Na u e Physics | Volume 19 | Decembe 2023 | 1821–1826 1821
na u e physics
h ps://doi.o g/10.1038/s41567-023-02235-9A icle
Resonan enhancemen o pho o-induced
supe conduc i i y in K3C60
E. Rowe1, B. Yuan 1, M. Buzzi 1, G. Jo zu 1, Y. Zhu1, M. Fechne 1, M. Fö s 1,
B. Liu1,2, D. Pon i oli 3, M. Riccò 3 & A. Ca alle i 1,4
Pho o-exci a ion a e ahe z and mid-in a ed equencies has eme ged
as an e ec i e way o manipula e unc ionali ies in quan um ma e ials,
in some cases c ea ing non-equilib ium phases ha ha e no equilib ium
analogue. In K3C60, a me as able ze o- esis ance phase was obse ed
ha has op ical p ope ies, nonlinea elec ical anspo and p essu e
dependencies compa ible wi h non-equilib ium high- empe a u e
supe conduc i i y. He e we demons a e a wo-o de s-o -magni ude
inc ease in pho o-suscep ibili y nea 10 THz exci a ion equency. A hese
d i e equencies, a me as able supe conduc ing-like phase is obse ed
up o oom empe a u e. The disco e y o a dominan equency scale
sheds ligh on he mic oscopic mechanism unde lying pho o-induced
supe conduc i i y. I also indica es a pa h owa ds s eady-s a e ope a ion,
limi ed a p esen by he a ailabili y o a sui able high- epe i ion- a e op ical
sou ce a hese equencies.
The sea ch o new non-equilib ium unc ional phases in quan um ma e-
ials, such as op ically induced e oelec ici y
1,2
, magne ism
3–5
, cha ge
densi y wa e o de
6,7
, non- i ial opology
8,9
and supe conduc i i y
10–18
,
has become a cen al esea ch heme in condensed-ma e physics. In
he case o K
3
C
60
(Fig. 1a), mid-in a ed op ical pulses ha e been ex en-
si ely documen ed o yield an uncon en ional non-equilib ium phase
ha exhibi s me as able ze o esis ance14, ex ao dina ily high mobil-
i y and a supe conduc ing-like gap in he op ical conduc i i y12,14 ha
educe wi h applied p essu e
13
, and nonlinea cu en – ol age cha -
ac e is ics19. All hese obse a ions a e indica i e o non-equilib ium
high- empe a u e supe conduc i i y, obse ed a base empe a u es
a exceeding he highes equilib ium supe conduc ing c i ical em-
pe a u e o any alkali-doped ulle ide (Fig. 1b).
Typical expe imen al esul s epo ed un il now a e displayed in
Fig. 2c. K
3
C
60
powde s we e held a a base empe a u e T = 100 K ≫
T
c
= 20 K and i adia ed wi h 1-ps-long pulses wi h 170 meV pho on
ene gy (wa eleng h λ ≈ 7.3 µm, equency ≈ 41 THz) a a luence o
18 mJ cm
−
². This s ong exci a ion egime yielded a long-li ed ansien
s a e wi h p onounced changes in bo h he eal and imagina y pa s o
he op ical conduc i i y, measu ed using phase-sensi i e e ahe z
ime-domain spec oscopy. The ansien op ical p ope ies displayed
in Fig. 2c a e eminiscen o hose o he equilib ium supe conduc ing
s a e measu ed in he same ma e ial a T ≪ T
c
= 20 K (c . Fig. 2b) and a e
sugges i e o ansien high- empe a u e supe conduc i i y. These
signa u es consis o pe ec e lec i i y, a gap in he eal pa o he
op ical conduc i i y
σ1(ω)
and an imagina y conduc i i y
σ2(ω)
ha
di e ges owa ds low equencies as
σ2(ω)∝1/ω
. The di e gen
σ2(ω)
implies ( h ough K ame s–K onig ela ions) he p esence o a peak in
σ1
cen ed a ze o equency, wi h a wid h limi ed by he li e ime o he
s a e ha also de e mines he ca ie mobili y.
These da a we e ob ained by accoun ing o he inhomogene-
ous exci a ion o he p obed olume using a mul ilaye model. He e
we show he esul s o his econs uc ion unde he assump ion o a
linea ( illed blue ci cles) and sublinea (open symbols)20 dependence
o he pho o-induced changes in he e ahe z e ac i e index on he
mid-in a ed pump luence. Two sublinea models a e shown, wi h an
assumed squa e- oo luence dependence in blue ci cles and sa u a ing
luence dependence in b own iangles, as de ailed in Supplemen a y
Sec ion 6. Allowing o a ini e- empe a u e supe conduc o in which
a a ying densi y o uncondensed quasipa icles also con ibu es
Recei ed: 18 Janua y 2023
Accep ed: 29 Augus 2023
Published online: 5 Oc obe 2023
Check o upda es
1Max Planck Ins i u e o he S uc u e and Dynamics o Ma e , Hambu g, Ge many. 2Paul Sche e Ins i u e, Villigen, Swi ze land. 3Dipa imen o di Scienze
Ma ema iche, Fisiche e In o ma iche, Uni e si à degli S udi di Pa ma, Pa ma, I aly. 4Depa men o Physics, Cla endon Labo a o y, Uni e si y o Ox o d,
Ox o d, UK. e-mail: and ea.[email p o ec ed].de
Na u e Physics | Volume 19 | Decembe 2023 | 1821–1826 1822
A icle h ps://doi.o g/10.1038/s41567-023-02235-9
has emained ou o each. Many po en ially impo an esonances a
lowe equencies (hν < 80 meV) ha e emained unexplo ed, p ima ily
due o he lack o a sui able high-in ensi y pump sou ce ha ope a es
in his ange. In he p esen wo k, we explo e exci a ion a ene gies
be ween 24 and 80 meV (6–20 THz). This ene gy ange hos s many
exci a ions, bo h ib a ional (phonons) and elec onic in na u e,
including a b oad pola onic peak seen in
σ1
cen ed a abou 60 meV
(15 THz). The possible ele ance o his exci a ion has been highligh ed
in e . 22, al hough his p edic ion could no be es ed o da e.
To achie e wide uneabili y, we used a e ahe z sou ce based
on chi ped-pulse di e ence equency gene a ion, mixing he nea -
in a ed signal beams o wo phase-locked op ical pa ame ic ampli-
ie s23. This sou ce, illus a ed schema ically in Fig. 3a and desc ibed
in de ail in Supplemen a y Sec ion 4, was used o gene a e na ow-
bandwid h pulses wi h pho on ene gies spanning he ange om 24
o 145 meV (6–35 THz). All measu emen s epo ed he e we e ca ied
ou wi h an exci a ion bandwid h o hΔνpump ≈ 4 meV (1 THz) and
Δτpump ≈600
s pulse du a ion. The same p obing p o ocol as ha
epo ed in Fig. 2 was used he e o de ec changes in he complex op i-
cal p ope ies o p obe ene gies spanning 4–18 meV (1–4.5 THz).
Figu e 3b–d shows e lec i i y and complex conduc i i y spec a
measu ed a e pho o-exci a ion wi h pulses uned o 41 meV pho on
ene gy (λ ≈ 30 µm, ≈ 10 THz) a base empe a u es o 100 K and oom
empe a u e, espec i ely. The esponse is e y simila o he case
epo ed in Fig. 2 o 170 meV (41 THz) exci a ion, mani es ed on me a-
s able imescales bu pe sis ing he e up o oom empe a u e despi e
an exci a ion luence almos wo o de s o magni ude weake . Figu e 3e
displays he ime e olu ion o he op ical p ope ies wi h a ansien
ampli ying s a e a ea ly pump-p obe delays, as al eady epo ed in
e . 24, which elaxes in o a me as able s a e wi h supe conduc ing-like
op ical p ope ies.
Figu e 4a shows he scaling wi h luence o
R(ω)
and
σ1(ω)
(a e aged in he 5–10 meV ange), as well as he ac ional supe luid
densi y in esponse o pho o-exci a ion a 170 meV (41 THz) and 41 meV
(10 THz). These measu emen s we e ca ied ou a a pump-p obe ime
delay o 10 ps and hus e e o he me as able phase. The igu e shows
how all igu es o me i app oach hei equilib ium supe conduc ing-
s a e alues as he luence inc eases, wi h he luence equi ed being
oughly 50 imes less o 41 meV (10 THz) compa ed o 170 meV (41 THz)
exci a ion.
Simila luence dependence measu emen s we e ca ied ou by
a ying he pho on ene gy o he pump and main aining a cons an
4 meV (1 THz) bandwid h wi h 600 s pulse du a ion. Fo all exci a ion
pho on ene gies be ween 24 meV (6 THz) and 145 meV (35 THz), he
pho o-induced changes in he op ical p ope ies we e quali a i ely
simila o hose shown in Figs. 2 and 3, wi h only he size o he esponse
o a gi en luence di e ing. F om each luence dependence, we
ex ac ed a igu e o me i o he pho o-suscep ibili y, de ined as he
a e o deple ion o spec al weigh in
σ1
wi h exci a ion luence, in he
limi o low luence (Supplemen a y Sec ion 8). Plo s o he
pump- equency-dependen pho o-suscep ibili y a e shown in Fig. 4b
o bo h 10 ps and 50 ps pump-p obe ime delay. A peak cen ed a
41 meV (10 THz) wi h abou 16 meV FWHM wid h is obse ed in hese
measu emen s. Nex , we will discuss h ee dis inc ene gy scales ha
coincide wi h his esonance; sequen ially, hey ela e o ‘on-ball’ o bi al
exci a ions, phonons and exci ons.
Supe conduc i i y in alkali-doped ulle ides is belie ed o be
media ed by a dynamical Jahn–Telle dis o ion, which leads o an
e ec i e nega i e Hund’s coupling o he o bi als o a single bucky-
ball25 and o a low-spin S = 1/2 s a e. A heo e ical model based on
his assump ion has been success ul a p o iding a quan i a i ely
co ec phase diag am o ulle ide supe conduc o s om ab ini io
calcula ions26,27. In his model, he local g ound s a e o he sys em is a
six old degene a e low-spin s a e, which ea u es in ao bi al pai s ha
delocalize o e wo molecula o bi als. As de ailed in Supplemen a y
o he e ahe z esponse, he supe conduc ing-like na u e o he
ansien s a e is independen o he speci ic choice o assump ion21.
Only quan i a i e di e ences associa ed wi h he ela i e densi ies o
induced supe luid and hea ed quasipa icles, which can be ex ac ed
by i ing wi h a wo- luid model, eme ge. This modelling also e eals
ha he enhancemen o conduc i i y obse ed in hese expe imen s
is connec ed no o an inc ease in he ca ie densi y, which emains
cons an upon pho o-exci a ion, bu a he o a gian inc ease in he
ca ie mobili y.
Th ee spec ally in eg a ed igu es o me i a e ex ac ed om
he snapsho s o e lec i i y (R
(ω,τ)
),
σ1(ω,τ)
and
σ2(ω,τ)
and
plo ed as a unc ion o pump-p obe ime delay
τ
in Fig. 2e, showing
he ime e olu ion o he sys em. The i s wo quan i ies a e he
equency-a e aged alues o R(ω) and
σ1(ω)
om 5 o 10 meV, a e-
quency ange ha lies below he pho o-induced ene gy gap, o which
a ze o- empe a u e supe conduc o wi h in ini e li e ime would gi e
alues o 1 and 0, espec i ely. The hi d igu e o me i is he ac ional
supe luid densi y, which is p opo ional o he di e gence o
σ2(ω)
.
This is de e mined by i ing he pho o-exci ed op ical p ope ies wi h
a wo- luid model whe e one luid ep esen s he emaining no mal
ca ie s wi h a ini e sca e ing a e and he o he has ze o sca e ing
a e, gi ing a supe conduc ing-like con ibu ion. De ails o his i ing
p ocedu e a e gi en in Supplemen a y Sec ion 7.
Fo low exci a ion luences, he sys em becomes supe conduc ing-
like a e pho o-exci a ion and elaxes on a ime scale o a ew picosec-
onds. As al eady seen in he spec ally esol ed measu emen s, o high
exci a ion luences, he sys em en e s a me as able egime in which
he supe conduc ing-like op ical p ope ies pe sis o much longe
imes, up o se e al nanoseconds.
We no e ha he empe a u e dependence epo ed in e . 12
shows ansien supe conduc ing-like op ical p ope ies up o a em-
pe a u e o 150–200 K. Fo highe empe a u es, he gapping and
ex ac ed supe luid densi y a e se e ely educed. Examples o such
spec a measu ed a oom empe a u e a e shown in Fig. 2d. Ne e -
heless, he p essu e scaling epo ed in e . 13 sugges s ha aces
o non-equilib ium supe conduc i i y may su i e up o highe em-
pe a u es, aising he p ospec ha wi h mo e e ec i e d i ing, a ull
mani es a ion o he me as able supe conduc ing-like s a e may be
possible a 300 K.
Un il now, hese expe imen s ha e been limi ed o exci a ion
pho on ene gies be ween 80 and 165 meV (20–40 THz), such ha a
mo e comp ehensi e sea ch o a dominan exci a ion equency scale
AFI
PI Me al
Supe conduc o
Cs3C60 Rb3C60 K3C60
P essu e
Tempe a u e (K)
1
10
100
ba
Fig. 1 | C ys al s uc u e and phase diag am o K3C60. a, C ys al s uc u e o
he o ganic molecula solid K3C60. C60 molecules a e si ua ed a he e ices o a
ace-cen ed-cubic la ice. Po assium a oms ( ed) occupy he in e s i ial oids.
b, P essu e– empe a u e phase diag am o he cc-A3C60 alkali-doped ulle ide
amily o compounds showing he p esence o supe conduc ing, me allic,
pa amagne ic insula ing (PI) and an i- e omagne ic insula ing (AFI) phases.
Physical p essu e unes he spacing be ween he C60 molecules. The g ey line
indica es he bounda y be ween he insula ing and me allic/supe conduc ing
compounds. The blue shaded a ea indica es whe e supe conduc i i y is
obse ed a equilib ium. The s a indica es he K3C60 compound in es iga ed in
his wo k, which supe conduc s below he c i ical empe a u e (Tc) o 20 K.
Na u e Physics | Volume 19 | Decembe 2023 | 1821–1826 1823
A icle h ps://doi.o g/10.1038/s41567-023-02235-9
Sec ion 10, a i s se o local exci ed s a es also ea u es such pai s,
albei wi h a di e en angula momen um ( ha is, a di e en in e o -
bi al phase o he delocalized pai ). Ab ini io calcula ions p edic an
ene gy spli ing o 37 meV be ween hese wo se s o s a es
26,27
. The
obse ed esonance may he e o e be ela ed o he c ea ion o in e -
o bi al pai s wi h local angula momen um, which may also con ibu e
o supe conduc i i y, as sugges ed in he Suhl–Kondo mechanism28–30.
Howe e , i is no ye clea exac ly how his exci a ion is ans o med
in he p esence o unnelling be ween neighbou ing C60 molecules
and why he c ea ion o such pai s may suppo me as able supe con-
duc i i y a such high empe a u es. Fu he mo e, as he local pa i y
o his exci ed s a e would be di e en om ha o he g ound s a e,
condensa ion in his con igu a ion may gi e ise o a supe conduc o
wi h di e en symme y. This possibili y, whils an alizing, emains
specula i e and should be es ed wi h mo e comp ehensi e ul a as
p obing me hods.
THz
gene a ion
WLG
Th ee-s age OPA
Ti:Sa oscilla o Ti:Sa ampli ie ×2
T1u
173 meV
0
0.5
1.0
Re lec i i y
0
Ene gy (meV)Ene gy (meV)
4 10 20 404 10 20 404 10 20 40
0
300
600
900
σ2 (–1 cm–1)σ1 (–1 cm–1)
σ1* (–1 cm–1)
ns /n o
Ene gy (meV)
0
300
600
900
25 K > Tc
5 K < Tc
18 mJ cm–2
Re lec i i y*
0
0.5
1.0
0
150
0 5 10 50 100
Time (ps)
0.5
1.0
Equilib ium
Equilib ium
Pho oexci ed
Equilib ium
Pho oexci ed
T = 100 K
τ = 10 ps
T = 295 K
τ = 10 ps
a
b c d e
DFG
Fig. 2 | Pho o-induced me as able supe conduc i i y in K3C60 gene a ed wi h
in ense 170 meV exci a ion pulses. a, Schema ic o he expe imen al se up.
Pump pulses wi h 170 meV (41 THz) pho on ene gy (close o esonance wi h he
illus a ed phonon mode) we e gene a ed by means o whi e ligh gene a ion
(WLG), ollowed by op ical pa ame ic ampli ica ion (OPA) and subsequen
di e ence equency gene a ion (DFG) o he signal and idle beams. These
pulses we e s e ched o a du a ion o
Δτpump ≈1
ps by p opaga ion in a highly
dispe si e CaF2 od. The pho o-induced changes in he a -in a ed op ical
p ope ies o K3C60 we e de ec ed wi h phase-sensi i e ansien e ahe z (THz)
ime-domain spec oscopy. b, Re lec i i y (sample–diamond in e ace) and eal
and imagina y pa s o he op ical conduc i i y o K3C60 measu ed a e cooling
ac oss he equilib ium supe conduc ing ansi ion. c, Same quan i ies measu ed
a equilib ium ( ed lines) and 10 ps a e exci a ion (symbols). The da a in illed
blue ci cles, open blue ci cles and open b own iangles we e ob ained
accoun ing o he inhomogeneous exci a ion o he p obed olume unde he
assump ion o a linea , squa e- oo and sa u a ing ( espec i ely) luence
dependence o he pho o-induced changes in he complex e ac i e index o he
ma e ial (Supplemen a y Sec ion 6). These da a we e acqui ed a a base
empe a u e T = 100 K wi h an exci a ion luence o app ox. 18 mJ cm−2. d, Same
quan i ies as in c bu measu ed a a base empe a u e T = 295 K wi h an exci a ion
luence o app ox. 15 mJ cm−2. e, Time dependence o he a e age alue (indica ed
by *) o e lec i i y and eal pa o he op ical conduc i i y
σ1(ω)
in he 5–10 meV
spec al ange, and ligh -induced ‘supe luid densi y’ (ns ) ex ac ed om a
wo- luid model i and exp essed as a ac ion o he o al cha ge ca ie densi y
(n o ). Filled and open symbols indica e he esul s o he linea and squa e- oo
econs uc ion models, espec i ely. The ed do ed lines indica e he alue o
he co esponding quan i y in equilib ium. These da a we e acqui ed a a base
empe a u e T = 100 K wi h a luence o app oxima ely 18 mJ cm−2 and a
pump-pulse du a ion o
Δτpump ≈1
ps. T ansien op ical spec a co esponding
o hese measu emen s a e epo ed in Supplemen a y Fig. 6.3.
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A icle h ps://doi.o g/10.1038/s41567-023-02235-9
Tu ning o phonon exci a ions, we also no e ha he 41 meV eso-
nance equency iden i ied he e coincides wi h an in a ed-ac i e T
1u
phonon, which p edominan ly consis s o in amolecula mo ion o he
C a oms. Whe eas he a omic mo ions o he 170 meV molecula mode
discussed p e iously in e . 12 a e di ec ed along he angen ial di ec-
ions o he C
603−
molecule, hose o he 41 meV mode a e p edominan ly
along he adial di ec ions (Supplemen a y Sec ion 9). By pe o ming
ozen-phonon calcula ions using densi y unc ional heo y (DFT), we
e alua ed he di e en e ec o hese dis o ions on he h ee
1u
molecu-
la le els a he Fe mi ene gy, which we map ou om DFT wa e unc ions
as maximally localized Wannie unc ions (Supplemen a y Sec ion 9). In
he undis o ed C603− s uc u e, hese molecula le els a e degene a e.
Applying a dis o ion along a T
1u
coo dina e li s his degene acy, lea ing
a doubly degene a e 1u o bi al lowe ed in ene gy. This elec onic con igu-
a ion is p one o de eloping a Jahn–Telle dis o ion ha may lead o
an enhanced nega i e Hund’s coupling, possibly acili a ing he onse o
0
300
600
900
0
300
600
900
0
0.5
1.0
Re lec i i y
0
0.5
1.0
0
0.5
1.0
Re lec i i y*
0
150
0.5 mJ cm–2
Equilib ium
Pho oexci ed
T = 100 K T = 295 K T = 295 K
Ti:Sa ampli ie
2× h ee-s age OPAs
THz gene a ion
Pulse s e che s
DFG
WLG
T1u
43 meV
σ2 (–1 cm–1)σ1 (–1 cm–1)
Ene gy (meV)Ene gy (meV)
4 10 20 404 10 20 404 10 20 40
Ene gy (meV)
0 5 10 50 100
Time (ps)
σ1* (–1 cm–1)
ns /n o
τ = 50 psτ = 10 ps τ = 50 ps
a
b c d e
Fig. 3 | Pho o-induced me as able supe conduc i i y in K3C60 gene a ed wi h
41 meV exci a ion pulses. a, Schema ic o he expe imen al se up. Pump pulses
wi h 41 meV (10 THz) pho on ene gy (close o esonance wi h he illus a ed
phonon mode) a e gene a ed using win op ical pa ame ic ampli ie s (OPAs)
seeded by he same whi e ligh (WLG) h ough subsequen chi ped-pulse
di e ence equency gene a ion (DFG) o he wo s e ched signal beams. The
pho o-induced changes in he a -in a ed op ical p ope ies o K3C60 a e
de ec ed wi h phase-sensi i e ansien e ahe z ime-domain spec oscopy.
b, Re lec i i y (sample–diamond in e ace) and eal and imagina y pa s o he
op ical conduc i i y o K3C60 measu ed in equilib ium ( ed lines) and 50 ps a e
exci a ion (symbols). The da a in illed blue ci cles, open blue ci cles and open
b own iangles we e ob ained accoun ing o he inhomogeneous exci a ion o
he p obed olume unde he assump ion o a linea , squa e- oo and sa u a ing
( espec i ely) luence dependence o he pho o-induced changes in he complex
e ac i e index o he ma e ial (Supplemen a y Sec ion 6). These da a we e
acqui ed a base empe a u e T = 100 K wi h pump pulses uned o 41 meV
(10 THz) cen e equency and exci a ion luence o app ox. 0.4 mJ cm−2. c, Same
quan i ies as in b bu measu ed 10 ps a e pho o-exci a ion a base empe a u e
T = 295 K. d, Same quan i ies as in c bu measu ed 50 ps a e pho o-exci a ion.
e, Time dependence o he a e age alue (indica ed by *) o e lec i i y and eal
pa o he op ical conduc i i y
σ1(ω)
in he 5–10 meV spec al ange, and
ligh -induced ‘supe luid densi y’ (ns ) ex ac ed om a wo- luid model i and
exp essed as a ac ion o he o al cha ge ca ie densi y (n o ). Filled and open
symbols indica e he esul s o he linea and squa e- oo econs uc ion models,
espec i ely. The inse in he op panel highligh s he ea ly ime delays o which
ligh ampli ica ion (R > 1) is obse ed ( ed shading). The ed do ed lines indica e
he alue o he co esponding quan i y in equilib ium. These da a we e acqui ed
a a base empe a u e T = 100 K wi h pump pulses uned o 45 meV (11 THz)
pho on ene gy and exci a ion luence o app oxima ely 0.5 mJ cm−2. F equency-
esol ed spec a co esponding o hese measu emen s can be seen in
Supplemen a y Fig. 6.4.
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A icle h ps://doi.o g/10.1038/s41567-023-02235-9
supe conduc i i y a highe empe a u es. The s eng h o he induced
spli ing is quad a ic in he phonon coo dina e and is enhanced when
d i ing he 41 meV mode compa ed o he 170 meV one, sugges ing ha
he obse ed esonance may a ise om a mo e e icien manipula ion
o he elec onic deg ees o eedom when d i ing he 41 meV T
1u
mode.
Finally, we add ess he elec onic exci a ions discussed in e . 22,
whe e an enhanced e ec on uning he d i e o lowe equencies
was al eady p edic ed. This wo k p oposed he exis ence o a d essed
exci on in he exci a ion spec um o K3C60 a he same ene gy scale
as he esonance epo ed he e. Exci a ion o he sys em a his e-
quency would gene a e exci ons ha would ac as a ese oi able o
incohe en ly cool he quasipa icles, esul ing in he eeme gence o
supe conduc i i y a base empe a u es in excess o he equilib ium T
c
.
We expec he impo ance o his disco e y o be capi alized on
in u u e wo k. The ex eme e iciency imp o emen due o esonan
enhancemen , nea ing wo o de s o magni ude, is expec ed o also d a-
ma ically educe unwan ed dissipa ion. This, aken in conjunc ion wi h
he obse ed nanosecond-long li e ime, sugges s ha exci a ion o he
sample wi h a ain o pulses o only 400 µJ cm
−2
deli e ed a a 100 MHz
epe i ion a e—as de e mined by he in e se li e ime o his s a e—may
yield con inuous wa e ope a ion. Because his e ec is documen ed
he e o pe sis up o oom empe a u e, con inuous wa e ope a ion
would likely ha e impo an p ac ical implica ions. To make his egime
expe imen ally accessible, single-o de -o -magni ude imp o emen s
in he e iciency o he p ocess o he ligh –ma e coupling s eng h,
combined wi h sui able de elopmen s in high- epe i ion- a e e ahe z
sou ces, would be equi ed.
Online con en
Any me hods, addi ional e e ences, Na u e Po olio epo ing summa-
ies, sou ce da a, ex ended da a, supplemen a y in o ma ion, acknowl-
edgemen s, pee e iew in o ma ion; de ails o au ho con ibu ions
and compe ing in e es s; and s a emen s o da a and code a ailabili y
a e a ailable a h ps://doi.o g/10.1038/s41567-023-02235-9.
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0.001
0.01
0.1
1
0.01
0.1
1
Pho osuscep ibili y
(a.u.)
Pho osuscep ibili y
(a.u.)
0 40 80 120 160 200
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0
0.5
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Fluence (mJ cm–2)h pump (meV)
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Fig. 4 | Scaling o he ou -o -equilib ium ea u es o pho o-induced
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alue (indica ed by *) o he e lec i i y and eal pa o he op ical conduc i i y
σ1(ω)
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g adien o he los spec al weigh in
σ1
in he low- luence limi (Supplemen a y
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Na u e Physics | Volume 19 | Decembe 2023 | 1821–1826 1826
A icle h ps://doi.o g/10.1038/s41567-023-02235-9
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Publishe ’s no e Sp inge Na u e emains neu al wi h ega d o
ju isdic ional claims in published maps and ins i u ional a ilia ions.
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Na u e Physics
A icle h ps://doi.o g/10.1038/s41567-023-02235-9
Me hods
All me hods can be ound in he Supplemen a y In o ma ion.
Da a a ailabili y
Sou ce da a a e p o ided wi h his pape . All o he da a ha suppo
he plo s in his pape and o he indings o his s udy a e a ailable om
he co esponding au ho s upon easonable eques .
Acknowledgemen s
The esea ch leading o hese esul s ecei ed unding om he
Eu opean Resea ch Council unde he Eu opean Union’s Se en h
F amewo k P og amme (FP7/2007-2013)/ERC G an Ag eemen No.
319286 (QMAC, A.C.). We acknowledge suppo om he Deu sche
Fo schungsgemeinscha (DFG) h ough he Clus e o Excellence
‘The Hambu g Cen e o Ul a as Imaging’ (EXC 1074 – p ojec ID
194651731, A.C.). We hank M. Volkmann and P. Lich o hei echnical
assis ance. We a e also g a e ul o B. Fiedle and B. Höhling o hei
suppo in he ab ica ion o he elec onic de ices used on he
measu emen se up and o J. Ha ms o assis ance wi h g aphics.
Au ho con ibu ions
E.R., B.L., M. Fö s , M.B. and A.C. concei ed he expe imen . A.C.
supe ised he p ojec . The se up shown in Fig. 2 was buil and ela ed
measu emen s we e pe o med by M.B. and G.J. The se up shown
in Fig. 3 was buil by B.L. wi h suppo om M. Fö s , and ela ed
measu emen s we e pe o med by E.R., B.Y. and Y.Z. Da a analysis was
pe o med by E.R. and M.B. K3C60 samples we e p o ided by D.P. and
M.R. DFT ozen-phonon calcula ions we e pe o med by M. Fechne .
The single-molecule Hamil onian ea men was de eloped by G.J.
The manusc ip was w i en by E.R., M.B., G.J., M. Fechne and A.C.
wi h con ibu ions om all o he au ho s.
Funding
Open access unding p o ided by Max Planck Socie y.
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ma e ial a ailable a h ps://doi.o g/10.1038/s41567-023-02235-9.
Co espondence and eques s o ma e ials should be add essed
o A. Ca alle i.
Pee e iew in o ma ion Na u e Physics hanks he anonymous
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