The concept of non‐Hermitian systems, also known as exceptional points (EPs), has recently emerged as a novel approach for designing the response of systems that exchange energy with the external environment. The system behaves as a non‐Hermitian Hamiltonian (NH Hamiltonian), the real part of which is related to the internal dynamics of the system, and the imaginary part reflects the energy exchange between the system and the outside environment. By utilizing double EIT windows and adjusting the intensity of the dressing field, the number and positions of eigenvalues can be modulated to construct quantum entanglement sources for non‐Hermitian systems, thereby laying the foundation for quantum communication and quantum computing. To prepare photon entanglement sources, it is necessary to study the correlation of high‐dimensional quantized energy levels under PT symmetry and symmetry breaking induced by the dressing field; Hamiltonian correlation matrix of the non‐Hermitian system characterizes the relationship between gain and loss, detuning and dephasing rate in the reaction energy‐level system, and the coupling relationship of the dressing field. The energy‐level system itself is non‐Hermitian, and the study of symmetry breaking is conducted by controlling EPs during the level control process through the dressing field, thus eliminating the need for introducing artificial photonic structures. The third‐order non‐Hermitian characteristics of the PT‐NH system reflect the positional relationship between the cascade field and the nested field. When the Rabi frequency (dephase rate) of the dressing field is the dominant factor, the real (imaginary) part of the eigenvalues is split, resulting in in‐phase (out‐of‐phase) constructive (destructive) transformations of the dressing order.
The concept of non‐Hermitian systems, also known as exceptional points (EPs), has recently emerged as a novel approach for designing the response of systems that exchange energy with the external environment. The system behaves as a non‐Hermitian Hamiltonian (NH Hamiltonian), the real part of which is related to the internal dynamics of the system, and the imaginary part reflects the energy exchange between the system and the outside environment. By utilizing double EIT windows and adjusting the intensity of the dressing field, the number and positions of eigenvalues can be modulated to construct quantum entanglement sources for non‐Hermitian systems, thereby laying the foundation for quantum communication and quantum computing. To prepare photon entanglement sources, it is necessary to study the correlation of high‐dimensional quantized energy levels under PT symmetry and symmetry breaking induced by the dressing field; Hamiltonian correlation matrix of the non‐Hermitian system characterizes the relationship between gain and loss, detuning and dephasing rate in the reaction energy‐level system, and the coupling relationship of the dressing field. The energy‐level system itself is non‐Hermitian, and the study of symmetry breaking is conducted by controlling EPs during the level control process through the dressing field, thus eliminating the need for introducing artificial photonic structures. The third‐order non‐Hermitian characteristics of the PT‐NH system reflect the positional relationship between the cascade field and the nested field. When the Rabi frequency (dephase rate) of the dressing field is the dominant factor, the real (imaginary) part of the eigenvalues is split, resulting in in‐phase (out‐of‐phase) constructive (destructive) transformations of the dressing order.
Abstract Non-Hermitian degeneracies, also known as exceptional points, have recently emerged as a new way to engineer the response of open physical systems, we construct non-Hermitian systems through atomic electromagnetically induced transparency structures, based on which we study energy-level high-dimensional quantized photon correlations under dressing field induced parity-time (PT) symmetry and symmetry breaking. We study the symmetry breaking through exceptional point (EP) control in dressing-controlled energy-level process is natural EP, which are born to be non-Hermitian without artificial photonic structures. When the dressing Rabi frequency (de-phase rate) dominates, the real part (imaginary part) splits, and leads to in-phase (out-of-phase) constructive (destructive) dressing quantization. It can also be used to develop atomic-like symmetry-breaking photonic chips and pseudo-spin devices in the future.
Abstract The non‐Hermitian singularity control of multimode entanglement in the energy‐level cascaded four‐wave mixing system within a single atomic vapor is of great significance and importance. In this study, a non‐Hermiticity system by means of quasi‐quantization of energy‐band based on non‐Hermiticity systems is constructed. By employing atomic coherence in the non‐Hermiticity system, high‐dimensional quantized photon correlations underdressed field‐induced parity‐time (PT) symmetry and symmetry breaking through the quantization of energy levels are studied. Such a phenomenon happens at microscopic (nanoscale) when the eigenvalues of dressed energy‐level and multimode entanglement are considered for both real and imaginary parts symmetry breaking. Double dressing effect is observed with more coherent channels and larger information capacity than single dressing in the energy‐level cascaded four‐wave mixing system. The study found that the splitting of the real part is larger than an imaginary part in a second‐order system, and the imaginary part splitting is also greater than the real part splitting in a third‐order system. The real part (in phase) is constructive dressing quantization, and the imaginary (out of phase) is destructive dressing quantization. Exceptional points (EP points) can be used to enhance sensitivity detection of entanglement quantum state.
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 Manipulating the dissipative dynamics of multiphoton entangled states offers a novel paradigm for quantum information processing. Here, we theoretically investigate the topological dynamics of time‐energy entangled tripartite W‐states generated via spontaneous six‐wave mixing in an atomic ensemble. By constructing an effective non‐Hermitian Hamiltonian, we map energy‐level splitting onto the temporal rates of coincidence counts (RCC). We reveal that multichannel quantum interference manifests as damped Rabi oscillations, with double cascaded and double nested dressing configurations inducing complete and incomplete non‐Hermitian jumps, respectively. Furthermore, we uncover a topological “Multi‐Jump” phenomenon driven by multi‐dressed high‐order Hamiltonian exceptional points (HEPs). Under critical parameter matching, the dressing phase acts as a topological switch, guiding the system across Riemann branch cuts to form closed loops, thereby exhibiting semi‐quantum characteristics that fuse macroscopic wave evolution with microscopic discrete jumps. Deviations from criticality lead to the rupture of topological connectivity. This work provides a foundation for simulating non‐unitary jump dynamics via HEP frameworks and for designing topological‐response‐based quantum sensors.
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.
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.