Optimal mode matching in cavity optomagnonics

Abstract

Inelastic scattering of photons is a promising technique to manipulate magnons but it suffers from weak intrinsic coupling. We theoretically discuss an idea to increase optomagnonic coupling in optical whispering gallery mode cavities, by generalizing previous analysis to include the exchange interaction. We predict that the optomagnonic coupling constant to surface magnons in yttrium iron garnet (YIG) spheres with radius 300 µm can be up to 40 times larger than that to the macrospin Kittel mode. Whereas this enhancement falls short of the requirements for magnon manipulation in YIG, nanostructuring and/or materials with larger magneto-optical constants can bridge this gap.Magnetic insulators such as yttrium iron garnet (YIG) are promising for future spintronic applications such as low power logic devices [1], long-range information transfer [2], and quantum information [3]. Their excellent magnetic quality [4,5] implies spin waves or magnons, the excitations of the magnetic order, are long-lived. Microwaves in high quality cavities and striplines couple strongly to magnons with long (mm) wavelengths [6][7][8][9][10][11][12], i.e. the rate of energy exchange between the two systems is higher than their individual dissipation rates, but not to short wavelengths (except under special geometries [13]). Magnons can be injected electrically by metallic contacts [14,15], but only in rather small numbers. Here, we focus on the coherent coupling of magnetic order and infrared laser light with sub-µm wavelengths, that is enhanced by using the magnet as an optical cavity [16][17][18].By the high dielectric constant and almost perfect transparency in the infrared [19,20], sub-mm YIG spheres support long-living whispering gallery modes (WGMs) [16,21]. The photons, with energy deep within the band gap, scatter inelastically by absorbing or creating magnons [22,23]. This is known as Brillouin light scattering (BLS) [24], which is enhanced in an optical cavity [16-18, 21, 25-29]. These results led to predictions of the Purcell effect [30] (optically induced enhancement of magnon linewidth), magnon lasing [31] and magnon cooling [32]. However, the models addressed only the magnetostatic magnon modes, i.e. ignored retardation and the exchange interaction, with only small overlap with the WGMs [16-18, 25, 29, 33, 34]. Thus, the observed and predicted coupling rates were too low to be able to optically manipulate magnons [31,32]. Higher optomagnonic coupling can be achieved by reducing the size of the magnets down to optical wavelengths [35], but this requires nanostructuring of the magnet [36][37][38]. Coupling to magnons in a non-uniform magnetization texture is large [39]. Here, we suggest and analyze a method to increase coupling in a conventional set-up of a uniformly magnetized sub-mm YIG sphere by coupling to exchange-dipolar modes with wavelengths comparable to the WGMs.Bulk magnons in films with both exchange and dipo-lar interactions have been extensively studied [40][41][42]. In thick films, exchange reduces the life tim...

Stationary Entanglement between Light and Microwave via Ferromagnetic Magnons

“…[24] The potentially feasible solutions are that use other magnetic materials with larger Verdet constant, like CrBr 3 with Verdet constant 8700 rads cm −1 for the light at 500 nm at 1.5 K environment, [39,46] to replace the YIG material for enhancing the optomagnonical coupling, or resort to advanced micro-and nanofabrication technology to reduce the surface roughness, thus enhancing the quality factor of YIG sphere. Furthermore, under some certain conditions, the interaction between optical photon and magnon can reach the strong coupling regime, [32,33,[47][48][49] which can be utilized to generate significant L-M entanglement based on our model. We turn to investigate the entanglement properties of three bipartite subsystems and analyze the influence from electromagnonical coupling g mb on the entanglement.…”

“…[24] But, we also mention some potential solutions in Section 4 to enhance the quality factor of YIG sphere and reach the strong-coupling regime in optomagnonics, such as replacing the YIG material with CrBr 3 possessing larger Verdet constant, reducing the surface roughness of YIG sphere by advanced fabrication technology, and others. [32,33,[46][47][48][49] What is more, the frequency mismatch in experiments between the TE, TM WGMs, and magnon frequency may also limit the L-M entanglement;…”

Antiferromagnetic cavity optomagnonics

“…(4) assumes perfect mode matching. Imperfect mode overlap can be accounted for by a mode-volume ratio factor [44] and it is responsible for a suppression of the coupling in current experiments with YIG [19,63]. The second term in Eq.…”

Coherent pumping of high-momentum magnons by light

“…These have a small overlap with the light fields and corresponding low intrinsic scattering efficiency, but become observable because a large magnon density can be resonantly excited by microwaves. On the other hand, magnons with wavelengths ∼ 100 − 500 nm in the dipolar-exchange regime have almost perfect overlap with the photon modes in magnetic spheres [18], but couple only very weakly to microwaves (as do the relevant magnons in magnetic vortices [17]). Here, we propose to coherently pump a large number (∼ 10 6 − 10 8 ) of high-momentum magnons by optical lasers, similar to the resonant excitation of Kittel magnons by microwaves.…”

“…by an optical cavity, specific magnons modes can be excited [16]. The interaction can be large enough [17,18] to cool [19] or herald (generating single magnon states) [20] them, making BLS a promising probe into their quantum nature. Present experiment focus on the long wavelength 'Walker' (including the 'Kittel') magnons in optical resonators [21][22][23][24][25].…”