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.
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 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 Nonclassical multiphoton have attracted extensive attention to serve as entangled resources for quantum information technology. Here, the continuous‐mode hyper‐entangled W‐class triphotons are theoretically generated through spontaneous six‐wave mixing (SSWM) in 85Rb. In nonlinear optical response, Zeeman sub‐states are high‐dimensionally quantized by polarized dressing. High‐dimensional entanglement is structured via atomic non‐Hermitian nature. Through linear optical response, the temporal correlations are shaped via diverse polarized dressing. SSWM‐based triphoton is a genuine triphoton possessing non‐Gaussian tripartite entanglement. The high production rate is due to co‐action of three strong input fields, electromagnetically induced transparency (EIT) protection, and slow light effect. Non‐Hermitian nature endows the system with sensitive adjustability around exceptional points (EP). Eventually, the results demonstrate multiple SSWMs causing oscillations with multiple periods in three‐photon temporal correlations for the nonlinear region, build a high‐dimensional three‐body entangled quantum network and transform multifarious profiles of the three‐photon temporal correlations for the linear region. Especially, both high‐dimensional and hyper entanglements are obtained, contributing to high quantum information capacity. Further, the system is switched among multiple states when non‐Hermitian nature is manipulated by polarized dressing. The research opens a broad prospect for generating the hyper‐entangled multiphoton with potential application in adjustable quantum networks of high information capacity.
Non-Hermitian quantum systems — characterized by parity–time symmetry and the emergence of exceptional points — have attracted increasing interest, particularly in light–matter interaction platforms where dissipation and radiative losses play a fundamental role. In this work, we investigate the modulation of coupling states between atomic energy levels during the generation of backward W-state triphotons via a spontaneous six-wave mixing (SSWM) process. By employing tunable external control beams, we realize dynamic modulation from the weak to the strong coupling regime, accompanied by a qualitative transition in triphoton coincidence statistics from anti-bunching to damped Rabi oscillations. Remarkably, the appearance of single exponential decays in the triphoton coincidence count traces marks the onset of an exceptional point in the non-Hermitian system. Furthermore, triphoton correlations in the τ21 and τ31 directions can be independently modulated by selectively tuning of the coupling state via ED1 and ED2, respectively. These results provide a versatile and coherent platform for the one-step generation of backward entangled triphoton states and offer a promising approach to engineering high-dimensional entanglement, with potential applications in quantum communication and quantum information processing.
We investigate fourth-order non-Hermitian dynamics in rare-earth-ion-doped microcrystals using phase-controlled loops and four-wave mixing. We demonstrate that the complex eigenvalue space enables transitions in nontrivial topological loops. First, single-, double-, and triple-dressing configurations form a perfect nontrivial topological loop at the exceptional point (EP) with less quantum jumps due to weak dressing phase interactions. Still, the loop breaks down far from the EP. Such a topological loop is protected by PT–APT symmetry, which can be broken down by sequence quantization. Moreover, nested and cascade triple dressing form a quasi-topological nontrivial loop due to sequential interactions resulting multi-jump. Here, nested displays more jumps (above 100) due to strong three-dressing interaction, while cascade, nested–cascade, and cascade–nested triple dressing show above 50 jumps due to relatively weaker three-dressing interaction. However, at critical points in the phase-controlled topological loop, the system merged from four to two eigenvalues, creating stable degeneracies and enabling fourth-order non-Hermitian switching between multi-quantum states. Thus, multi-jump dynamics result from high-order dressing phase interaction and internal–external dressing interaction. We propose a quantum random number generator device that generates multi-jumps with 96% efficiency. Non-Hermitian topology enables controlled fourth-order quantum-state switching via quantum jump statistics, applicable to quantum random number generation and information processing.
Multiphoton entangled states are pivotal resources for implementing optical quantum information protocols. Recently, energy-time-entangled triphotons have been observed in hot atomic ensembles. However, in these protocols, the complex fifth-order nonlinear susceptibility entailed by four- or five-level systems limits our understanding of triphoton generation. Here, to directly capture the generation mechanism of triphotons and their associated optical properties, we investigate the generation of energy-time-entangled triphotons in a six-level cold atomic ensemble. The fifth-order nonlinear susceptibility indicates the existence of two sets of spontaneous six-wave mixing in the system. Notably, triphoton generation in this system is subject to stringent timing constraints. Collectively, these characteristics give rise to threefold coincidence counts, which -- dominated by the fifth-order nonlinear susceptibility -- exhibit asymmetrically damped Rabi oscillations in the two-dimensional time domain. Furthermore, we analytically derive that the temporal correlation properties of conditional two-photon states are preserved -- a unique feature of W-class tripartite entanglement. These results not only lay the groundwork for the experimental preparation of triphotons using six-level systems but also provide key support for understanding the generation mechanism of triphotons involving more complex fifth-order nonlinear susceptibilities.
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.