High-dynamic-range quantum sensing of magnons and their dynamics using a superconducting qubit APS 06/12/2025 10630084 10.1103/6dmm-mnxd Physical Review Applied 2331-7019 23 6 Sonia RaniXi CaoAlejandro E BaptistaAxel HoffmannWolfgang Pfaff Magnons, the quanta of collective spin excitations in magnetic materials, may enable functionalities, such as nonreciprocity and transduction in hybrid quantum devices. To assess the potential of such applications, it is necessary to understand magnon dynamics beyond the simple harmonic oscillator regime, where theory predicts effects like population-dependent damping and quantum fluctuations in the form of magnon shot noise. Probing these phenomena requires sensors with high sensitivity and the ability to resolve magnon properties across different excitation regimes. Here, we demonstrate accurate and sensitive detection of magnon population and decay over a wide range of occupation numbers. We use a superconducting qubit to probe magnons in a ferrimagnet over approximately 2000 excitations. Using qubit control and parametrically induced qubit-magnon interactions, we demonstrate few-excitation sensitive detection of magnons with a dynamic range of approximately 30 dB, and are able to accurately resolve their decay with few-ns sensitivity. These capabilities offer a powerful and practical technique for probing magnon dynamics in or beyond the linear regime over a wide range of excitations.

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A pr o misi n g a p pr o a c h f or s e nsiti v e m a g n o n c h ar a ct eri z ati o n is t o us e a s u p er c o n d u cti n g q u bit as a q u a nt u m s e ns or [1 6 ], a n d it is a n i ntri g ui n g q u esti o n, w hi c h m a g n o n * C o nt a ct a ut h or: s o ni ar 2 @illi n ois. e d u † C o nt a ct a ut h or: w pf a ff @illi n ois. We o bt ai n t h e si g n al as f oll o ws [ Fi g. 2( c) ]. We first pr e p ar e eit h er n m or n m m a g n o ns, a n d t h e n a p pl y a π p uls e at fr eq u e n c y ω q + n m χ q m , t h e St ar k-s hift e d q u bit fr e q u e n c y f or n m m a g n o ns. T h e si g n al is t h e di ff er e n c e i n q u bit e x cit e dst at e pr o b a biliti es b et w e e n t h e t w o c as es, δ P e = P e -P e . T h e n ois e aris es fr o m t h e u n c ert ai nt y i n d et er mi ni n g P e wit h a gi v e n n u m b er of s a m pl es.

Q u a ntif yi n g s e nsiti vit y r e q uir es a c ali br ati o n of m a g n o n n u m b er as a f u n cti o n of p u m p p o w er, as w ell as t h e disp ersi v e s hift p er m a g n o n, χ q m . B ot h q u a ntiti es c a n b e o bt ai n e d i n d e p e n d e ntl y b y m e as uri n g t h e q u bit St ar k s hift a n d d e p h asi n g r at e as a f u n cti o n of t h e m a g n o n dri v e a m plit u d e. T h e s hift i n m e as ur e d q u bit fr e q u e n c y is gi v e n b y f q = ( χ q m / 2 π ) n m . A d diti o n all y, fl u ct u ati o ns i n t h e m a g n o n n u m b er d e p h as e t h e q u bit at a r at e γ m

w h er e ω c , ω m , ω q r e pr es e nt t h e fr e q u e n ci es a n d ĉ , m , q r e pr es e nt t H dis p = ω c ĉ † ĉ + ω m m † m + ω q q † q + α 2 ( q † q ) 2 + χ q c q † q ĉ † ĉ t er ms of χ q c as χ q m = (g m c / m c ) 2 χ q c . Si mil arl y, χ m c c a n b e e x pr ess e d t hr o u g h χ q m . mi ni mi zi n g t h e e ff e ct of str a y fi el d fr o m t h e p er m a n e nt m a g n et o n t h e q u bit. T h e q u bit-c a vit y c o u pli n g str e n gt h a

f or t h e c a vit y m o d e at c e nt er of t h e c a vit y, i n t h e Y Z pl a n e. Os cill ati n g E fi el ds ar e c o n c e ntr at e d at t h e q u bit p ositi o n o n t o p. T h e v e ct or pl ot o n t h e ri g ht cl e arl y s h o ws t h e o p p osit e E fi el d dir e cti o n. ( b) Fi nit e-el e m e nt si m ul ati o ns of m a g n eti c ( H ) fi el d f or t h e c a vit y m o d e at c e nt er of t h e c a vit y, i n t h e Y Z pl a n e. Os cill ati n g H fi el ds ar e m a xi m al n e ar t h e YI G s p h er e p ositi o n. D as h e d li n e is us e d t o r ef er t o t h e ori gi n ( c e nt er) of t h e c a vit y. ( c) P h ot o gr a p h of t h e m ai n c o m p on e nts of t h e d e vi c e. T h e c a vit y is m a d e of t hr e e C u pi e c es t h at ar e st a c k e d o n t o p of e a c h ot h er a n d b olt e d t o g et h er wit h s cr e ws. B ott o m pi e c e is s h o w n l eft, mi d dl e pi e c e (i n cl u di n g q u bit c hi p) o n t h e ri g ht. A li d t h at m o u nts t o t h e t o p of t h e mi d dl e pi e c e is n ot s h o w n. YI G s p h er e b ar el y visi bl e at t h e c e nt er of t h e b ott o m pi e c e. O n e of t h e p er m a n e nt m a g n ets us e d is visi bl e o n t h e si d e of
D e vi c e d esi g n Fi nit e-el e m e nt si m ul ati o ns ( o bt ai n e d fr o m A ns ys H F S S) of t h e l u m p e d-el e m e nt c a vit y ar e s h o w n i n Fi g. 5( a) . T h e s p ati all
n d t h e c orr es p o n di n g dis p ersi v e s hift ar e e v al u at e d b y c al c ul ati n g t h e e n er g y p arti ci p ati o n r ati o of t h e tr a ns m o n j u n cti o n [4 9 ]. T h e m a g n o n-c a vit y c o u pli n g is e v al u at e d wit h t h e m a g n eti c-fi el d v al u e i nt e gr at e d o v er t h e YI G s p h er e v ol u m e n or m ali z e d t o h alf-p h ot o n e n er g y [ 3 1 ]. A pi ct ur e of t h e p h ysi c al d e vi c e is

(B 1 ) F or t h e q u bit d e p h asi n g, w e c a n writ e t h e t ot al d e p h asi n g r at e as [3 4 ] wit h dis pl a c e m e nts ξ = ( i e -iω i t ) /(( ω q -ω i ). We c a n n o w e xtr a ct a s w a p t er m ∝ ˆq † m w h os e c o e ffi ci e nt is gi v e n b y q m / 2, w h er e q m ∝ α ϕ 2 q ϕ 2 m e i( ω q -ω m )t κ m , yi el di n g t h e a p pr o xi m at e s ol uti o n q ≈ ˆq (0 )e -2 q m t/ 2 κ m .

(C 6 )

Cl e arl y, t h e d e c a y r at e of q u bit i n t his c as e is κ = 2 q m / κ m . F or δ = 0, w e c a n writ e e v ol uti o n of q as q ≈ ˆq (0 )e -t

6 9 , 1 ( 1 9 8 0). [ 4

2] Y. Li, V. G. Yefr e m e n k o, M. Lis o v e n k o, C. Tr e villi a n, T. P ol a k o vi c, T. W. C e cil, P. S. B arr y, J. P e ars o n, R. Di v a n, V. T y b er k e v y c h, C. L. C h a n g, U. Wel p, W.-K. K w o k, a n d