The fifth-order nonlinear polarizability has been extensively studied in the field of quantum communication due to its ease of manipulation. By adjusting the relative size of the Rabi frequency and dephasing rate of the dressing field, natural non-Hermitian exceptional points can be generated, and further evolution can be achieved by varying the types of dressing fields. However, as the demand for information capacity in quantum communication continues to increase, research on the higher-order seventh-order nonlinear polarizability, based on four-photon states, and the number of coherent channels and resonance positions has gradually come to the forefront. This paper focuses on the simultaneous generation of a seventh-order nonlinear polarizability through a spontaneous eight-wave mixing (SEWM) process in an atomic medium involving four photons. Compared to the fifth-order nonlinear polarizability, the seventh-order polarizability shows an exponential increase in coherent channels and resonance positions due to its strong dressing effect. Additionally, the interaction between the four photons is stronger than that between three photons, making it possible for even the difficult-to-dress eigenvalues to be influenced by the dressing field and dephasing rate, resulting in more complex coherent channels. These are manifested as more complex, damped Rabi oscillations, with periods that can be controlled by the dressing field. These findings may contribute to a promising new method for quantum communication.
The fifth-order nonlinear polarizability has been extensively studied in the field of quantum communication due to its ease of manipulation. By adjusting the relative size of the Rabi frequency and dephasing rate of the dressing field, natural non-Hermitian exceptional points can be generated, and further evolution can be achieved by varying the types of dressing fields. However, as the demand for information capacity in quantum communication continues to increase, research on the higher-order seventh-order nonlinear polarizability, based on four-photon states, and the number of coherent channels and resonance positions has gradually come to the forefront. This paper focuses on the simultaneous generation of a seventh-order nonlinear polarizability through a spontaneous eight-wave mixing (SEWM) process in an atomic medium involving four photons. Compared to the fifth-order nonlinear polarizability, the seventh-order polarizability shows an exponential increase in coherent channels and resonance positions due to its strong dressing effect. Additionally, the interaction between the four photons is stronger than that between three photons, making it possible for even the difficult-to-dress eigenvalues to be influenced by the dressing field and dephasing rate, resulting in more complex coherent channels. These are manifested as more complex, damped Rabi oscillations, with periods that can be controlled by the dressing field. These findings may contribute to a promising new method for quantum communication.
A natural non- Hermitian system is constructed based on 85Rb atoms and multi-dressing fields. On this basis, the influence of different dressing fields on symmetry breaking and energy level degeneracy during four-photon spontaneous eight-wave mixing based on seventh-order nonlinear effects is investigated, and four-photon correlations are analyzed. When the dressing Rabi frequency dominates, the real part splits, leading to in phase constructive dressing, its symmetry breaking is localized, non-degenerate, Abelian and has low symmetry. When the dephase rate dominates, the imaginary part splits, leading to out-of-phase destructive dressing, its symmetry breaking is nonlocal, degenerate, non- Abelian and highly symmetric. The interactions between the dressing fields and the eigenvalue splitting modes of two double dressing effects that have third-order EPs are compared, and the role of the internal and external dressing fields in the formation of third-order EPs is clarified. The third-order non-Hermitian interaction between two dressing fields of the nested scheme is strongest and weakest for the parallel scheme, with the cascade scheme intermediate between them. This study is of value for the detection and quantum storage of quantum states.
Abstract With a wide range of potential applications, the generation of nonclassical multiphoton and number states has attracted renewed interest recently. Here, a correlated quadphoton with seventh‐order nonlinear susceptibility is reported in which all four photons are simultaneously created via an eight‐wave mixing (EWM) process in an atomic medium. The efficiency of the pure EWM process is low, which results from the small order of magnitude of the seventh‐order nonlinear susceptibility (the quadphoton correlation with four periods corresponding to 8 channels and 12 resonance positions). But the EWM process has a strong dressing effect. It not only increases the nonlinear susceptibility, but also produces 15 or 16 resonance positions in the dressing state picture. In addition, with the energy conservation of these positions, 12 coherent channels can be generated in this system. According to the interference between multichannels of the quadphoton, the quadphoton coincidence count appears as a damped Rabi oscillation, which has eight or ten oscillation periods. If only the nonlinear optical response is considered, the coincidence counts of the quadphoton behave as a damped Rabi oscillation with periods that can be controlled by the dressing field. These outcomes may contribute to a new promising method for quantum communication.
Abstract The generation of a nonclassical multi-photon has aroused renewed interest in recent years. Here, we propose a new method to generate tri-photon and quad-photon correlations in time via a double-dressing spontaneous six-wave mixing and eight-wave mixing process in an atomic ensemble, respectively. When we only consider the nonlinear optical response, the coincidence counts of tri and quad photon serves as damped coherent Rabi oscillation. The coincident count of tri (quad) photon contains three (four) conditional two-photon correlation with 10 or 30 (26, 28 or 38) periods, corresponding to 11 or 19 (18 or 20) modes. These mode and periods of tri and quad photon result from destructive interference from the possible 4 or 8 six wave and 18 eight wave coherent channels, respectively. In addition, for tri-photon, the greater double-dressing field strength is, the fewer the number of periods are. The coherent times are also controlled by the double-dressing effect. Such results have potential applications in multi-mode quantum communication and quantum network.
Multipartite entanglement has emerged as a valuable quantum resource for constructing large-scale quantum networks. However, the presence of non-Hermitian features induced by natural microscopic quantum systems significantly modifies the overall response of nonlinear parametric processes, thereby enabling direct manipulation of multipartite entanglement properties. In this study, we demonstrate the generation of multimode entanglement through atomic four-wave mixing (FWM) and analyze the properties of exceptional points (EP) under dressing control in non-Hermitian systems. By leveraging dressing-controlled atomic nonlinearity, we achieve versatile EPs and higher-order EPs by carefully tuning the atomic multi-parameter in the cascading FWM system. Additionally, we investigate the entanglement properties of various permutations of the output signal modes using the positive partial transpose (PPT) criterion. Notably, under non-Hermitian control, the application of single-, double-, and N-dressing splits leads to coherent multichannel control and further extends the scale of quantum entanglement. The outcomes of our research offer a novel approach to actively control non-Hermitian quantum phenomena without relying on artificial photonic structures. Furthermore, this paves the way for the realization of complex quantum information tasks by exploiting the non-Hermitian characteristics of the light-matter interaction.
Non-Hermitian degeneracy, also known as exceptional point, has been recently seen as a new way to engineer the response of open physical systems. Based on natural non-Hermitian atomic coherence, we investigate spontaneous six-wave mixing (SSWM) and eight-wave mixing (SEWM) processes under both parity–time (PT) and anti-parity–time (anti-PT) symmetry, and we obtain high-dimensional coherent channels under third-order energy-level splitting. Finally, we reveal that the third-order non-Hermitian interaction between two dressing fields of the nested scheme is the strongest, and the parallel scheme is the weakest, with the cascade scheme considered intermediate between them. It can also be used to develop quantum memory devices with enhanced sensitivity in the atom-like system.
The response of open physical systems has recently been recognized as a novel way to engineer non-Hermitian degeneracies, also known as exceptional points (EPs). We investigate the fourth-order parity-time (PT) and anti-parity-time (APT) symmetries for phase conjugation and self-diffraction under spontaneous six-wave mixing (SSWM) processes across various dressing schemes, including parallel, parallel-cascade, parallel-nested, pure-nested, cascade-nested, pure-cascade, and nested-cascade triple dressing schemes. Our investigation reveals that during the “self-diffraction” process sequential fourth-order non-Hermitian interactions between nested and cascade-nested triple dressing fields, where the photon dressing Rabi frequency exhibits dominance, lead to the sequential fourth-order quantization characterized by five EPs. Meanwhile, a sequential third-order PT–APT quantization is governed by six EPs under the dominance of the dephasing rate. Pure-cascade and nested-cascade triple dressing schemes exhibit a third-order quantization accompanied by four EPs. Additionally, the differential interplay between two dressing dephasing rates yields eight EPs in the pure-cascade triple dressing scheme. In the context of phase conjugation, pure-nested and cascade-nested dominated by the photon dressing Rabi frequency manifest a fourth-order PT–APT symmetric quantization characterized by two EPs. Simultaneously, a third-order PT–APT quantization characterized by six EPs results from an enhanced dephasing rate. Finally, three dressing schemes (parallel, parallel-nested, and parallel-cascade) exhibit second-order quantization arising from weakest non-Hermitian interaction. These outcomes are used to develop quantum memory devices with enhanced sensitivity in the atomic system.