Generation of Entanglement by Two-Magnon Interference

Abstract

Two-particle interference, i.e., the Hong-Ou-Mandel (HOM) effect [1], is used in many quantum technologies to detect and generate entanglement [2]. HOM has no classical analog and is expressly quantum in nature, making it ideal to study fundamental quantum properties. HOM was first observed with photons in a 50:50 beam splitter (BS) [1] and has been studied in other quantum objects using various interference systems [2], but the effect has not yet been studied in quantum magnonics [3, 4].Here, we propose a model system for two-magnon interference. The system is an elliptical pillar of 2 antiferromagnetically-coupled ferromagnetic (FM) layers (see Fig. 1 inset) with resonant frequencies ω1 and ω2. With no bias magnetic field (B=0) ω1=ω2 and the FM layers are strongly coupled, but they are virtually independent when B≠0. This means that a time-dependent magnetic field B(t) can dynamically tune the system off-resonance (ω1≠ω2) to excite and detect magnons individually in each FM layer, and on-resonance (ω1=ω2) to allow for interaction of the magnons in two FM layers.The magnonic BS operation is achieved when the system is on-resonance for some time τ such that the probability for single magnon scattering between layers is ½. Our numerical simulations in Fig. 2 show the evolution of the system initially prepared in a two-magnon unentangled state │11〉. After the BS pulse, a maximally entangled N00N state (│20〉+│02〉)/√2 is formed. The relative phase between │20〉 and │20〉 components of the N00N state can be controlled by shaping the profile of the magnetic field B(t). The magnonic BS is a reversible unitary operation so it can also detect different N00N states. In summary, we found that a dynamically tuned magnon resonance can be used to form a magnonic BS that can generate and detect entanglement by two-magnon interference.  Fig. 1. Dependence of the resonant frequencies on magnetic field B. Solid lines: collective frequencies. Dashed lines and symbols: independent frequencies ω1,2. Gray highlight: strongly coupled region. Inset: elliptical FM/NM/FM pillar geometry.  Fig. 2. Evolution of unentangled state │11〉 into entangled superposition of states (│20〉+│02〉)/√2 under a magnonic beam splitter operation (gray highlight).