$\mathcal{PT}$-assisted control of Goos-H\"anchen shift in cavity magnomechanics

TL;DR

This paper demonstrates how to control the Goos-H"anchen shift in a non-Hermitian cavity magnomechanical system using $ ext{PT}$ symmetry and exceptional points, enabling enhanced or suppressed lateral shifts for potential quantum applications.

Contribution

It introduces a $ ext{PT}$-symmetric cavity magnomechanical scheme that allows coherent control of the GHS via exceptional points and system parameters, advancing non-Hermitian magnomechanics.

Findings

Realization of $ ext{PT}$ symmetry with a third-order exceptional point ($ ext{EP}_3$)

Enhanced GHS near $ ext{EP}_3$ and $ ext{EP}_2$ transitions

Suppression of GHS when effective magnomechanical coupling exceeds threshold

Abstract

We propose a scheme to manipulate the Goos-H\"{a}nchen shift (GHS) of a reflected probe field in a non-Hermitian cavity magnomechanical system. The platform consists of a yttrium-iron-garnet sphere coupled to a microwave cavity, where a strong microwave drive pumps the magnon mode and a weak field probes the cavity. The traveling field's interaction with the magnon induces gain, yielding non-Hermitian dynamics. When the traveling field is oriented at $\pi/2$ relative to the cavity's $x$-axis, the system realizes $\mathcal{PT}$ symmetry; eigenvalue analysis reveals a third-order exceptional point ($\mathrm{EP}_3$) at a tunable effective magnon-photon coupling. Under balanced gain-loss and finite effective magnomechanical coupling, we demonstrate coherent control of the GHS by steering the system across the $\mathcal{PT}$-symmetric transition and through $\mathrm{EP}_3$ via the effective magnon-photon coupling, enabling pronounced enhancement or suppression of the lateral shift. Furthermore, we show that without effective magnomechanical coupling, the system exhibits a second-order exceptional point ($\mathrm{EP}_2$) with a distinct GHS phase transition. This phase transition vanishes when the effective magnomechanical coupling exceeds a parametric threshold, where strong absorption at resonance suppresses the GHS. We also identify the intracavity length as an additional control parameter for precise shift tuning. Notably, the $\mathcal{PT}$-symmetric configuration yields substantially larger GHS than its Hermitian counterpart. These results advance non-Hermitian magnomechanics and open a route to GHS-based microwave components for quantum switching and precision sensing.