Researchers have, for the first time, incorporated a magnon into a quantum system with feedback control, a step enabled by employing a Long Short-Term Memory network to efficiently model the complex dynamics. The work reveals that the level of magnon-atom entanglement, measured by a property called concurrence, oscillates predictably as the distance between the cavity mirrors changes. These results demonstrate a new approach to quantum state engineering in hybrid magnonic systems, potentially advancing quantum networks and information processing, and show that feedback significantly enhances both antibunching and bunching when the detuning is varied.

Long Short-Term Memory Networks Simulate Magnon-Atom Dynamics

A Long Short-Term Memory network, a form of machine learning, was employed to model the quantum behavior of a system integrating a magnon within a feedback-controlled environment, circumventing the computational challenges of solving the Schrödinger equation for these complex hybrid platforms. This approach allowed researchers to efficiently propagate probability amplitudes to a steady state, a feat previously difficult to achieve with traditional methods given the non-Markovian dynamics introduced by time-delayed feedback.

The LSTM network’s ability to capture long-range dependencies helped simulate the system’s evolution and stabilize the intracavity state. This dynamic relationship between entanglement and physical positioning offers a potential control mechanism for manipulating quantum states within the hybrid system. The application of coherent feedback demonstrably enhanced both antibunching and bunching of photons, particularly as the detuning parameter was varied, suggesting a pathway toward on-demand quantum state engineering.

Cavity-Magnon-Photon Coupling Drives Hybrid Quantum Systems

The distance between cavity mirrors directly influences the level of entanglement between magnons and atoms, according to work from China Jiliang University and Great Bay University. Researchers discovered that the concurrence, a measure of this entanglement, exhibits periodic oscillations as the cavity-mirror distance changes, offering a potential mechanism for dynamic control of quantum states within hybrid systems. This observation moves beyond static entanglement, demonstrating a manipulable relationship between physical positioning and quantum correlation.

This control is achieved through coherent feedback, implemented via a mirror within a waveguide, which actively stabilizes the intracavity state. The study’s findings extend beyond simulation, demonstrating a pathway for on-demand quantum state engineering with potential applications in quantum networks and quantum information processing. The ability to tune the system’s quantum output using the mirror distance, acting as a “periodic phase knob,” provides a real-time switching capability. This approach, the researchers suggest, is fully achievable in microwave-frequency cavity magnomechanical systems.

Magnon Properties Advance Spin Wave Information Carriers

The team trapped a magnon and a two-level atom within an optical cavity, then implemented coherent feedback using a mirror embedded in a waveguide. The experimental setup relies on a specific geometry; the distance between the cavity and the mirror, denoted as L, dictates the feedback delay. By varying L, the researchers observed how the photon-photon correlation function and the concurrence oscillate, indicating a dynamic relationship between the physical layout and the quantum state. The study’s Hamiltonian, $H_{e f f}$ , incorporates detunings and coupling strengths to model the interactions between photons, magnons, phonons and the atom.

Zeeman Interaction Enables Ultrastrong Magnon-Photon Coupling

This interaction, between the magnetization of a ferrimagnetic material and a microwave cavity field, creates a coherent beam-splitter effect, and is central to the observed dynamics. A key aspect of this work lies in the detailed modeling of the system’s behavior, which necessitated the use of a Long Short-Term Memory network. The researchers specifically examined how observable quantities change with variations in parameters like the distance L between a mirror and the cavity, the detuning Δ and the strength of external drives.

Periodic Oscillations Link Mirror Distance to Entanglement

The level of magnon-atom entanglement within a cavity magnomechanical system demonstrably changes with the physical positioning of a mirror. Researchers found that the concurrence, a metric quantifying this entanglement, undergoes periodic oscillations directly correlated to variations in the distance between the optical cavity and the mirror implementing the feedback loop. Specifically, the team observed that the $g^{2} (0)$ value oscillates periodically with changes in the cavity-mirror distance, as depicted in their analysis.

This synchronized behavior confirms that the mirror distance is a “periodic phase knob,” allowing real-time adjustment of the quantum output. Beyond the mirror distance, the system’s detuning, the difference between magnon and laser frequencies, also plays a significant role in influencing entanglement levels. While maximal entanglement does not always coincide with extreme photon statistics, the researchers demonstrated that feedback and detuning can be tuned to prioritize the creation of specific entangled states.

Coherent Feedback Stabilizes Intracavity Quantum States

Employing machine learning techniques, researchers propagated probability amplitudes to the steady state, a necessary step given the complexity of numerically solving the dynamics of this hybrid quantum system. This application of artificial intelligence demonstrates a novel approach to tackling complex quantum problems, streamlining the analysis of hybrid magnonic systems. This dynamic behavior suggests a means of controlling entanglement through physical manipulation of the system’s components.

Specifically, the photon-photon correlation function mirrors this oscillation, indicating a synchronized response to alterations in the cavity environment. This manipulation of photon statistics is achieved through a feedback loop functioning as an external, tunable By actively switching between phases, the system can favor either single-photon states (antibunching, g^(2)(0) < 1) or two-photon states (bunching, g^(2)(0) > 1).

Photon Statistics Reveal Enhanced Bunching and Antibunching

The ability to manipulate photon behavior extends beyond conventional methods, with researchers now demonstrating control over the statistical distribution of photons, specifically, enhancing both bunching and antibunching, through coherent feedback. The results reveal that the photon-photon correlation function and the concurrence, a measure of magnon-atom entanglement, exhibit periodic oscillations with the cavity-mirror distance, and that feedback significantly enhances both antibunching and bunching when the detuning is varied.

This active enhancement capability represents an advance in controlling quantum light sources. The manipulation of photon statistics is intrinsically linked to the system’s entanglement. The researchers computed the concurrence, a measure of magnon-atom entanglement, alongside the $g^{2} (0)$ values, revealing a tunable relationship between these two quantum properties. This allows for optimization of the system for specific quantum information tasks, such as generating single photons or creating entangled pairs.

The feedback loop functions as a tunable actively switching between classical and quantum light statistics from the same system. This amplification of nonlinearity, coupled with the ability to directly manipulate entanglement, demonstrates the power of feedback control in stabilizing specific entangled states and tailoring the system’s output for diverse applications.

👉 More information
🗞 Time-delayed feedback control of entanglement in hybrid magnonic systems via machine learning
✍️ Yiping Lu, Yulong Hu, Zhuzheng Han and Shirong Lin
🧠 DOI: http://link.aps.org/doi/10.1103/dmj6-b3gd

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