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Quantum Science and Technology

Stationary quantum entanglement and steering between two distant macromagnets

Ji-kun Xie, H. Y. Yuan, Sheng-li Ma, Shaoyan Gao, Fuli Li, R. A. Duine

Published May 15, 2023• 23 citations

Abstract

Abstract Generating and manipulating magnon quantum states for quantum information processing is a central topic in quantum magnonics. The conventional strategy amplifies the nonlinear interaction among magnons to manifest their quantum correlations at cryogenic temperatures, which is challenging for magnets with vanishingly small nonlinearities. Here we propose an unconventional approach to prepare entangled states of two distant magnon modes by applying a two-tone Floquet field to each magnet inside a microwave cavity. The Floquet driving can effectively generate parametric interaction between magnons and photons, and thus opens an indirect entanglement channel between the two magnon modes mediated by cavity photons. By optimizing the relative ratio of the magnon–photon coupling and the detuning between the magnon modes, the two magnon modes can reach a stationary and robust entanglement, of which the strength is enhanced compared with entanglement generated via magnetic nonlinearities. Furthermore, one-way steering between the two magnets is realized by engineering unequal damping rates of the two magnets while the steering asymmetry can be efficiently modulated by tuning the coupling strength of magnons and cavity photons. The essential physics of our findings universally applies to a wide class of magnets with small nonlinearities and may find promising applications in engineering robust magnon quantum states for quantum information science.

DOI: 10.1088/2058-9565/acd576

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Abstract Generating and manipulating magnon quantum states for quantum information processing is a central topic in quantum magnonics. The conventional strategy amplifies the nonlinear interaction among magnons to manifest their quantum correlations at cryogenic temperatures, which is challenging for magnets with vanishingly small nonlinearities. Here we propose an unconventional approach to prepare entangled states of two distant magnon modes by applying a two-tone Floquet field to each magnet inside a microwave cavity. The Floquet driving can effectively generate parametric interaction between magnons and photons, and thus opens an indirect entanglement channel between the two magnon modes mediated by cavity photons. By optimizing the relative ratio of the magnon–photon coupling and the detuning between the magnon modes, the two magnon modes can reach a stationary and robust entanglement, of which the strength is enhanced compared with entanglement generated via magnetic nonlinearities. Furthermore, one-way steering between the two magnets is realized by engineering unequal damping rates of the two magnets while the steering asymmetry can be efficiently modulated by tuning the coupling strength of magnons and cavity photons. The essential physics of our findings universally applies to a wide class of magnets with small nonlinearities and may find promising applications in engineering robust magnon quantum states for quantum information science.

Abstract A scheme is proposed to prepare quantum entanglement and quantum steering between two indirectly coupled microwave cavity modes within a hybrid cavity magnonic system. The system consists of two microwave cavities individually coupled to a common YIG sphere driven by a two‐tone Floquet field, while the output field of the second microwave cavity is fed back into the input port of the first microwave cavity via a coherent feedback loop. Floquet driving can effectively generate two interactions between magnons and photons. Magnons with higher dissipation can serve as a cooling channel for the two cavity modes. Optimal quantum correlations between the cavity modes can be achieved when the competition between these two interactions reaches equilibrium. Subsequently, a comparative analysis is performed on the evolution of quantum correlation with and without coherent feedback, revealing that the presence of a coherent feedback loop in the system not only significantly enhances entanglement and steering but also induces inherent asymmetry in quantum steering regardless of the decay rates within subsystems. Moreover, under the influence of the coherent feedback loop, the enhanced quantum correlations exhibit increased robustness against rising environmental temperatures. This work significantly expands the validity of implementation and provides a promising avenue for the preparation of stable quantum correlations.

We show how to implement stationary one-way quantum steering with strong entanglement in a cavity magnonic system that consists of two magnon modes and a microwave cavity. The cavity is driven by a squeezed vacuum field generated by a flux-driven Josephson parameter amplifier and coupled to two Kittel modes via magnetic dipole interaction. We find that the steering directivity only depends on the ratio of two coupling rates (i.e., the ratio of coherent information exchange frequencies) and is barely affected by the dissipation of the system. Meanwhile, the entanglement and steering can be significantly enhanced due to the squeezed vacuum field and thus are more robust against thermal noises. This provides an active method to manipulate the steering directivity instead of adding asymmetric losses or noises to subsystems at the cost of reducing steerability.

Abstract We present a scheme to entangle two magnon modes in a cavity magnomechanical system. The two magnon modes are embodied by collective motions of a large number of spins in two macroscopic ferrimagnets, and couple to a single microwave cavity mode via magnetic dipole interaction. We show that by activating the nonlinear magnetostrictive interaction in one ferrimagnet, realized by driving the magnon mode with a strong red-detuned microwave field, the two magnon modes can be prepared in an entangled state. The entanglement is achieved by exploiting the nonlinear magnon-phonon coupling and the linear magnon-cavity coupling, and is in the steady state and robust against temperature. The entangled magnon modes in two massive ferrimagnets represent genuinely macroscopic quantum states, and may find applications in the study of macroscopic quantum mechanics and quantum information processing based on magnonics.

Abstract We show how robust magnon-magnon (or photon-magnon) entanglement and asymmetric quantum steering can be achieved in a nonlinear cavity-magnon system composed of a microwave cavity and two yttrium-iron-garnet (YIG) spheres, which are each driven by external microwave driving fields. The self-Kerr nonlinearity (SKN) of two magnons drives this behaviour and we study how two-fold periodically-modulated driving fields influence the system dynamics. We find that beating occurs both in the classical average of the cavity mode and in the entanglement between modes. Moreover, the use of modulated driving fields can enhance the degree of entanglement generated as well as giving rise to asymmetric quantum steering effects that would not otherwise be present. Finally, we show that the entanglement generated this way has improved robustness to thermal noise opening the way to potential applications of magnon-based hybrid systems in quantum information processing and studies of fundamental physics.

We propose a scheme for preparing magnon squeezed states in a hybrid cavity-magnon-qubit system. The system consists of a microwave cavity that simultaneously couples to a magnon mode of a macroscopic yttrium-iron-garnet sphere via the magnetic-dipole interaction and to a transmon-type superconducting qubit via the electric-dipole interaction. By far detuning from the magnon-qubit system, the microwave cavity is adiabatically eliminated. The magnon mode and the qubit then get effectively coupled via the mediation of virtual photons of the microwave cavity. We show that by driving the qubit with two microwave fields and by appropriately choosing the drive frequencies and strengths, magnonic parametric amplification can be realized, which leads to magnon quadrature squeezing with the noise below vacuum fluctuation. We provide optimal conditions for achieving magnon squeezing, and moderate squeezing can be obtained using currently available parameters. The generated squeezed states are of a magnon mode involving more than

{10}^{18}

spins and thus macroscopic quantum states. This work may find promising applications in quantum information processing and high-precision measurements based on magnons and in the study of macroscopic quantum states.

We study phase-controlled quantum entanglement and one-way quantum steering in a cavity magnonic system, where two magnon modes couple to two microwave cavities driven by squeezed fields. The magnon-magnon entanglement and the steering directivity can be controlled by adjusting the ratio of the coupling strengths between cavity modes and magnon modes. In particular, the quantum entanglement and one-way quantum steering can be significantly enhanced by the squeezed vacuum field, which also exhibits robustness against temperature variations. More intriguingly, both quantum entanglement and steering between two magnon modes are susceptible to variations in the phase difference of two Josephson parametric amplifiers, and thus the phase-controlled quantum entanglement and one-way quantum steering can be achieved. Our scheme may have potential applications in quantum information.