J-coupling NMR spectroscopy with nitrogen vacancy centers at high fields

PHYSICAL REVIEW RESEARCH 6, 043017 (2024) J-coupling NMR spec oscopy wi h ni ogen acancy cen e s a high ields Pol Alsina-Bolí a ,1,2,*A. Bi e i-U iba en,1,2,*C. Munue a-Ja aloy,1,2and J. Casano a1,2,3,† 1Depa men o Physical Chemis y, Uni e si y o he Basque Coun y UPV/EHU, Apa ado 644, 48080 Bilbao, Spain 2EHU Quan um Cen e , Uni e si y o he Basque Coun y UPV/EHU, Leioa, Spain 3IKERBASQUE, Basque Founda ion o Science, Plaza Euskadi 5, 48009 Bilbao, Spain (Recei ed 5 Decembe 2023; accep ed 16 Sep embe 2024; published 4 Oc obe 2024) A diamond-based senso u ilizing ni ogen- acancy (NV) cen e ensembles pe mi s he analysis o mic on- sized samples h ough nuclea magne ic esonance (NMR) echniques a oom empe a u e. Cu en e o s a e di ec ed owa ds ex ending he ope a ing ange o NV cen e s in o high magne ic ields, d i en by he po en ial o la ge nuclea spin pola iza ion o he a ge sample and he p esence o enhanced chemical shi s. Especially in e es ing is he access o J-couplings as hey ca y in o ma ion o chemical connec i i y inside molecules. In his wo k, we p esen a p o ocol o access J-couplings in bo h homonuclea and he e onuclea cases wi h NV cen e s a high magne ic ields. Ou p o ocol leads o a clea spec um exclusi ely con aining J-coupling ea u es wi h high esolu ion. This esolu ion is limi ed p ima ily by he decohe ence o he a ge sample, which is mi iga ed by he noise- il e ing capaci ies o ou me hod. DOI: 10.1103/PhysRe Resea ch.6.043017 I. INTRODUCTION Nuclea magne ic esonance (NMR) spec oscopy has es- ablished i sel as a undamen al ool o explo ing ma e ials since i s incep ion in he 1950s [1–3]. This echnique is essen- ial o analyzing molecula s uc u e and unc ion. I inds ex ensi e applica ions in he examina ion o mac oscopic biological issues and unc ional s udies in medical imag- ing [4–6]. Howe e , he inhe en low sensi i i y o s anda d NMR spec oscopy es ic s i s applica ion o bulky sam- ples, ypically equi ing mic oli e olumes wi h con en ional mac oscopic coils o nanoli e olumes wi h mic ocoils [7]. In his scena io, newly de eloped solid-s a e quan um sen- so s open up new a enues o spec oscopic measu emen s wi h unp eceden ed sensi i i y and spa ial esolu ion, enabling s udies a he cellula [8] and single-molecula le el [9–11]. In pa icula , quan um senso s consis ing on NV ensembles ha e demons a ed hei u ili y in conduc ing NMR spec oscopy on mic oscopic samples a oom empe a u e, eaching sample olumes o picoli e s [7,12–14]. The pu sui o ex ending he ope a ing ange o NV-based senso s in o he high magne ic ield egime is d i en by he ad an ages o e ed by ele a ed ields. Namely, a la ge he mal nuclea spin pola iza ion and enhanced ene gy shi s ha simpli y da a ex ac ion. The abili y o access J-couplings—also known as scala o indi ec couplings—is o pa icula in e es in he ac ual *These au ho s con ibu ed equally o his wo k. †Con ac au ho : jcasano [email p o ec ed] Published by he Ame ican Physical Socie y unde he e ms o he C ea i e Commons A ibu ion 4.0 In e na ional 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. spec oscopic amewo k. J-couplings a e indi ec in amolec- ula dipole-dipole in e ac ions media ed h ough chemical bonds. They a e esponsible o complex spli ings in NMR spec al lines, and he examina ion o J-coupling pa e ns allows scien is s o ob ain in o ma ion ega ding nuclea con- nec i i y wi hin a molecule. Hence, accessing J-couplings a he mic oscale egime would open new a enues in mass- limi ed scena ios o applica ions in, e.g., combina o ial chemis y, as well as in cell and memb ane biology [15]. Ne e heless, J-couplings a e no i ial o de ec since (i) hey a e independen o he ex e nally applied ield. Then, a high magne ic ields o he ield-dependen e ms domina e he dynamics, and (ii) long cohe ence imes a e equi ed o esol e he spec al peaks co esponding o J-couplings owing o hei weak alue ( ypically, on he o de o a ew He z). In his wo k, we p esen J-coupling induced nuclea sig- nal wi h ex ended cohe ence ime (J-INSECT). This p o ocol enables he de ec ion o homonuclea and he e onuclea J- couplings wi h NV ensembles ( hus, accessing mic oscale samples) in he egime o high magne ic ields. J-INSECT in eg a es he e odyne echniques [16–19] and exe s noise il e ing o e he sample e ec i ely enhancing i s cohe ence. This esul s in na owe peaks in he spec a, he eby in- c easing equency esolu ion and hus enabling o esol e quan i ies on he o de o a ew he z (such as J-couplings). Addi ionally, ou me hod p o ides he capabili y o a ge speci ic ypes o couplings. In complex molecules, whe e nume ous peaks may a ise due o ex ensi e couplings be- ween nuclei, his allows o he selec i e a ge ing o only he couplings o in e es , simpli ying he spec a. We in es iga e he pe o mance o J-INSECT in egimes including bo h a educed and a la ge numbe o measu emen s, and analyze he impac o dis inc noise sou ces (including he p esence o always-on J-couplings) demons a ing he easibili y o he me hod in common expe imen al condi ions. 2643-1564/2024/6(4)/043017(9) 043017-1 Published by he Ame ican Physical Socie y POL ALSINA-BOLÍVAR e al. PHYSICAL REVIEW RESEARCH 6, 043017 (2024) II. RESULTS AND DISCUSSION A. Molecula a ge Hamil onian To exempli y he me hod we conside an iso opic liquid sample [20] con aining a a ge molecula ensemble wi h wo ypes o a oms, i.e., each molecule comp ises NHhyd ogens (H om now on) and a numbe NAo nuclei o he “A” species. The esul ing Hamil onian is H/¯h=ωH NH  i=1 Sz i+ NH  i=1 δH iSz i+ NH  i<j JH i,j Si· Sj +ωA NA  i Iz i+ NA  i=1 δA iIz i+ NA  i<j JA i,j Ii· Ij + NH  i NA  j JH−A i,j Si· Ij + NH  i H i( )Sx icos (ω1 )+ NA  i A i( )Ix icos (ω2 ), (1) whe e we deno e he spin ope a o s o H nuclei as Sx,y,z k, and hose o he Aspecies as Ix,y,z k. On he i s line we ha e La - mo e ms o he NHH (wi h ωH=|γH|Bex ), hei chemical shi s, and he homonuclea J-couplings o magni ude JH i,j.The e ms on he second line a e he equi alen in e ac ions o he Aspecies in he a ge molecule. The hi d line comp ises he e onuclea J-couplings be ween H and Anuclei (JH−A i,j), while he las one con ains he RF con ols o e H and A nuclea spins. Due o signi ican di e ences in gy omagne ic a ios among dis inc spin species, c oss alk e ec s a e sa ely neglec ed using he o a ing-wa e app oxima ion (RWA), es- pecially in high- ield scena ios. By se ing he RF ields such ha ω1≡ωHand ω2≡ωA, in a o a ing ame wi h espec o (w. . ) La mo e ms, Eq. (1) simpli ies o H/¯h=Hshi + NH  i<j neq JH i,jSz iSz j+ NA  i<j JA i,jIz iIz j + NH  i NA  j JH−A i,jSz iIz j+Hc,(2) whe e Hshi =NH i=1δH iSz i+NA i=1δA iIz iand Hc= NH iH iSx i+NA iA iIx i. Fo he sake o simplici y in he p esen a ion o he me hod, Eq. (2) assumes he elimina ion o he ans e sal spin ope a o s (Ix,y i,Ix,y j,Sx,y i, and Sx,y j). This applies in a scena io such ha |ωH−ωi|JH−A i,j, |δH i−δH j| JH i,j, and |δA i−δA j|JA i,j(no e he alidi y o hese condi ions is s onge a high magne ic ields). In addi ion, he label “neq” in he i s summa ion indica es ha he homonuclea J-couplings among magne ically equi alen nuclei (i.e., hose wi h iden ical chemical shi s) a e no included in Eq. (2) since hey do no ha e an impac in he dynamics as con i med ia nume ical simula ions. As a summa y, Eq. (2) ea u es only ZZ- ype in e ac ions and se es as a model o explain he basics o ou p o ocol. We ema k ha ou nume ical simula ions conside de ia ions w. . . Eq. (2) due o sho comings in he applica ion o p io app oxima ions and he conside a ion o all J-couplings h oughou he en i e p o ocol. This encompasses ins ances du ing he applica ion o ini e-wid h RF pulses, whe e de ia ions in he Rabi equency a e also aken in o accoun . B. P o ocol J-INSECT is illus a ed in Fig. 1. This s a s wi h an ini ial π 2pulse o e he H nuclei ha ans e hei he mal pola iza- ions o he x-axis and con inues by al e na ing encoding and de ec ion s ages. Du ing ee e olu ions (o leng h τ/2) a he encoding s ages, Eq. (2) simpli ies o H/¯h=Hshi + NH  i<j neq JH i,jSz iSz j+ NH  i NA  j JH−A i,jSz iIz j,(3) as NA i<jJA i,jIz iIz jcommu es wi h e e y o he e m in Eq. (3) and does no impac he dynamics o H nuclei— he emi e s in J-INSECT—(check he eadou s age). πpulses a e deli e ed in he middle o he encoding s age wi h a wo old objec i e. On he one hand, hey cancel Hshi mi iga ing he b oadening caused by spa ial inhomogenei ies in he ex e nal magne ic ield. In o he wo ds, he e ocusing πpulses leng hen he nuclea cohe ence ime om T∗ 2 o T2. This enables a longe scanning du a ion o he nuclea sample, which p o es espe- cially ad an ageous o es ima ing J-couplings due o hei ela i ely weak alues. On he o he hand, πpulses o e H (and A) enable he selec i e encoding o JH i,j(and JH−A i,j)in he sys em dynamics. This becomes e iden upon calcula ing he e ec i e p opaga o a he end o he encoding s age a e deli e ing πpulses o e H nuclei, esul ing in U1( )=exp ⎡ ⎢ ⎢ ⎣ −i NH  i<j neq JH i,jSz iSz j⎤ ⎥ ⎥ ⎦ .(4) Al e na i ely, in he scena io whe e synch onized πpulses a e applied o H and A, esembling a double nucleus-nucleus esonance, one ge s U2( )=exp ⎡ ⎢ ⎢ ⎣ −i ⎛ ⎜ ⎜ ⎝ NH  i<j neq JH i,jSz iSz j+ NH  i NA  j JH−A i,jSz iIz j⎞ ⎟ ⎟ ⎠ ⎤ ⎥ ⎥ ⎦ . (5) In addi ion, he in luence o addi ional nuclea species (such as B) is nega ed wi hin he dynamics due o he e ocusing in oduced by J-INSECT. Tha is, he una oidable p esence o ex a nuclea spin iso opes in he a ge sample would no al e he sys em dynamics unless a πpulse ha synch onously lips he Bspecies is in oduced on pu pose (see la e ). Then, he ini ial π 2pulse along he y-axis akes he he mal s a e o hyd ogen nuclei o he x-axis (see Fig. 1) while ZZ in e ac ions ha go e n he encoding s age—i.e., hose in Eqs. (4)o (5)—encode J-couplings in he dynamics o Sx i and Sy io H nuclei. Impo an ly, owing o he ini ializa ion o he he mal pola iza ion along he x-axis, i can be demons a ed ha ollowing he encoding s age, Sx iexhibi s 043017-2 J-COUPLING NMR SPECTROSCOPY WITH NITROGEN … PHYSICAL REVIEW RESEARCH 6, 043017 (2024) FIG. 1. Scheme o J-INSECT wi h RF and MW con ols. Each channel (black bold ho izon al line) deno es he adia ion pa e n o e each sys em cons i uen . The uppe RF channel co esponds o he pulses o e nonhyd ogen nuclea species. In his espec : o de ec he e onuclea J-couplings, simul aneous πpulses o e H and ano he iso ope a e deli e ed. The cen al channel pic u es he RF ha mus be applied o H nuclei, i.e., an ini ial (π/2)ypulse, ollowed by an al e na ion o (π)xpulses and wo ull Rabi oscilla ions along Y o de ec ion, wi h winding-unwinding mechanism o obus ness as o iginally p oposed in [17] and u he de eloped in [21]. The esul an magne iza ion o hyd ogen nuclei,  M∝NH i[Sx i,Sy i,Sz i] (see Appendix B), a di e en ins an s is ep esen ed wi h ed a ows in he sphe es: dashed a ows indica e he magne iza ion a he beginning o each p o ocol s ep (pulses o ee e olu ions), while he solid a ow indica es he magne iza ion a he end o he s ep. The e olu ion o he magne iza ion ou side he xy-plane (induced by RF d i ings) is depic ed wi h blue a ows indica ing he magne iza ion’s ajec o y. Du ing he de ec ion s age, he Y¯ Ypulse induces a magne ic ield (Bz) on he NV ensemble along he NV axis ha p ecess a a con ollable speed depending on he RF Rabi equency. The ampli ude o Bza he n h de ec ion pe iod is p opo ional o he ampli ude o he ed solid a ow (i.e., o he magne iza ion a he end o he n h encoding pe iod). The Y¯ Ypulses b ing he magne iza ion back o he s a e a he s a o he de ec ion s age as hey induce wo 2π o a ions. Bzis cap u ed by he NV ensemble ia a MW con ol sequence (e.g., he XY4 in he lowe channel), while g een pulses indica e he s anda d ini ializa ion and eadou o he NVs. signi ican ly g ea e ampli ude han Sy i(app oxima ely 105 imes la ge ), as de ailed in Appendix A1. In his manne , J-INSECT is uned o a ge Sx iin he de ec ion s ages. A a gene ic n h de ec ion s age, owing o a o a ion o he H nuclei along he y-axis (see Fig. 1), he magne ic ield Bn z induced by he sample o e he NV ensemble is along he NV axis and eads [22] (see Appendix B) Bn z( )=B0(nτ)sin(H ),(6) whe e His he Rabi equency o he Yand ¯ Ypulses (see Fig. 1) while, impo an ly, B0(nτ)∝2 NHSx i =nτ.(7) In conclusion, he subsequen magne ic ield Bn z( ) has an ampli ude p opo ional o Sx io H nuclei, and oscilla es wi h a con ollable equency H. This is, i espec i e o he in ol ed La mo equencies, wha enables o ope a e a high magne ic ields. No e ha , a 2 T hyd ogen La mo s each ≈(2π)×85 MHz, posing a echnically challenging ask o hei acking. On he con a y, Hcan be uned, o ins ance, o ens o kHz [23,24], such ha he oscilla ions o Bn z( ) a e easily ollowed by he NV ensemble by applying, e.g., a s anda d XY4 sequence. Reco ding he esul an phase acquisi ion o he NV ensemble a e e e y de ec ion pe iod leads o a di ec econs uc ion o he e olu ion o Sx io H nuclei, hus o he J-couplings encoded in Sx i.In his ega d, i is wo h no ing ha , unlike s anda d he e odyne measu emen schemes, J-INSECT does no impose es ic- ions on he sepa a ion be ween consecu i e measu emen s. This means hey can be placed a bi a ily in ime, p o ided ha he elapsed ime be ween measu emen s is eco ded, as his is c ucial o ex ac ing chemical in o ma ion. Fo sim- plici y in he p o ocol, hey a e placed equidis an , sepa a ed by τ. No ice ha since hyd ogens a e le in he same s a e as be o e he measu emen (due o he o a ion being a mul iple o 2π, he nex encoding pe iod can be applied di ec ly, wi h- ou he need o epola ize he sample). Finally, i is impo an o no e ha he NV cen e s a e ac i e only du ing he de ec ion pe iods; his implies a high spec al esolu ion cons ained no by he senso , bu by he T2(>T∗ 2) o H nuclei. C. Nume ical esul s We conside a picoli e sized liquid sample on op o a diamond hos ing an NV ensemble a mic ome e dep h [12] and a s a ic magne ic ield o Bex =2 T aligned wi h he NV axis. To exempli y J-INSECT we add ess a sample consis - ing on luo ome hanol molecules (CH2FOH) ha con ains i e spin-1/2 nuclei o h ee di e en species: H, ca bon, and luo ine (13Cand F om now on, no e oxygen has no spin) in a he mal s a e, see he scheme o he molecule in 043017-3 POL ALSINA-BOLÍVAR e al. PHYSICAL REVIEW RESEARCH 6, 043017 (2024) FIG. 2. Simula ed spec a o he luo ome hanol molecule. Ob ained om 1000 epe i ions o he p o ocol wi h 600 encoding +de ec ion s ages. Due o he dephasing ime T2=0.6 s, he FWHM is app oxima ely 1 Hz. Wi hin each igu e, he e is an illus a i e depic ion o he molecule, highligh ing he a ge ed J-couplings. Colo ed nuclei signi y he species upon which πpulses a e applied. Addi ionally, each igu e includes a boxed scheme de ailing he RF pulse ain applied on each case. (a) Ta ge ing only H and 13C, i e peaks a ise, which encode J,J1and J2. (b) Ta ge ing he H, he 13Cand he F, en peaks a ise, encoding: J,J1,J2,JF 1,andJF 2. inse o Fig. 2. Ou p o ocol enables accessing he e onu- clea J-couplings among H and he 13Cnucleus, as well as wi h he F. Mo eo e , i gi es access o he homonu- clea coupling be ween nonequi alen H ( he wo H nuclei in Fig. 2labeled as Haa e magne ically equi alen , whe eas Hbis magne ically unequi alen wi h espec o he o me ). We choose alues alling wi hin he ypical ange ound in he li e a u e [2], namely: JHaHb≡J=(2π)×8Hz,JHaC≡ J1=(2π)×130 Hz, JHbC≡J2=(2π)×6 Hz, while in e - ac ions wi h he F nuclei a e JHaF≡JF 1=(2π)×80 Hz and JHbF≡JF 2=(2π)×4 Hz, whe eas JCF =(2π)×160. Fu - he mo e, o a magne ic ield Bex =2 T, he chemical shi s a e δHa=(2π)×512 Hz, δHb=(2π)×236Hz, δC= (2π)×85Hz,and δF=(2π)×450 Hz. Ou nume ical simula ions s a wi h Hamil onian (1) in an in e ac ion pic u e w. . he La mo e ms ωHNH i=1Sz i+ωANA iIz i. In his manne , he only app oxima ion made is simpli ying he he e onuclea coupling e m NH iNA jJH−A i,j Si· Ijin Eq. (1) o only ZZ in e ac ions [i.e., o NH iNA jJH−A i,jSz iIz j,likeinEq.(2)]. This can be done since |ωH−ωi|∼(2π)×10 MHz JH−A i,j∼ (2π)×100 Hz, hus, he o a ing wa e app oxima ion sa ely applies. The eade can ind he ull simula ed Hamil onian in Appendix B. To main ain he Hamil onian close o Eq. (2) he condi ion τ>1/(|δHa−δHa|) mus hold, such ha he homonuclea e m o H spins app oaches o a ZZ in e ac ion. The p e ious condi ion imposes a lowe bound on τ, limi ing he amoun o measu emen s ha can be ca ied ou o a gi en expe - imen al ime. In ou case, we se τ=1.2/(|δHa−δHa|)= 4.3 ms (no e la e we explo e he J-INSECT pe o mance wi h a la ge numbe o measu emen s, i.e., depa ing om his condi ion). In addi ion, he ampli ude o he RF a ge ing HisH=(2π)×50 kHz while, o obus ness pu poses, πpulses o e H a e implemen ed ia a CORPSE a chi ec u e [25] which educes he impac o de unings du ing pulse execu ion. We obse e no disce nible impac on he sys em dynamics when s anda d op-ha pulses a e applied o 13Cand F, hus we exclusi ely deploy CORPSE pulses o e Hs. This esul s in CORPSE π=43.3µs, C π=39.7 µs and F π=10.6µs. Ou simula ions i s conside 600 measu emen s ( ha is, 600 encoding and de ec ion s ages in a single expe imen al un) hence he du a ion o he J-INSECT pe expe imen al un is T o al =600 (τ+ CORPSE π+2/H)≈2.66 s, whe e he e m 2/Hco esponds o he du a ion o wo ull RF Rabi oscilla ions du ing he eadou s age. Rega ding e o and impe ec ions, ou nume ical simula- ions comp ise he ollowing: (1) always on chemical shi s and J-couplings; (2) RF c oss- alk e ec s du ing RF i adi- a ion; (3) e o s on he ampli ude o he RF d i ings ( hese a e simula ed h ough an O ns ein-Uhlenbeck p ocess [26–28] wi h a 1% ampli ude shi and a noise co ela ion ime o 1 ms); and (4) a nuclea dephasing ime T2=0.6s[12], inco - po a ed ia an exponen ial decay in he ield emi ed by he sample. We conside wo cases. When he J-INSECT a ge s H and 13Cnuclei (case 1) we ge he spec um in Fig. 2(a). No e ha in his case, F does no ac i ely pa icipa e since we do no apply πpulses o e i , al hough i is included in ou nume ical model. Case 1 exhibi s i e esonances a di e en equencies iencoding he e onuclea J-couplings be ween H and 13Cand homonuclea J-coupling be ween H nuclei. The assignmen o J-couplings based on he ob ained ican be accomplished ei he by analy ically sol ing he e olu ion in Eq. (5)(see Appendix A2) o by employing s anda d spin mul iplici y echniques [29]. Con e sely, simul aneous a ge ing o he F nuclei wi h an addi ional πpulse (case 2) esul s in he eme gence o en esonances, as illus a ed in Fig. 2(b).No e in his second scena io he he e onuclea coupling be ween he F and H nuclei is also encoded in B0(nτ). The esul ing es ima ions o he J-couplings in cases 1 and 2 a e collec ed in Table I. In summa y, J-INSECT e ec i ely discloses J-couplings wi h la ge spec al esolu ion esul ing in a ull wid h a hal maximum (FWHM) o , a mos , 1 Hz, co esponding o he chosen alue o T2=0.6 s. Rega ding sensi i i ies, he use o ele a ed magne ic ields allows achie ing a signal- o-noise a io (SNR) o 30 wi h app oxima ely 18 000 epe i ions o he p o ocol. (The es ima ion ca ied ou o TABLE I. J-coupling alues ob ained om he spec a shown in Fig. 2(a) ( i s ow) and Fig. 2(b) (second ow). Values and hei unce ain y a e gi en in He z. JJ1J2JF 1JF 1 Case 1 8.1±0.5 130.1±0.86.1±0.9– – Case 2 8.1±0.5 130.1±0.96±180.0±0.94±1 043017-4 J-COUPLING NMR SPECTROSCOPY WITH NITROGEN … PHYSICAL REVIEW RESEARCH 6, 043017 (2024) case 1 wi h pho on s a is ics o NV expe imen s, assuming a 7% o luminescence con as . Addi ional de ails conce ning case 1 and he de elopmen o case 2, which yields sim- ila esul s, a e a ailable in Appendix C.) This implies an expe imen al ime o ∼13 h. Hence, J-INSECT acili a es a high- ideli y e ie al o J-couplings wi hin a easonable signal-collec ing ime, wi h he po en ial o u he educe he expe imen al du a ion by inco po a ing complemen a y me hods, such as p io hype pola iza ion o he sample e- po ed in Re s. [13,14] o ad anced eadou echniques such as epe i i e eadou [30,31]. In e ms o sensi i i y, p e ious wo ks using quan um he e odyne measu emen s a mode a e magne ic ields (88 mT) [12] epo sensi i i ies in he ange o ∼25–75pT ·Hz−1/2. Since ou wo k ope a es a high mag- ne ic ields, which enhance pola iza ion by a ac o o ∼30, we an icipa e a sensi i i y o app oxima ely ∼1–5pT ·Hz−1/2. Addi ionally, ou app oach ex ends he cohe ence ime o he sample om T∗ 2 o T2, which will u he educe he sensi i i y. An in e es ing inal aside o conside is enhancing he a e o measu emen s, as a s a egy o ex a educe expe imen- al ime. To exempli y he p ocedu e we inspec he simple case 1. Enhancing he measu emen a e implies educing τin he encoding s ages, hence depa ing om he condi- ion τ>1/(|δHa−δHa|). In his scena io he spec um is no longe gi en by he usual mul iplici y ules [i.e., he homonu- clea e ms, H-H, he in e ac ion Hamil onian Eq. (2)a eno longe ZZ in e ac ions], hus we es ima e he alues o he J-couplings by pe o ming Bayesian in e ence. In pa icula , we choose o ex end he numbe o measu emen s on each un (i.e., he numbe o de ec ion s ages) om 600 o 6553 and educe he o e all expe imen al ime ou imes ( om ∼13 h o ∼3h30 ). In his case, he in e ence gi es J=8.2±0.5, J1=130.1±0.6,and J2=5.7±0.4 (see Appendix D). III. CONCLUSION We in oduce J-INSECT, a p o ocol ha enables he de ec- ion o homonuclea and he e onuclea J-couplings wi h NV ensembles a high magne ic ields. J-INSECT inco po a es he e odyne echniques and exe s noise il e ing, enhancing he sample’s cohe ence hus enabling highly p ecise es- ima ions o J-couplings limi ed by T2>T∗ 2. We explo e J-INSECT’s pe o mance in wo scena ios, conside ing bo h educed and enhanced da a ha es ing. We assess he in- luence o di e en noise sou ces, including he pe sis en p esence o always-on J-couplings, showcasing he me hod’s easibili y in expe imen al condi ions. The comple e da ase suppo ing he indings o his wo k is a ailable upon eques om he co esponding au ho . On he one hand, seconda y da a eused and/o analyzed om o he s udies is speci ied along he ex . On he o he hand, o iginal da a gene a ed in his s udy ( ia nume ical simula- ions) a e also a ailable upon eques . The sou ce code and associa ed ma e ials used in his e- sea ch a e a ailable upon eques . ACKNOWLEDGMENTS P.A.B. and A.B.U. acknowledge he inancial suppo o he IKUR STRATEGY (IKUR-IKA-23/22) and (IKUR-IKA- 23/04), espec i ely. C.M.J. acknowledges he p edoc o al MICINN G an No. PRE2019-088519. J.C. acknowledges he Ramón y Cajal (RYC2018-025197-I) esea ch ellowship. The au ho s acknowledge he Quench p ojec ha ecei ed unding om he Eu opean Union’s Ho izon Eu ope–The EU Resea ch and Inno a ion P og amme unde G an Ag ee- men No. 101135742, he inancial suppo om he Spanish Go e nmen ia he Nanoscale NMR and complex sys ems (PID2021-126694NB-C21) p ojec , he ELKARTEK p ojec Disposi i os en Tecnologías Cuán icas (KK-2022/00062), and he Basque Go e nmen G an No. IT1470-22. APPENDIX A: SPIN DYNAMICS OF THE SAMPLE In his sec ion, we p o ide u he de ails ega ding he nuclea spin dynamics in he sample. 1. Ampli udes o he σx iand σy icomponen s We conside an e olu ion go e ned by he nex p opaga o [no e his is simila o hose in Eqs. (4) and (5)in hemain ex ] U =i,je−iφi,j 2σz iσz j,(A1) o e an ini ial s a e such ha ρx 1... ρx kρz k+1... ρz N,(A2) whe e ρx,z ja e he mal s a es pola ized along xand zdi ec- ions. This is, ρz j=1 2I+Bn 4σzwhile ρx j=eiπ 4σy jρz je−iπ 4σy j= 1 2I−BH 4σx, wi h BH=¯hγhBex KbTand Bn=¯hγnBex KbTbeing small quan i ies a oom empe a u e (on he o de o 10−5 o a magne ic ield o 2 T). In he p e ious exp essions, Bex =2T is he ex e nal magne ic ield, ¯h=1.054×10−34 J·sis he Planck cons an di ided by 2π,γH=(2π)×42.57 MHz/Tis he gy omagne ic a io o he H and γn he co esponding one o o he nuclei, KB=1.38×10−23 J/K he Bol zmann con- s an , and he empe a u e T=300 K. He e we di e en ia e among he mal s a es co esponding o he H nuclei, i.e., he nuclea spin which is o a ed o he Xaxis a he s a o he p o ocol (deno ed by ρx j), and he o he gene ic nuclea spin, which is ep esen ed wi h ρz j. On he one hand, one can demons a e ha σx 1=T U ρx 1... ρx kρz 1... ρz kU† σx 1 =T =1e|ρx 1|g... ρx kρz k+1... ρz Nj>1e−iφ1,jσz j +g|ρx 1|e... ρx kρz k+1...ρz Nj>1eiφ1,jσz j,(A3) whe e T =1[...] ep esen s he ace o e all spins excep ing he i s one. Using e|ρx 1|g=g|ρx 1|e=− BH 4one eaches σx 1=− BH 4k j=1cos φ1,jN j=k+1cos φ1,j−iBn 2sin φ1,j −BH 4k j=1cos φ1,jN j=k+1cos φ1,j+iBn 2sin φ1,j. (A4) 043017-5 POL ALSINA-BOLÍVAR e al. PHYSICAL REVIEW RESEARCH 6, 043017 (2024) On he o he hand, one can demons a e ha σy 1leads o σy 1=− iBH 4k j=1cos φ1,jN j=k+1cos φ1,j−iBn 2sin φ1,j +iBH 4k j=1cos φ1,jN j=k+1cos φ1,j+iBn 2sin φ1,j. (A5) No e he abo e exp essions hold o any H, hus o any quan i y σx iand σy i ha in ol es a H spin in he a ge sample. No ice how he leading o de o each expec a ion alue di e s by i e o de s o magni ude: σx 1∝O(BH) and σy 1∝ O(BHBn). Thus, σx iis ∼105 imes g ea e han σy i. 2. Fluo ome hanol esonances We compu e he esonance posi ions o he speci ic case o he luo ome hanol molecule. Fo he sake o simplici y we conside a pola ized H, and he o he nuclei in he maximally mixed s a e, ha is, ρx i=1 2(I+σx i) o H and ρm i=1 2I o o he nuclei. No e hese conside a ions only al e he ampli- ude o he signal, no he esonance posi ion. Howe e , he esul s in he main ex conside he mal s a es o all nuclei in he luo ome hanol molecule. Thus, ollowing Eq. (A3), we ha e Sx i=σx i 2=1 2N j=1cos φi,j, whe e φ1,ico esponds o he phase accumula ed due o he in e ac ion be ween he i h and j h spins du ing a ime , ha is, φi,j( ) =Ji,j 2 . When H nuclei and 13Ca e a ge ed in he luo ome hanol molecule (co esponding o case 1 in he main ex ), he e- sul ing signal is 3  i=1 Sx i( ) =1 6cos J 2 2 cos J1 2  +cos J 2 cos J2 2 , which leads o he esonance peaks in Fig. 2(a) o he main ex , 1=±J2/2, 2=±(J2−2J)/2, 3=±(J2+2J)/2, 4=±(J1−J)/2, and 5=±(J1+J). In he case whe e he F is also a ge ed wi h πpulses (co esponding o case 2 in he main ex ), one inds 3  i=1 Sx i( ) =1 6cos J 2 2 cos J1 2 cos JF 1 2  +cos J 2 cos J2 2 cos JF 2 2 , wi h he co esponding esonances depic ed in Fig. 2(b) o he main ex . These a e 1=±(J2−JF 2)/2, 2=±(+2J−J2− JF 2)/2, 3=±(J2+JF 2)/2, 4=±(2J+JF 2−J2)/2, 5= ±(2J+J2−JF 2)/2, 6=±(2J+J1+JF 1)/2, 7=±(J1− JF 1−J)/2, 8=±(J+J1−JF 1)/2, 9=±(J1+JF 1−J)/2, and 10 =±(J+J1+JF 1)/2. Al e na i ely, he esonan equencies can be ob ained ia s anda d NMR mul iplici y ules [29]. Tha is, when a nuclei A is coupled wi h nxspin-1 2nuclei o an iso ope X, heAsignal spli s in o nx+1 lines. I Ais also coupled o an elemen di - e en o X(le s sayY) his induces addi ional ny+1 spli ings in each p e ious peak. In ou case, since he b oadening is mi iga ed, all J- coupling peaks end o be cen e ed a 0 Hz. Thus, when H and 13Ca e a ge ed, he signal o Ha( ecall he Haand Hba e magne ically inequi alen hyd ogen g oups in he molecule, e e o Fig. 2o he main ex ) is spli in o 2×2=4 peaks due o couplings wi h Hband he 13C, while he signal o Hb is spli in o 3×2=6 peaks, h ee due o he pai o equi alen Ha, and wo due o he 13C. Then, we a e le wi h 6 +4=10 peaks a ound 0 Hz. I J coupling in e ac ions wi h F a e also exci ed, he signal o Hais spli in o 2×2×2=8( wo pe e e y o he elemen ), while he signal o Hbspli s in o 3×2×2=12 peaks, leading o a o al o 20 peaks, see, e.g., Re . [6] o mo e in o ma ion. APPENDIX B: FROM THE SAMPLE TO THE NV CENTERS The oscilla ion o hyd ogens in he de ec ion s age o J- INSECT impac s on he NV ensemble (which is conside ed a a mic ome e dep h om diamond su ace) as a classical magne ic ield. In his espec , see, e.g., Re s. [12,22]). In he high ield egime, he magne ic signal induced by he sample in he o hogonal di ec ions (i.e., xand y) wi h espec o he ex e nal magne ic ield (o ien ed wi h he NV axis, i.e., z) can be neglec ed as i apidly oscilla e a a speed γNBzwi h Bzbeing se e al Tesla. The esul an ield emana ed om he sample du ing an n h de ec ion pe iod (n∈N) can be well app oxima ed by [12,22] Bz( )=Bn 0sin(H ),(B1) whe e H=γHBRF is he ampli ude o he RF d i ing. On he o he hand, he ampli ude o he magne ic ield is Bn 0=(2π)2(¯hγH)2μ0ρHBzF3 16πKBTMx,(B2) whe e Mxis he xcomponen o he no malized magne iza- ion, de ined as  M=2 NHi Si(nτ). No e ha he quan i y i Si(nτ) is compu ed ia nume ically e ol ing he nex molecula Hamil onian H/¯h=δHASz 1+Sz 2+δHBSz 3+δCIz+δFPz +JHaHa S1· S2+JHaHb( S1· S3+ S2· S3) +JHaCSz 1+Sz 2Iz+JHbCSz 3Iz +JHaFSz 1+Sz 2Pz+JHbFSz 3Pz+JCFIzPz.(B3) In addi ion, ¯h=1.054×10−34 J·s is he Planck’s cons an di ided by 2π,γH=(2π)×42.57 MHz/T is he gy omag- ne ic a io o he H, μ0=4π×10−7H/m he magne ic pe meabili y o ee space, ρH≈6.6×1028 m−3 he H den- si y o he sample, Bz=2 T he ex e nal magne ic ield, KB=1.38×10−23 J/K he Bol zmann cons an , T=300 K he empe a u e and F3=4.1 cha ac e izes he geome y o he sample [12]. 043017-6 J-COUPLING NMR SPECTROSCOPY WITH NITROGEN … PHYSICAL REVIEW RESEARCH 6, 043017 (2024) FIG. 3. Simula ing an expe imen . Panel (a) co esponds o case 1, while (b) holds o case 2. Inse s: In blue a e he signals wi hou conside ing luminescence issues, while ed squa es a e he ou come ha esul s om a e aging 18000 epe i ions o he espec i e p o ocol wi h 2.5×108NV cen e s assuming a con as o 7%. Main igu es: In blue a e he spec a ha co espond o he signals wi hou luminescence issues, while he ed squa es a e he FT o a e aged signal in he inse ( hus, ca ying eadou noise). Bo h spec a a e no malized by a common ac o , ensu ing ha he maximum peak in case 1 has ampli ude 1. In case 1, e e encing he ampli ude o he smalles peak, he co esponding SNR is jus abo e 30. In case 2 unde he same e e ence c i e ion, i is sligh ly below 15. The Hamil onian o a gene ic NV in he ensemble unde he in luence o Bz( )is HNV =σzγe 2Bz( )+Hc,(B4) whe e Hcaccoun s o he MW d i ing on he NV ensemble. In pa icula , applying a XY4 con ol sequence du ing he de ec ion s age o e he NV ensemble wi h RF =21 Hand he spacing be ween he MW pulses TMW = RF/4, yields σyNV ≈2γe RF πBn 0,(B5) p o ided ha 2γe RF πBn 01. APPENDIX C: READOUT CONSIDERATIONS To e alua e he impac o he measu emen a e o he p o ocol unde he high ex e nal magne ic- ield pa adigm, we make an es ima ion o he equi ed signal a e aging ime leading o a signal o noise a ion (SNR) o 30. In Re . [30] he au ho s eco ded he mean numbe o pho on-coun pe measu emen when a single NV is in |0, ha is, n0=0.016, and a pho on coun di e ence be ween he g ound and exci ed spin s a es o n0−n1=0.005, yielding a 30% inc ease o luminescence con as be ween bo h s a es. In his case, since we a e wo king wi h NV ensembles, we conside a luo escence con as o 7%, which was achie ed by lowe ing he pho on emission n0. Employing he la e pho- on s a is ics, and aking as a basis he signal wi h no eadou e o [in pa icula , he in e se Fou ie ans o m o he spec a in Fig. 2(a), no e ha his signal ca ies he es o e o s desc ibed in he main ex ], we ep oduce an expe imen al ou come. In pa icula , we assume a con igu a ion simila o ha in Re . [12]. This is an NV cen e densi y o 0.8×1023 m3,a beam diame e o 20 µm, and a 10 µm hick laye o NV cen e s sensi i e o he he mal spin signal. This leads o a senso con aining ≈2.5×108ac i e NV cen e s. The p o ocol is epea ed 18 000 imes. Tha is, we a e age he emi ed signal ac oss 18 000 epe i ions o he p o ocol, which leads o a du a ion o 18 000 ×2.66s ≈13h20. Speci ically, in case 1, he noise in he esul ing a e aged signal has a s anda d de ia ion o app oxima ely 6 ×10−5 while he signal’s ampli ude is σz NV∼1×10−3,seeinse o Fig. 3(a). This leads o a SNR o abou 30 in he spec um by aking he he heigh o he smalles peak. Fo case 2, he noise s anda d de ia ion is simila . Howe e , he SNR is app oxima ely 15. This is because e en hough bo h signals ( om case 1 and case 2) ha e simila ampli udes, he spec um o case 2 exhibi s mo e peaks which esul s in peaks o smalle ampli ude as i can be seen in Fig. 3 o cla i ica ion. In conclusion, he he mal pola iza ion induced by he high ex e nal magne ic ield is enough o balance ou he ela i ely 043017-7 POL ALSINA-BOLÍVAR e al. PHYSICAL REVIEW RESEARCH 6, 043017 (2024) FIG. 4. (a) Top, scheme o he RF sequence employed o he high measu emen - a e p o ocol [wi h (π)xand (π)−xpulses al oge he wi h CORPSE s uc u es o e Hs du ing encoding o enhanced obus ness] and he co esponding spec um (bo om). This shows he esul ob ained wi h 6553 measu emen s (solid blue) while, o compa ison, we include he spec um ob ained wi h 600 measu emen s (dashed ed), which co esponds o he same spec um shown in Fig. (a) o he main ex . (b) Pos e io dis ibu ions o each scanned pa ame e ia Bayesian in e ence. I: Pos e io dis ibu ion co esponding o J; II: o J1; and III: o J2. The exac alue o each pa ame e is ma ked by a e ical do ed line in I, II, and III. The unce ain ies a e he s anda d de ia ion σθ,gi enbyσ2 θ=(θ−θ)2=(θ−θ)2P(θ|D) dθ,whe eθs ands o J,J1,andJ2. low measu emen a e, yielding a de ec able signal ( hus o clean J-coupling spec a) unde easonable expe imen al ime in bo h cases. APPENDIX D: BEYOND τ>1.2/(|δHa−δHa|) To inc ease he numbe o measu emen s on each expe i- men al un, we educe τin encoding s ages om τ=4.3ms o τ=75 µs and pe o m 6553 measu emen s ins ead o 600. We conside impe ec pulses (wi h 1% e o on he ampli- ude d i ing) as well as always-on J-couplings and eadou e o s (see p e ious sec ion). This inc ease in he numbe o measu emen s leads o a educ ion on he o al expe imen al epe i ions o be pe o med. In his case he p o ocol includes an ex a (π) pulse du ing he encoding pe iod o u he educe he impac o impe ec d i ings (see he scheme o he pulse sequence in Fig. 4). On he o he hand, he educ ion on τleads o an in i- ca e spec um wi hou clea esonance peaks, see Fig. 4(a). Thus, o in e he alues o J-couplings we pe o m Bayesian analysis. As an inpu o he Bayesian in e ence we employ he p e iously desc ibed noisy signal wi h impe ec pulses and eadou e o s. Rega ding he pa ame e se , as he p io knowledge we assume a uni o m dis ibu ion. To sum up, ia Bayes in e ence, simplici y o he spec a can be aded o sho e expe imen al imes. As a igu e o me i , we simula e he esul ing sig- nal pe o ming ou imes less a e ages ( hus a ou - imes sho e expe imen ). This esul s in o a eadou e o wice g ea e . The pos e io dis ibu ions a e depic ed in Fig 4(b), om which he ollowing alues and unce ain ies a ise ( e- spec i ely): J=8.2±0.5Hz,J1=130.1±0.6 Hz, and J2=5.7±0.4Hz. [1] C. P. Slich e , P inciples o Magne ic Resonance (Sp inge , Be lin, 1978). [2] M. H. Le i , Spin Dynamics: Basics o Nuclea Magne ic Res- onance, 2nd ed. (Wiley, Chiches e , England, 2008). 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