Cooperative polariton dynamics in feedback-coupled cavities

Abstract

The emerging field of cavity spintronics utilizes the cavity magnon polariton (CMP) induced by magnon Rabi oscillations. In contrast to a single-spin quantum system, such a cooperative spin dynamics in the linear regime is governed by the classical physics of harmonic oscillators. It makes the magnon Rabi frequency independent of the photon Fock state occupation, and thereby restricts the quantum application of CMP. Here we show that a feedback cavity architecture breaks the harmonic-oscillator restriction. By increasing the feedback photon number, we observe an increase in the Rabi frequency, accompanied with the evolution of CMP to a cavity magnon triplet and a cavity magnon quintuplet. We present a theory that explains these features. Our results reveal the physics of cooperative polariton dynamics in feedback-coupled cavities, and open up new avenues for exploiting the light-matter interactions.

Fig. 1

Device architecture. a The A-P-M device consists of a passive cavity (P), an active cavity A with a voltage tuneable gain (G _n), and an YIG sphere with magnons (M). b The Q-factor and G _n of the A-P cavity circuit are tunable up to 81,500 and 360,000, respectively, by changing V. c, |S ₂₁| spectra of the cavity mode measured at V = 0 and 7 V, together with a fitted theoretical curve

Fig. 2

Distance dependent Rabi frequency. a |S ₂₁| spectra measured at Δ = 0 and V = 0 V, for d = 1.3, 0.9, and 0.6 mm. The corresponding Rabi frequencies Ω ₀ are determined by line shape fitting. b Rabi frequency as a function of d. The solid (open) circles represent data measured at V = 0 V (7 V). The solid curve represents Ω ₀/2π calculated from Eq. (1) by using η determined from a Maxwell’s equations solver, where the dashed curve is calculated with Ω _f = 1.5Ω ₀. c |S ₂₁| spectra measured at Δ = 0 and V = 7 V. The Rabi frequencies Ω _f are determined from the mode splitting

Fig. 3

Voltage dependent Rabi frequency. a |S ₂₁| spectra measured at Δ = 0 and d = 0.58 mm (Ω ₀/2π = 7.5 MHz), for a series of V. b The measured (circles) and calculated (curve) ratio of Rabi frequencies Ω _f/Ω ₀ plotted as a function of V and G _n. The error bar is the maximum uncertainty caused by the error when fitting the Rabi frequency. c Schematic dressed states of both CMP modes. At Δ = 0, they produce the Mollow triplet with Ω ₊ = Ω ₋. At $\Delta \ne$0, they produce the magnon quintuplet with ${\Omega }_{+}\ne {\Omega }_{-}$. The detuning between the bare states is not shown for brevity

Fig. 4

Magnetic field dependent measurement. a |S ₂₁| spectra measured at d = 0.6 mm (Ω ₀/2π = 7.2 MHz) and V = 7 V (f = 0.78), for five different H fields as marked in b. The dispersion of the measured magnon quintuplet is plotted as a function of b, the magnetic field H, and c, the detuning Δ/2π. The curves in c are calculated by using eq. (3)