Parameter estimation and quantum entanglement in PT symmetrical cavity magnonics system (2012.01890v1)

Abstract: We investigate the parameter estimation in a magnon-cavity-magnon coupled system. PT symmetrical two magnons system can be formed in the gain magnetic materials by the adiabatic elimination of the cavity field mode. We show that the optimal estimation will not appear at the exceptional point due to that the quantum fluctuations are the strongest at the exceptional point. Moreover, we demonstrate that the measurements at the exceptional point tend to be optimal with the increase of prepared time. And the direct photon detection is the optimal measurement for the initial state in the vacuum input state. For the open PT symmetrical two magnons system, the quantum fluctuations will greatly reduce the degree of entanglement. Finally, we show that a higher estimated magnetic sensitivity can be obtained by measuring the frequency of one magnon in the PT symmetrical two magnons system.

• The paper models a two-dimensional PT symmetrical system using adiabatic elimination to capture dissipative magnon-magnon interactions.
• The research finds that optimal frequency estimation occurs away from exceptional points, as prolonged measurement reduces adverse quantum fluctuations.
• The paper demonstrates that direct photon detection maximizes measurement precision, enhancing magnetic sensitivity beyond conventional sensor technologies.

PT Symmetrical Cavity Magnonics for Parameter Estimation and Quantum Entanglement

The paper "Parameter estimation and quantum entanglement in PT symmetrical cavity magnonics system" by Dong Xie, Chunling Xu, and An Min Wang explores the interplay between parameter estimation and quantum entanglement in a system involving PT (Parity-Time) symmetrical non-Hermitian Hamiltonians, particularly focusing on a magnon-cavity-magnon setup. The authors aim to understand the precision limits of estimating parameters such as frequency and to examine how quantum fluctuations influence these estimates, especially around the exceptional points in the system.

Key Findings

1. PT Symmetrical Hamiltonian Modeling: The paper outlines the modeling of a PT symmetrical system involving two magnons coupled to a cavity mode. By utilizing adiabatic elimination techniques, the authors derive a two-dimensional PT symmetrical Hamiltonian describing dissipative magnon-magnon interactions.
2. Parameter Estimation and Exceptional Points: The work investigates the quantum metrology of frequency estimation, asserting that the optimal estimation does not occur at the exceptional points due to high quantum fluctuations. Notably, the precision of parameter estimation improves with the increase of prepared time, indicating that the effect of quantum fluctuations is reduced over extended periods.
3. Optimal Measurements: Direct photon detection emerges as the optimal measurement strategy in the vacuum input state. The researchers calculate the estimation precision for the frequency, showing that the methodology outperforms conventional techniques, particularly at values further from the exceptional points.
4. Quantum Fluctuations and Entanglement: It is demonstrated that quantum fluctuations significantly diminish the degree of entanglement between magnons in an open PT symmetrical system. This is in contrast to previous closed-system models where entanglement could be more readily achieved.
5. Magnetic Field Measurement: A practical application outlined in the paper is the measurement of magnetic fields using the magnon frequency, which is sensitive to the magnetic field strength. Employing their model, the authors estimate a magnetic sensitivity that surpasses current magnetoelectric sensors, highlighting the potential for improvements in weak-coupling scenarios.

Implications and Future Directions

The findings presented in this paper address both theoretical and practical aspects of quantum physics and metrology. On the theoretical front, the relationship between exceptional points, parameter estimation, and quantum fluctuations provides insights into the behavior of non-Hermitian systems. Practically, the paper proposes improvements in magnetic sensitivity using PT symmetrical systems, suggesting new directions for developing advanced sensors. Future research could build on these results by devising experimental setups to verify theoretical predictions and expand the understanding of entanglement reduction due to quantum fluctuations in open systems. Additionally, exploring other types of measurements or states could further enhance the precision of parameter estimation in complex quantum systems.

Overall, this paper contributes to the understanding of PT symmetry in quantum systems and its implications for quantum metrology and sensor development, establishing a foundation for future exploration and technological advancements.