. In particular, we find that CPB and UPB can occur simultaneously under the same parameters. In addition, we also prove that the appropriate values of nonreciprocal coupling and two-photon driving are favorable to the improvement of PB. Our proposal provides an idea for simultaneously realizing CPB and UPB in the optomechanical system and offers a route for constructing high-quality single-photon sources.