Macroscopic Quantum Effect Of Magnons And Microwave Fields In Cavity Magnomecanical System

Cavity magnomechanics is an emerging direction composed of microwave cavity mode,magnon mode,and phonon mode.A magnon is an excitation of a large number of spins in a magnetic material,that is,the quantization of spin waves.The phonon mode is a vibration mode generated by magnetostrictive force of magnetic material which is induced by varying magnon excitations.The cavity mode is in the microwave frequency.In particular,the magnon mode has very low damping in some insulating ferromagnetic materials.For example,in yttrium iron garnet we use in this article,the coherence time in the interaction between the magnons and microwave photons is longer than their decay time,plus the high spin density in the magnetic material,several orders of magnitude higher than conventional spin systems(e.g.,atomic ensembles),and the interaction can reach a strong coupling regime.Since the frequency of the magnon mode is also in the microwave frequency band and can be adjusted by changing an external bias magnetic field,magnons can be coupled with the microwave cavity photons through magnetic dipole interaction.This coupling is linear,similar to the role of a beam-splitter interaction in quantum optics,responsible for the exchange of the states of two modes.Phonons and magnons are coupled to each other through magnetostriction.The coupling between these two is non-linear.It is similar to the radiation pressure effect in cavity optomechanics.The coupling strength can be enhanced by applying a microwave pump onto the magnon mode.When entering the strong coupling regime,and the quality factor Q is much greater than 1,some quantum effects can occur in the system,such as magnon-phonon entanglement.Therefore,in the study of cavity magnomechanics,magnetostriction plays a central role.So far,we know that the magnon mode can interact with both cavity photons and phonons.These three different modes can be coupled to each other through magnons to form a cavity magnomechanical system consisting of cavity photons,magnons,and phonons.The coupling of these three modes makes it possible to convert the information encoded on three different physical platforms to each other,so it brings a great possible boost to the development of advanced technologies such as classical,quantum communication,and quantum information processing ect.We know that the magnon mode contains a large number of spins and thus the study of entanglement between magnon modes is of importance for the study of macroscopic quantum effect.The non-linear effects of magnons and phonons in a cavity magnomechanical system can be used to entangle each other.This entanglement can also be transferred to the magnon-photon,photon-phonon subsystems.It may also be used to entangle the two microwave fields if two microwave modes couple to a magnon mode.After investigation,there are currently many methods for entangling two microwave fields,including the use of the nonlinearity of Josephson amplifiers,injecting a squeezed vacuum microwave field through a linear microwave beam splitter,or coupling two microwave fields to a common mechanical resonator via radiation pressure force.Entanglement of two microwave fields by magnetostriction has not been explored.This thesis is divided into four chapters,and the specific chapters are arranged as follows:The first chapter is the introduction.Firstly,the research background of the emerging research direction of cavity magnomechanics and the current development status at home and abroad are introduced,and then the significance of this paper is pointed out.Subsequently,the theoretical basis and research methods used in this paper are introduced,that is,the concept of magnon mode,ferromagnetic material yttrium iron garnet,strong coupling system of photon and magnon mode in microwave cavity,magnetostriction,Gaussian state and its mathematical expression-covariance matrix.In chapter 2,we introduce the cavity magnomechanical system,give the Hamiltonian and Langevin equations,and show the details of solving these equations.Based on the experimental parameters,we quantitatively calculate the entanglement amount of the two magnon modes,and also give the analytical expression under the optimal conditions.In Chapter 3,we take advantage of the non-linear effects of magnons and phonons in ferromagnetic materials,that is,magnetostriction interaction.We provide a solution for entanglement of two microwave fields in a cavity magnomechanical system.Starting from the system Hamiltonian,we solve the Langevin equations and quantitatively calculate the entanglement of the two microwave fields based on feasible experimental parameters.We also discuss how to implement our theoretical scheme experimentally.The fourth chapter summarizes the main conclusions and innovations of this paper,and proposes the next research plan.