Switchable Dissipative Ising coupling Based on Three-Body Coupling in magnon systems

Abstract

Magnonic systems present a compelling platform for quantum technology, owing to their strong capacity to form hybrid quantum systems via diverse couplings. To unlock the full potential of these systems, the engineering of flexible coupling between multiple magnon modes is essential. Here, we propose a method to realize switchable dissipative Ising coupling in magnon systems, leveraging the three-body coupling among photon, phonon, and magnon. This type of dissipative coupling is a critical component for constructing Ising machines designed to solve complex combinatorial optimization problems. By dynamically tuning the phase of a nonlinear mechanical pump, we demonstrate the realization of both ferromagnetic and antiferromagnetic dissipative interactions. The validity of the scheme is confirmed by numerical simulations, which also demonstrate its robustness against a strong uncontrollable part of dissipation. Our work provides a versatile tool that can facilitate the implementation of magnon-based quantum computing and the exploration of many-body magnon physics.

Figures (8)

• Figure 1: (a) Schematic diagram of the triple-body system. The system involves three distinct modes: the magnon mode ($a$), the phonon mode ($b$), and the photon mode ($c$). The operators $a^\dagger$, $b^\dagger$, and $c^\dagger$ denote the creation operators for the magnon, phonon, and photon modes, respectively. $\lambda$ represents the coupling strength among the three modes. (b) Physical realization of the hybrid system. The system is composed of a magnon mode (a YIG microsphere), a phonon mode (a mechanical cantilever), and a photon mode (a transmission line). The YIG sphere is placed below the cantilever. The transmission line (indicated by the purple line) is positioned above the cantilever, illustrating the geometry of the coupling elements.
• Figure 2: The wigner function of the squeezed phonon mode in the phase space. The Fock-space truncation is $N=25$. The evolution time is set to 20(in units of $s_b$). (a) The state is squeezed in the displacement quadrature, corresponding to the effective squeezing parameter $s_b=2.4i$, (b) The state is squeezed in the momentum quadrature, corresponding to $s_b=-2.4i$.
• Figure 3: The Wigner function of the magnon mode ($a$) under the effects of phonon squeezing and intrinsic magnon dissipation. The Fock-space truncation is $N=20$. The coupling strength is $\lambda_s=0.8$, the Kerr non-linearity is $K=0.75$, and the driving amplitude is $s_a=1$. The evolution time is set to $t=20$ (in units of $s_a$).The subfigures illustrate the magnon Wigner function under different phonon squeezing parameters ($s_b$):(a) Strong squeezing in the displacement quadrature, $s_b = 2.4i$.(b) Strong squeezing in the momentum quadrature, $s_b = -2.4i$.(c) Moderate squeezing in the displacement quadrature, $s_b = 1.5i$.(d) Moderate squeezing in the momentum quadrature, $s_b = -1.5i$.
• Figure 4: Schematic illustration of an extended hybrid system module. This system incorporates two YIG microspheres placed below the mechanical cantilever. Two transmission lines (indicated in purple) are positioned above the cantilever.
• Figure 5: The joint Wigner function for the two magnon modes. The numerical simulation parameters are $N=15$ (Fock-space truncation), driving amplitude $s_a=1$, coupling strength $\lambda_d=0.8$, and Kerr non-linearity $K=0.75$. The evolution time is set to $t=20$ (in units of $s_a$). The subfigures display two-dimensional projections of the four-dimensional Wigner function:(a) and (b) projection onto the displacement and momentum quadratures when the phonon squeezing parameter is $s_b = 2.4i$. (c) and (d) Projection onto the displacement and momentum quadratures when the phonon squeezing parameter is $s_b = -2.4i$.