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Advanced Quantum Technologies

Non‐Hermitian Photon Blockade With Quantum Jumps

S. Yin, X. Q. Hao, X. X. Yi

Published Jul 1, 2026• 0 citations
Publisher

Abstract

ABSTRACT Recent studies demonstrate that the anharmonicity caused by losses, encoded in the imaginary parts of the eigenvalues of the non‐Hermitian Hamiltonian, can lead to strong photon antibunching, known as the non‐Hermitian photon blockade (NHPB). The non‐Hermiticity of the system might originate from the effective non‐Hermitian Hamiltonian derived from the Lindblad master equation by neglecting the quantum jumping terms. However, neglecting these terms means the system‐environment interactions are not fully considered, leading to features missed in the blockade effect. This motivates us to study the effects of these jumps on NHPB. In this work, we employ the effective Hamiltonian approach to the master equation to investigate the blockade effect. This approach treats the jumping terms as perturbations, making the analysis clear. We show that jumps can increase the relative second‐order correlation () and weaken the blockade. This highlights that quantum jumps can degrade the strong photon antibunching. Furthermore, we demonstrate that this feature can be attributed to the joint effect of the reduction in both the second‐order correlation () and the intensity (), which can be interpreted as jump‐induced changes in the mean photon numbers in the steady state.

DOI
10.1002/qute.70358

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ABSTRACT Recent studies demonstrate that the anharmonicity caused by losses, encoded in the imaginary parts of the eigenvalues of the non‐Hermitian Hamiltonian, can lead to strong photon antibunching, known as the non‐Hermitian photon blockade (NHPB). The non‐Hermiticity of the system might originate from the effective non‐Hermitian Hamiltonian derived from the Lindblad master equation by neglecting the quantum jumping terms. However, neglecting these terms means the system‐environment interactions are not fully considered, leading to features missed in the blockade effect. This motivates us to study the effects of these jumps on NHPB. In this work, we employ the effective Hamiltonian approach to the master equation to investigate the blockade effect. This approach treats the jumping terms as perturbations, making the analysis clear. We show that jumps can increase the relative second‐order correlation () and weaken the blockade. This highlights that quantum jumps can degrade the strong photon antibunching. Furthermore, we demonstrate that this feature can be attributed to the joint effect of the reduction in both the second‐order correlation () and the intensity (), which can be interpreted as jump‐induced changes in the mean photon numbers in the steady state.
One possible realization of non-Hermitian systems is based on open quantum systems by omitting quantum jumping terms in the master equation. This is a good approximation at short times where the effects of quantum jumps can be ignored. However, the jumps can affect the long-time dynamics of the system, motivating us to take the jumps into account in these studies. In this paper, by treating the quantum jumps as perturbations, we examine the effect of the quantum jumps on the non-Hermitian system. For this purpose, we first derive an effective Hamiltonian to describe the dynamics of the open quantum system based on the master equation, then expand the eigenstates and eigenenergies up to the first and second order in the quantum jumps. Finally, we apply our theory to a dissipative two-level system and dissipative fermionic superfluids. The effect of the quantum jump on the dynamics and the nonequilibrium phase transition is demonstrated and discussed.
Abstract Non-Hermitian (NH) systems and the Lindblad form master equation have always been regarded as reliable tools in dissipative modeling. Intriguingly, existing literature often obtains an equivalent NH Hamiltonian by neglecting the quantum jumping terms in the master equation. However, there lacks investigation into the effects of discarded terms as well as the unified connection between these two approaches. In this study, we study the Su–Schrieffer–Heeger model with collective loss and gain from a topological perspective. When the system undergoes no quantum jump events, the corresponding shape matrix exhibits the same topological properties in contrast to the traditional NH theory. Conversely, the occurrence of quantum jumps can result in a shift in the positions of the phase transition. Our study provides a qualitative analysis of the impact of quantum jumping terms and reveals their unique role in quantum systems.
Abstract 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.
Under the weak driving limitation, we find that the strong photon blockade can be triggered when all the eigenvalues of the non-Hermitian Hamiltonian are equal to zero, so we name this the zero eigenvalues of a photon blockade induced by a non-Hermitian Hamiltonian. The possibility of realizing single- and two-photon blockades is investigated in the cavity QED system. A negative effective decay rate of the cavity is required, so the gain medium is needed to compensate the intrinsic loss rate of the cavity. The photon antibunching can be realized in both strong and weak nonlinear regimes, which is different from the conventional photon blockade and unconventional photon blockade. Our scheme has paved an avenue towards the study of photon blockades.
We investigate the relation between non-Hermitian Hamiltonian and Lindblad dynamics in nonequilibrium open quantum systems. Non-Hermitian models can extend phase diagrams and enable sensing advantages, but such effects often rely on postselection, raising questions about their relevance for unconditional dynamics. Using a minimal two-qubit setup mediating a heat current, we compare local and global Markovian master equations with their non-Hermitian counterparts. We observe that exceptional points emerge only in the local master equation and in the corresponding non-Hermitian Hamiltonian at sufficiently strong nonequilibrium. We further consider hybrid configurations, where one bath is treated with a Lindblad description and the other with a non-Hermitian approach, interpolating between the two extremes. Our results contribute understanding the role of quantum jumps and exceptional points in nonequilibrium open quantum systems and identify a simple, experimentally accessible architecture, realizable, for instance, in circuit-QED platforms, for their exploration.
ABSTRACT We investigate how parity‐time () symmetry influences photon blockade in an atom‐coupled dual‐cavity quantum electrodynamics (QED) system, with a focus on distinguishing the underlying mechanisms. Statistical analysis demonstrates that photon blockade exhibits qualitatively distinct behaviors in the ‐symmetric and symmetry‐broken phases, thereby providing a clear signature of the phase transition. In this ‐symmetric structure, the two‐level atom provides the required nonlinearity, while cavity‐cavity coupling under ‐symmetric control cooperatively enhances photon antibunching, leading to simultaneous photon blockade in both the passive and the active cavities. These phenomena are comprehensively analyzed using both analytical solutions of the Schrödinger equation and numerical simulations of the master equation. Comparisons with non‐‐symmetric configurations reveal that symmetry significantly enhances photon antibunching, mean photon number and promotes cooperative blockade behavior across both cavities. In contrast to conventional photon blockade schemes, our approach remains effective under weak coupling and weak nonlinearity conditions, offering a robust and tunable pathway toward realizing high‐performance single‐photon sources in non‐Hermitian quantum systems.