Quantum entanglement (QE) and quantum steering (QS) are of importance for quantum information processing and computation. Though there are several schemes proposed for their realization, how to increase their degrees encounters a great challenge. In the present manuscript, it is proposed to enhance steady QE and control Gaussian QS for two magnons using a two‐photon field acting on either magnon. The cavity‐magnetic hybrid system consists of a microwave cavity in which two identical Yttrium‐iron‐garnet spheres are placed and the cavity is driven by a Josephson parametric amplifier (JPA) so as to generate steady QE and control Gaussian QS for the two Kittel modes. Besides, a two‐photon driving field acting on either magnon in order to enhance the degree of QE and the ability of QS. The best condition to maximum entanglement and steering degrees for the two magnon modes at ε≈0.8$\varepsilon \approx 0.8\nobreakspace $ MHz and r≈2$r \approx 2$ is found via the competitive relationship between the two‐photon driving and JPA. Furthermore, it is revealed that steering direction for the two magnons can be controlled not only by the ratio between the two photon‐magnon coupling parameters but also by the two‐photon driving field, making controllable steering direction become easier.

Enhancement of Steady Quantum Entanglement and Directional Controllability of Quantum Steering in Cavity Magnetic Hybrid Systems

The nonlinear parametric process is of great significance for achieving high-quality coherent optical signals and quantum correlated photons. With the development of classical and quantum information processing, the study of the properties of parametric processes is evolving in complex scenarios of multimode, which is limited in conventional nonlinear media due to strict phase matching, e.g. nonlinear crystals. Here we study the dressing-energy-level-cascaded four-wave mixing process to generate multimode optical parametric signals. Via cascading double-Λ type configuration of 85Rb D1 line, the non-degenerate energy-level-cascaded FWM is constructed to generate multimode self-parametric amplification. Moreover, with the dressing effects based on atomic coherence, the spatial and frequency multimode characteristics of energy-level-cascaded FWM parametric amplification, i.e., the modes number and pattern, are actively modulated by the pump fields detuning. Also, the spatial modes from the coupling of two coexisting spontaneous parametric FWMs can be controlled to reach tremendous scalability via the atomic coherence and Kerr non-linearity. The atomic coherence effects and unique phase-matching symmetry nature allow flexible modulation of the multimode property of the generated parametric signals within a nonlinear device, which paves a way for multimode classical and quantum information processing.

Experimental realization of multimode nonlinear parametric amplification from cascading four-wave mixing of dressed atoms.

The universal quantum computation provides a new paradigm for information processing. One feasible approach is measurement‐based one‐way quantum computation utilizing cluster states. Generally, the generation of cluster states with different structures for implementing on‐demand quantum computation needs different experimental setup, which limits its scalability. Here, the reconfigurable hexapartite cluster states created by postprocessing the quadrature information of hexapartite entangled state are demonstrated. Without altering the experimental layout, nine quantum correlated states with different structures, especially three cluster states, are implemented. In particular, such method can effectively reduce the excess noise introduced by creating cluster states under limited squeezing resources. This approach provides an avenue for realizing large‐scale reconfigurable cluster states without changing the experimental architecture.

Reconfigurable Hexapartite Cluster States by Four‐Wave Mixing Processes with a Spatially Structured Pump

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. 

Non‐Hermitian Control of Multimode Duan‐PPT Criteria and Steering in Energy‐Level Cascaded Four‐Wave Mixing Processes

The effect of environmental coherence on bipartite and tripartite quantum entanglements using quantum collision models is studied. In the collision model, an open quantum system of two qubits indirectly interacts with the reservoir via auxiliary qubits. The reservoir is modeled as a collection of initially uncorrelated qubits prepared in an identically nonthermal state. It is shown that the coherence of the nonthermal reservoir contributes to the generation and protection of entanglement. It is found that adding coherence to the initial state of the reservoir qubit can significantly enhance the steady‐state entanglement of the system, and the presence of coherence in the reservoir allows steady‐state entanglement to be obtained in a higher temperature region.

Improving Entanglement Generation Using the Coherence of a Nonthermal Reservoir

Multipartite entanglement plays an important role in quantum information processing and quantum metrology. Here, the dressing-energy-level-cascaded four-wave mixing (FWM) processes are proposed to generate all-optical controlled multipartite entanglement within a single device. The entanglement characteristics of the produced states of light are characterized by applying the Duan criterion and the positivity under partial transposition criterion. Moreover, by using an internal dressing field to modulate atomic coherence, multiple quantum coherent channels of FWM are simultaneously constructed, which result in a great extension of entanglement mode number and quantum information capacity. We find that the violation of the entanglement criteria inequalities is coherent-channel dependent, and the produced states can be directly modulated via atomic coherence. Our system can integrate the generation and modulation of the entangled states in one process. It may help provide a compact method for realizing large-scale quantum networks. 

Atomic-coherence-assisted multipartite entanglement generation with dressing-energy-level-cascaded four-wave mixing

Multimode properties, based on nonlinear parametric processes, have potential research value on entanglement imaging. This paper studies the spatial and frequency multimode from dressing parametric‐amplified six‐wave mixing (PA‐SWM) process with three entangled signals. The S1 signal contains fifth‐order nonlinearity, the S2 signal contains electromagnetically induced absorption and fifth‐order nonlinearity, and the S3 signal contains Autler–Townes splitting (AT), second‐ and fifth‐order nonlinearity. The frequency multimode is attributed to dressing energy level splitting in spontaneous SWM (SSWM) process. The spatial multimode is due to frequency multimode and beam splitting via Kerr nonlinearity. In the spatial domain, it finds the optimal conditions of intensity difference squeezing (IDS) and spatial imaging along with their competitive relationship. On the one hand, the light spots with single spatial mode are contributed to the maximum IDS but not conducive to entanglement imaging; on the other hand, the light spots with multiple spatial modes are instrumental in entanglement imaging but not appropriate for the IDS. This research has potential applications in squeezed light sources for quantum metrology, and correlated imaging of spatial signals.

Multichannel Six‐Wave Mixing with Spatial Multimode and Squeezing via Atomic Coherence

: Multipartite entanglement plays an important role in quantum information processing and quantum metrology. Here, the dressing-energy-level-cascaded (DELC) four-wave mixing (FWM) processes are proposed to generate all-optical controlled multipartite entanglement within a single device. The entanglement characteristics of the produced states of light are characterized by applying the Duan criterion and the positivity under partial transposition criterion. Moreover, by using an internal dressing field to modulate atomic coherence, multiple quantum coherent channels of FWM are simultaneously constructed, which result in a great extension of entanglement mode number and quantum information capacity. We find that the violation of the entanglement criteria inequalities is coherent-channel dependent, and the produced states can be directly modulated via atomic coherence. Our system can integrate the generation and modulation of the entangled states in one process. It may help provide a compact method for realizing large scale quantum networks. value of PPT criterion smaller than 0 directly means the presence of entanglement. The results of the bipartite entanglement characterized by PPT criterion are similar as Duan criterion. The PPT value of 1 3 ˆ ˆ- a a is larger than 0 for any G 1 > 1 and G 2 > 1, which is consistent with previous analysis. The entanglement

Atomic Coherence Assisted Multipartite Entanglement Generation with DELC Four-Wave Mixing

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.

Multipartite entanglement generation with high-order non-Hermitian exceptional points from dressing-controlled atomic nonlinearity

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