Monoli hic equency comb pla o m based
on in e band cascade lase s and de ec o s
BENEDIKT SCHWARZ,1,*JOHANNES HILLBRAND,1MAXIMILIAN BEISER,1AARON MAXWELL ANDREWS,1
GOTTFRIED STRASSER,1,2 HERMANN DETZ,2,3 ANNE SCHADE,4ROBERT WEIH,5AND SVEN HÖFLING4,6
1Ins i u e o Solid S a e Elec onics, TU Wien, Vienna, Aus ia
2Cen e o Mic o- and Nanos uc u es, TU Wien, Vienna, Aus ia
3Cen al Eu opean Ins i u e o Technology, B no Uni e si y o Technology, B no, Czech Republic
4Technische Physik, Physikalisches Ins i u , Uni e si y Wü zbu g, Am Hubland, 97074 Wü zbu g, Ge many
5Nanoplus Nanosys ems and Technologies GmbH, 97218 Ge b unn, Ge many
6SUPA, School o Physics and As onomy, Uni e si y o S And ews, S And ews, KY16 9SS, UK
*Co esponding au ho : benedik [email p o ec ed]
Recei ed 26 Ap il 2019; e ised 8 June 2019; accep ed 11 June 2019 (Doc. ID 366112); published 12 July 2019
New insigh s in o he lase dynamics o in e band cascade lase s e eal he possibili y o gene a e equency-modula ed
combs by u ilizing hei inhe en gain nonlinea i y. The esul ing comb s a e is cha ac e ized by chi ped ins an aneous
equency, which appea s o be uni e sal o equency combs based on gain-induced ou -wa e mixing. The as
dynamics in he injec o s u he allow he ealiza ion o excep ionally sensi i e and high-speed pho ode ec o s,
ope a ing a oom empe a u e, using he e y same epilaye s uc u e. Wi h he capabili y o in eg a ing e-
quency combs and ul a- as de ec o s on a single chip consuming less han a wa o elec ic powe , in e band cascade
lase echnology p o ides a comple e and unma ched pla o m o u u e monoli hic and ba e y-d i en dual-comb
spec ome e s.
Published by The Op ical Socie y unde he e ms o he C ea i e Commons A ibu ion 4.0 License. Fu he dis ibu ion o his wo k mus
main ain a ibu ion o he au ho (s) and he published a icle’s i le, jou nal ci a ion, and DOI.
h ps://doi.o g/10.1364/OPTICA.6.000890
1. INTRODUCTION
Senso s a e he hea o e e y sma echnology. They allow us o
cap u e da a abou en i onmen al pollu ion, plan in ec ions, o
ou cu en physiological condi ion. The mid-in a ed egion is
he spec al egion o choice when i comes o sensing and spec-
oscopy. No o he spec al egion p o ides he same sensi i i y o
selec i i y o molecula inge p in ing. Es ablished mid-in a ed
spec ome e s a e mos ly based on ee-space op ics and mo ing
pa s. None o hese concep s can be su icien ly down-scaled o
single-chip dimensions. Dual-comb spec oscopy [1–4] o e s he
possibili y o di ec ly map he op ical spec um o he adio-
equency (RF) domain. Dual-comb spec ome e s do no equi e
mo able pa s and can be minia u ized wi hou losing spec al
esolu ion— he e is no ela ion be ween he spec al esolu ion
and he spa ial dimension. I s ull po en ial o p ac ical applica-
ions can be unlocked i bo h equency comb gene a o s and
he e odyne de ec o s a e minia u ized, d i en by a ba e y and
ideally in eg a ed on a single chip.
Fo a long ime, equency comb gene a ion in he mid-
in a ed was limi ed o able- op ins umen s [5,6]. Rela i ely
compac se ups can be ealized using nea -in a ed equency
combs combined wi h di e ence equency gene a ion [7,8].
E en mo e po en ial o in eg a ion was demons a ed u ilizing
he Ke nonlinea i y in passi e mic o esona o s [9,10]. While
mic o esona o combs ecen ly eached he ma u i y o enable
compac and ba e y-d i en sys ems a elecom wa eleng hs [11],
equency comb gene a ion in he mid-in a ed is s ill es ic ed
o ex e nal pump lase s. An al e na i e concep employs he non-
linea i y o he lase i sel . This pe se monoli hic app oach is ideal
o he ealiza ion o minia u ized spec ome e s and was ound in
quan um cascade lase s (QCLs) a ew yea s ago [12]. Recen ly,
passi e mode-locking was achie ed using GaSb-based ype I cas-
cade diode lase s [13]. Wi h his, mode-locked semiconduc o
diode lase s a e s a ing o be a ailable in he ange o 2–3.5 μm.
An ideal low-powe al e na i e ope a ing also a longe wa e-
leng h up o 6 μm is cons i u ed by in e band cascade lase s
(ICLs) [14–16]. Thei powe consump ion is 1–2 o de s o mag-
ni ude smalle han ha o QCLs. Also, in e ms o ou pu powe
and e iciency, ICLs a e ca ching up apidly [15,17,18,19]. Thei
po en ial o mul i-he e odyne spec oscopy was al eady high-
ligh ed using mul i-mode Fab y–Pe o ICLs and compu a ional
co ec ion algo i hms o acqui e 16 lines in pa allel [20]. Robus
low-phase noise equency comb ope a ion, as demons a ed he e,
will enable dual-comb spec oscopy wi h he capabili y o simul-
aneously acqui e mo e han a hund ed modes.
In his wo k, we p esen a monoli hic equency comb sensing
pla o m u ilizing he as dynamics in ICLs. These as dy-
namics enable equency-modula ed comb ope a ion as well as
2334-2536/19/070890-06 Jou nal © 2019 Op ical Socie y o Ame ica
Resea ch A icle Vol. 6, No. 7 / July 2019 / Op ica 890
he ealiza ion o ul a- as pho ode ec o s using he same ICL
ma e ial and hence p o ide a monoli hic pla o m o dual-comb
spec oscopy. Ou indings and conclusions on equency comb
ope a ion a e di e en om hose o ecen wo ks ha ocused
on comb gene a ion ia passi e mode-locking o ICLs [21]
and sugges ha a ca e ul ein e p e a ion o hose esul s is e-
qui ed. (Recen esul s on passi e mode-locking o ICLs [23]
include bo h a second-o de au oco ela ion as well as a mul i-
he e odyne bea ace, which show no sign o pulse o ma-
ion, lacking he 8:1 a io in he au oco ela ion and pulses
in he mul i-he e odyne bea ace.) The ICL equency combs
p esen ed in his le e ely on he inhe en gain nonlinea i y
caused by he as -gain dynamics. They do no equi e a sa u able
abso be , and show hey he same phase cha ac e is ics as QCL
equency combs.
2. FREQUENCY-MODULATED COMBS USING
ICLS
In o de o in es iga e equency comb ope a ion o ICLs, we ab-
ica ed a wo-sec ion de ice [Fig. 1(a)]. The sho sec ion is op i-
mized o a low pa asi ic capaci ance o he con ac s o e icien
adio- equency (RF) ex ac ion and injec ion. I s DC bias can be
adjus ed o al e he locking p ope ies [24]. I is impo an o
no e ha he DC bias emains in he o wa d di ec ion and he e
is only used o ine- une he g oup eloci y dispe sion o he spec-
al lineshape o he ound- ip gain. This is undamen ally di e -
en o passi e mode-locking, e.g., in quan um well lase s, whe e
he sho sec ion is used o p o ide as sa u able loss using a
s ong e e se bias [13]. The high equency-modula ion esponse
p o ides impo an in o ma ion abou he in e nal gain dynamics.
The ex ac ed equency esponse is la up o 20 GHz and e eals
ha he cha ac e is ic esponse ime o he popula ion in e sion
τΔnis as enough such ha popula ion oscilla ions can occu
a leas a he i s wo ha monics o he epe i ion equency.
Since he condi ion τΔn ep ≲1is sa is ied, ou -wa e mixing
ia popula ion in e sion oscilla ions can be assumed o be he
dominan con ibu ion o he gain nonlinea i y [25] and enables
sel -s a ing equency comb ope a ion.
A i s indica ion o equency comb ope a ion is he obse -
a ion o a na ow bea no e. In mul i-mode lase s, each mode
pai causes a bea ing a hei di e ence equency. In equency
combs all modes a e equidis an , esul ing in a na ow bea no e.
Hence, he obse a ion o a na ow bea no e is a i s indica ion
o equency comb ope a ion. This bea no e can be obse ed us-
ing a as pho ode ec o (op ical) o di ec ly ex ac ed om he
lase d i ing cu en (elec ical)—p o ided ha he gain dynamics
a e as enough o ollow he bea ing. Figu e 1(b) shows he
(a)
(d) (e) ( )
(b) (c)
Fig. 1. ICL equency comb. (a) F equency-modula ion capabili ies o he op imized de ices measu ed op ically ia a as QWIP ( ed) and elec ically
ia RF ec i ica ion [22] (blue). The black cu e is co ec ed by he con ibu ion due o he pa asi ic capaci ance o he ICL and QWIP esponse o ex ac
he po ion due o he esponse o he gain medium. Inse : ske ch o he wo-sec ion de ice. (b) The spec al lines o he ICL bea oge he , leading o a
modula ion o he lase in ensi y a he ca i y ound- ip equency. The esul ing elec ical bea no e can be measu ed by eco ding he RF spec um o he
abso be cu en and unes wi h he abso be bias. Regions o sel -s a ing comb ope a ion a e highligh ed by he ec angles. (c) Na ow elec ical bea no e
wi h a linewid h o 4 kHz. (d, e) Shi ed Wa e In e mode Bea Fou ie T ans o m Spec oscopy (SWIFTS) analysis and co esponding ime-domain
signal o he ICL equency comb. The in e mode di e ence phases co e he ange om π o −π. This and he minimum in he SWIFTS in e e og ams
a ze o-phase a e cha ac e is ic o he supp ession o ampli ude modula ion. The spec um consis s o 114 modes spaced by 0
ep 10.17 GHz. The
mode g ouping migh be due o pa asi ic e lec ions in he wo-sec ion lase . ( ) Time-domain signal o a QCL equency comb [23]. I espec i e o he
sign, he bo h combs show he same cha ac e is ic dominan ly equency-modula ed ou pu . This sugges s ha he ICL equency comb is indeed
go e ned by he inhe en gain nonlinea i y, which is connec ed o he supp ession o ampli ude modula ions.
Resea ch A icle Vol. 6, No. 7 / July 2019 / Op ica 891
elec ically ex ac ed lase bea no e depending on he sho
sec ion bias. The la e can be al e ed o une he ICL in o he
sel -locking egime. The e, he bea no e appea s na ow wi h a
linewid h on he kilohe z (kHz) le el [Fig. 1(c)].
In o de o unequi ocally p o e equency comb ope a ion, we
employ shi ed wa e in e mode bea Fou ie ans o m spec os-
copy (SWIFTS) [26,27]. This echnique p o ides a comple e
cha ac e iza ion o a comb s a e by measu ing he cohe ence
and phase be ween each pai o comb lines ( o de ails, see he
me hods sec ion). The SWIFTS analysis o he ICL equency
comb is plo ed in Fig. 1(d). The ampli udes o he SWIFTS spec-
um ma ch he bea ing ampli udes ex ac ed om he in ensi y
spec um (blue do s), which se es as a p oo o comb ope a ion
o e he en i e emission spec um. The minimum o he SWIFTS
in e e og ams a ze o pa h di e ence is a clea sign o he sup-
p ession o ampli ude modula ions. This phenomenon is known
o be ela ed o as -gain dynamics [12]. E en mo e exci ing is
addi ional in o ma ion p o ided by he phases. The in e modal
phases ollow a chi ped pa e n co e ing a ange o 2π. The same
pa e n was ecen ly obse ed in QCLs [28]. Figu es 1(e) and 1( )
show he di ec compa ison o he ime-domain signals o an ICL
and a QCL equency comb. Al hough he lase ansi ion li e-
imes di e by 2 o de s o magni ude and ope a e a a di e en
wa eleng h, bo h equency combs show he linea ly chi ped
ins an aneous equency accompanied by he supp ession o
ampli ude modula ions. This ema kable simila i y indica es ha
he comb o ma ion is indeed go e ned by he same physical
mechanism— ou -wa e mixing due o popula ion in e sion os-
cilla ions. A s a e wi h small-ampli ude modula ion maximizes
he ound- ip gain, as ampli ude modula ions lead o a s onge
gain sa u a ion in as -gain media. This is he opposi e o passi e
mode-locking in slow-gain media wi h a as sa u able abso be ,
whe e he gain sec ion is oo slow o espond o in e mode bea -
ings. The e, he o ma ion o pulses is ad an ageous, as i min-
imizes he ound- ip loss. Recen heo e ical wo k e ealed ha
phase-locking in equency-modula ed combs is go e ned by he
combined e ec s o a Ke nonlinea i y due o a non-ze o line-
wid h enhancemen ac o (asymme ic spec al gain p o ile) in
as -gain media and he g oup eloci y dispe sion [29]. The sign
o hese e ec s de ine he di ec ion o he chi p, which migh be
due o an in-plane dispe sion ela ion ha leads o opposi e signs
o he linewid h enhancemen ac o in QCLs and ICLs.
Recen indings e ealed ha he epe i ion equency o a
QCL equency comb can be injec ion-locked o an ex e nal RF
oscilla o while main aining ull in e modal cohe ence [23]. This
enables all-elec ic s abiliza ion simila ly o phase-locked loops
[30] and addi ionally inc eases he ange o comb ope a ion and
he s abili y agains op ical eedback. This echnique can also be
employed wi h ICL equency combs. Figu e 2(a) shows he op-
ically measu ed bea no e spec um while sweeping he injec ion
equency ac oss he bea no e o h ee di e en injec ion powe
le els. As he equency o he injec ed signal app oaches he bea
no e, he la e is pulled owa ds i . The lase bea no e is ully
con olled by he ex e nal RF oscilla o wi hin a locking ange
o 1, 2, and 4 MHz, depending on he powe o he injec ed
signal. Figu es 2(b) and 2(c) show he in ensi y spec um as well
as he in e modal cohe ence spec um depending on he injec ion
equency. The colo map in Fig. 2(c) shows ha ull in e modal
cohe ence and hus equency comb ope a ion is achie ed wi hin
he locking ange.
3. MONOLITHIC ULTRA-FAST DETECTORS
USING ICLS
In eg a ing a comple e dual-comb spec ome e on a chip equi es
a echnology ha is capable o bo h equency comb ope a ion
and high-speed mul i-he e odyne de ec ion. This can be achie ed
by sel -de ec ion [31] o using on-chip in eg a ed pho ode ec o s.
An elegan solu ion is building he lase and de ec o om he
e y same ma e ial. This so-called bi- unc ional ope a ion was
i s demons a ed using QCLs [32] and igged he ealiza ion
(a) (b) (d)
(c)
(e) ( )
Fig. 2. Cohe en injec ion-locking and on-chip de ec ion capabili ies. (a) Op ical bea no e spec um o he ICL depending on he injec ion equency
o h ee di e en injec ion powe s. The la ge locking ange is due o he op imized RF injec ion. (b, c) In ensi y and SWIFTS spec al maps a 5 dB
injec ion powe as a unc ion o he injec ion equency. (d) Spec al esponsi i y and noise equi alen powe o he on-chip in e band cascade de ec o
(ICD), which was clea ed om he same chip. (e) Di ec modula ion esponse o he ICL measu ed wi h he ICD. ( ) Na ow bea no e o he ICL comb
measu ed wi h he ICD. ( 0
ep 10.17 GHz).
Resea ch A icle Vol. 6, No. 7 / July 2019 / Op ica 892
o a monoli hic lab-on-a-chip [33]. Howe e , he addi ional on-
chip de ec ion ea u e equi es signi ican modi ica ions o he
QCL design o ma ch he lase and de ec o wa eleng h. Hence,
bi- unc ional QCLs we e es ic ed o pulsed ope a ion o a long
ime [34]. Fo una ely he bi- unc ional ope a ion o ICLs comes
na u ally and does no equi e modi ica ions o he design [35].
The longe li e ime o he op ical ansi ion dec eases he he mal
noise and inc eases he in e nal quan um e iciency. Figu e 2(d)
shows he spec al esponsi i y o he in e band cascade de ec o
(ICD) ha was ab ica ed on he same chip and clea ed o
cha ac e iza ion. A b oadband spec al esponsi i y o o e
100 mA/W and an excep ionally low noise equi alen powe o
2.5pW ffiffiffiffiffiffi
Hz
pa e achie ed a oom empe a u e. The p o ided,
ye no op imized, ICD pe o mance is clea ly supe io o bi-
unc ional QCL ma e ial. In o de o demons a e he high-speed
ope a ion, which is essen ial o mul i-he e odyne de ec ion, we
measu ed he ICD equency esponse op ically using he ICL
[Fig. 2(e)]. The la ge de ec ion bandwid h e en enables he mea-
su emen o he bea no e o he ICL equency comb wi h
an SNR o 22 dB a oom empe a u e [Fig. 2( )]. The high-
equency cu o a ound 5 GHz includes bo h he lase and he
de ec o esponse. While his signi ican ly exceeds p e ious e-
po s on a 800 MHz combined cu o (1.3 GHz de ec o cu o )
[36], he high equency esponse emains limi ed by he pa asi ic
capaci ances o he de ices and sugges s ha he undamen al ca -
ie ansi ime limi is s ill no eached. E en highe cu o s o
26 GHz ha e been ealized using quan um well in a ed pho o-
de ec o s (QWIPs) [37], as he ypically much la ge numbe o
pe iods educes he pa asi ic capaci ance. These esul s highligh
he ema kable de ec ion capabili ies p o ided by he ICL comb
pla o m. In eg a ed on he same chip, he coupling e iciencies
a e much highe compa ed o ee-space op ics, and u he , he
size o he de ec o can be dec eased o educe he noise [33,34].
In p inciple, a monoli hic senso chip wi h a ew cen ime e s o
in e ac ion leng h can hus achie e he same de ec o noise lim-
i ed sensi i i y as a se up wi h disc e e elemen s and an in e ac ion
leng h o a ew me e s. We u he wan o highligh he majo
bene i o he dual-comb echnique o in eg a ion wi h espec o
elec ical c oss alk, which was he main limi ing ac o in p e ious
in eg a ed lase /de ec o senso chips ope a ing in pulsed mode.
The mul i-he e odyne bea signal is commonly eco ded a a e y
di e en equency ange (e.g., 10 MHz–1GHz)[30] compa ed
o he DC bias and he 10 GHz RF modula ion o he lase s and
hence should be ee om elec ical c oss alk.
4. CONCLUSION
We p esen ed new insigh s in o he dynamics o in e band cas-
cade lase s o equency comb gene a ion and highligh ed hei
eno mous po en ial o minia u iza ion. ICLs p o ide all he
p ope ies o u u e ul a-compac and ba e y-d i en dual-comb
senso s as summa ized in Table 1. We demons a ed sel -s a ing
ICL equency combs based on he inhe en gain nonlinea i y
caused by he as dynamics o he popula ion in e sion. The
esul ing equency comb s a e shows a dominan equency
modula ion and a linea ly chi ped phase signa u e, which is
cha ac e is ic o he supp ession o ampli ude modula ions in
as -gain media. ICL echnology educes he powe consump ion
by 2 o de s o magni ude compa ed o QCL o below 1 W, en-
abling ba e y-d i en senso s. Fu he mo e, ICLs p o ide excep-
ionally sensi i e and high-speed pho ode ec ion capabili ies ha
allow monoli hic in eg a ion o all ac i e op ical componen s.
Thus, ICL echnology p o ides all he p ope ies o all-solid-s a e
mid-in a ed senso s and will p omo e dual-comb spec oscopy
om undamen al esea ch o a b oadly used sensing pla o m.
APPENDIX A. METHODS
A. DEVICE FABRICATION
The in es iga ed ICLs we e g own a he Uni e si ä Wü zbu g
and a Nanoplus GmbH and p ocessed a he Cen e o Mic o-
and Nanos uc u es a TU Wien. The simula ed bands uc u e is
shown in Supplemen 1, Fig. S6. The lase idges (6 μm wide and
4 mm long) we e ab ica ed wi h s anda d mask pho oli hog a-
phy, eac i e ion e ching o de ine he lase wa eguides, silicon
ni ide o he passi a ion laye s, and spu e ed TiAu o he con-
ac pads. The subs a e was hinned o 160 μm, and TiAu was
spu e ed on he backside. The de ices we e moun ed epi-side-up
using indium on a coppe moun . Di e en hickness o he pas-
si a ion laye ha e been used o op imize he de ice pe o mance
in e ms o ou pu powe and modula ion capabili y.
B. MEASUREMENT SETUP
The de ices we e moun ed on a coppe submoun , he mo-
elec ically s abilized o 15°C. In o de o imp o e he noise p op-
e ies o ou lase d i e , we used home-buil low-pass il e s. The
accu acy o empe a u e s abiliza ion and he noise o he lase
d i e s play a c ucial ole o he s abili y o he equency comb.
The spec al esponse o he de ec o was measu ed using a he -
mal b oadband sou ce and a collima ion lens. The de ec o was
moun ed on a mo o ized x−y ansla ion s a e o measu e he
spa ial o e lap o he ace wi h he ocal spo o ob ain he cou-
pling e iciency. A calib a ed powe me e was used as a e e ence.
The he mal noise limi ed noise equi alen powe (NEP) was ex-
ac ed using he measu ed esponsi i y and de ice esis ance. A
mo e de ailed desc ip ion can be ound in Re . [38].
C. RELEVANCE OF THE SPATIAL BEAT NOTE PROFILE
An impo an aspec ha mus be conside ed o injec ion-locking
is he spa ial pa e ns o he lase bea no e in s anding-wa e lase s
[39]. Because o he bounda y condi ion o he modes in he
ca i y, all bea ings be ween adjacen lines will ollow a hal -wa e
cosine unc ion along he ca i y. Hence, he modula ion should
be applied a he end o he ca i y, whe e he lase is mos sus-
cep ible o injec ion-locking.
Table 1. The P esen ed ICL F equency Comb Pla o m
is he Only A ailable Mid-In a ed Technology ha
Mee s All Requi emen s o Build Ul a-Compac and
Ba e y-D i en Dual-Comb Spec ome e s
Requi emen s Mic o esona o QCL ICL
Comb ope a ion ∘∘•
S abiliza ion knobs ∘∘•
Compac –
a∘•
Ba e y-d i en –
a
–•
GHz on-chip de ec ion –∘•
(–) no demons a ed, (∘) demons a ed, (•) his wo k.
aOnly in he nea -in a ed [11].
Resea ch A icle Vol. 6, No. 7 / July 2019 / Op ica 893
APPENDIX B. SWIFTS
The SWIFTS concep was ealized using a as quan um well in-
a ed pho ode ec o (QWIP) placed a he ou pu window o a
Fou ie ans o m in a ed spec ome e (FTIR) (ske ch in
Supplemen 1, Fig. S5). The emi ed ligh o he ICL is shined
h ough he FTIR on o he QWIP. A local oscilla o mixes down
he op ical bea no e o he ICL o ≈40 MHz. By eco ding he
quad a u e componen s Xand Yo he QWIP signal in depend-
ence o he delay ime τusing a lock-in ampli ie , we ob ain he
wo SWIFTS quad a u e in e e og ams. The e e ence signal o
he lock-in ampli ie is ob ained by mixing ano he local oscilla o
wi h he RF sou ce used o injec ion in o he ICL. All in e e o-
g ams we e eco ded by he lock-in using he He–Ne igge o
he FTIR. Ou FTIR (B uke Ve ex 70 ) mo es each a m by
τ∕2. The complex sum o he in e e og ams is he e o e
gi en by
FXiY τX
n
AnAn−1cosω τ
2cosωn−1∕2τ:(B1)
By applying a as Fou ie ans o ma ion using ze o-padding
and peak i ing, bo h ampli ude and phase o all in e mode bea -
ings a e ob ained. The in e mode bea ings desc ibe he cohe ence
and phases be ween adjacen comb modes. The no malized in e -
modal cohe ence can be de ined as [27]
cjhAnAn−1eiφn−φn−1ij
hjAnjjAn−1ji , (B2)
whe e Ana e he ield ampli udes, φn he in e modal phases, and
he b acke s deno e empo al a e aging. The phases o he modes
can be calcula ed by he cumula i e sum o he in e mode bea ing
phases, which oge he wi h he in ensi y spec um allows he
econs uc ion o he ime-domain signal o a comb s a e.
Funding. Aus ian Science Fund (FWF) (F4909-N23,
P28914-N27, W1243); Eu opean Social Fund (ESF) (CZ.02.2.69/
0.0/0.0/16_027/0008371); Ai Fo ce O ice o Scien i ic
Resea ch (AFOSR) (FA9550-17-1-0340); Ös e eichische
Fo schungs ö de ungsgesellscha (FFG) (849614, 861581).
Acknowledgmen . The au ho s hank A. Belyanin o he
ui ul discussions a IQCLSW 2018. H. D. and A. M. A. we e
suppo ed by he ESF p ojec .
See Supplemen 1 o suppo ing con en .
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