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arXiv:2602.10581

General Theory of Stable Microwave-Optical Quantum Resources in Hybrid-System Dynamics

Fan Li, Shi-fan Qi, Z. D. Wang, Yan-Kui Bai

quant-phSubmitted Feb 11, 2026• Announced Feb 12, 2026• 0 citations
v1 · Feb 11, 2026v2 · Oct 5, 2026
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Abstract

We develop a general theoretical framework for characterizing stable quantum resources between microwave and optical modes in the dynamics of multipartite hybrid quantum systems with intermediary modes. The effective Hamiltonian for microwave-optical (MO) squeezing is formulated via strong interactions in the microwave-intermediary-optical hybrid system, and based on which rigorous solutions for the dynamics of MO entanglement and quantum steering are derived analytically. Remarkably, it is found that stable MO quantum resources can survive in the unsteady evolution beyond the steady one, and the unsteady evolution can exhibit the enhanced quality over the limit of quantum resources in the steady-state case. Furthermore, the stable MO entanglement as well as one-way and two-way quantum steerings are efficiently controllable by modulating the effective coupling strength. The validity of our theory is demonstrated by applying it to the typical models of electro-optomechanical and cavity optomagnomechanical hybrid systems.

Comments
8.5 pages, 6 figures plus the supplemental material

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Two-mode squeezed states as paradigmatic entangled resources have broad applications in quantum information processing. Here, we study the generation of stable optical-microwave squeezing in structured environments within a hybrid electro-optomechanical system, where a mechanical oscillator is simultaneously coupled to an optical cavity mode and a microwave mode of an LC resonator. Specifically, an effective Hamiltonian that captures the optical-microwave squeezing interaction is constructed by combining strongly modulated driving fields applied to both photonic modes with a mechanical parametric amplifier. Based on this effective model, the dynamical evolution of two-mode squeezing in structured environments is analyzed. It is remarkably shown that the non-Markovian noise can substantially enhance the squeezing level in comparison to the Markovian case, and that two-mode squeezing can persist even in the absence of external driving fields under non-Markovian conditions, thereby mitigating the detrimental effects of anti-squeezing. Furthermore, the persistence of the two-mode squeezed state is enhanced when the environmental spectral densities of the microwave and optical modes are identical. Our work provides a theoretical framework for generating and persisting two-mode squeezing in structured environments.
We propose a scheme to generate one-way steering, bipartite, and genuine tripartite entanglement in a five-mode hybrid cavity electro-optomechanical system consisted of an optical cavity, a mechanical resonator, and three microwave cavity modes with the help of a squeezed vacuum field. The optical cavity is pumped by a squeezed vacuum field. The mechanical resonator is formed by a freely vibrating silicon nitride membrane, which is a part of a capacitor in an inductor–capacitor circuit forming three microwave resonators. We find that there is robust entanglement and one-way steering between the optical cavity mode and microwave cavity modes in the presence of the squeezed vacuum field. Particularly, there is steady-state genuine tripartite entanglement between three microwave cavity modes, which is robust against thermal fluctuations. Our scheme could be useful for various quantum tasks based on hybrid electro-optomechanical systems fabricated on chips.
We have investigated the dynamical entanglement and quantum steering in a pulsed hybrid opto-electro-mechanical system. Using the symmetric and asymmetric criteria, the possibilities of bipartite entanglement, one-way steering, two-way steering, and collective tripartite steering have been studied between different output modes. In addition, the influence of the squeezing parameter on the amount of tripartite steering measurement is also examined. The results show that a higher electro-mechanical coupling rate leads to stronger tripartite steering. The microwave cavity mode can enhance the output quantum steering and remotely steers the optical cavity. Thus, the slower mode can steer the faster mode. Such hybrid systems can serve as frequency converters between microwave and optical domains and can have a profound impact on building quantum networks of microwave-operated superconducting quantum computers.
We propose an effective approach for generating highly pure and strong cavity-mechanical entanglement (or optical-microwave entanglement) in a hybrid modulated three-mode optomechanical system. By applying two-tone driving to the cavity and modulating the coupling strength between two mechanical oscillators (or between a mechanical oscillator and a transmission line resonator), we obtain an effective Hamiltonian where an intermediate mechanical mode acting as an engineered reservoir cools the Bogoliubov modes of two target system modes via beam-splitter-like interactions. In this way, the two target modes are driven to two-mode squeezed states in the stationary limit. In particular, we discuss the effects of cavity-driving detuning on the entanglement and the purity. It is found that the cavity-driving detuning plays a critical role in the goal of acquiring highly pure and strongly entangled steady states.
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Abstract Quantum technologies critically rely on maintaining coherence and controllable correlations in open systems, yet these resources are fragile under dissipation and noise. To address this challenge, we investigate a hybrid platform composed of two identical three-level atoms in a V-type configuration coupled to a single-mode cavity field prepared in a squeezed coherent state. Using the Lindblad master equation, we numerically simulate the system dynamics, allowing a rigorous treatment of coherent atom–field interactions, interatomic couplings, and cavity losses. Our analysis reveals that squeezing introduces nonclassical correlations that enhance field coherence and support the generation of entanglement under specific regimes. Strong interatomic coupling stabilizes entanglement, while squeezing mitigates decoherence-induced losses. Conversely, large photon amplitudes and cavity dissipation degrade both coherence and bipartite correlations. Quantum steering emerges as the most fragile correlation, yet its persistence can be moderately extended through squeezing. These results identify squeezing and interatomic interactions as complementary resources for optimizing coherence, entanglement, and steering, offering practical strategies for robust quantum communication, information processing, and engineered nonclassical states.