Supplementary Figure 1. Experiment and simulation with finite qudit. anharmonicity. (a), Experimental data taken after a 60 ns three-tone pulse.

Transcription

1 Supplmnar Fgur. Eprmn and smulaon wh fn qud anharmonc. a, Eprmnal daa akn afr a 6 ns hr-on puls. b, Smulaon usng h amlonan. Supplmnar Fgur. Phagoran dnamcs n h m doman. a, Eprmnal daa. Th hr-on puls s gnrad wh p=q=.86. b, Smulaon

2 wh fn anharmonc. Jaggd faurs ar sn o b cohrn SU4 ffcs. c, Smulaon wh nfn anharmonc. Populaons osclla smoohl. Supplmnar No In hs scon w show how fn anharmonc prvns confnmn of qud dnamcs o SO4 roaons and show addonal prmnal daa of h SU4 dnamcs and rlad numrcal smulaons. Th mpac of fn anharmonc on h dnamcal smmr s a gnral faur of mul-lvl ssms. In our prmn h four-lvl qud s drvn b a hr-on puls cos cos cos whch producs h followng amlonan:. In h nracon pcur, hs bcoms ' whr h off-rsonan mar s '

3 . A h lm of larg anharmonc rlav o h drv, h dnamcal avragng of hs mar s ro and w mmdal rcovr h rducon o SO4 Phagoran conrol, as dscussd n h man. Supplmnar Fgur a shows prmnal daa oband from masurmn and Supplmnar Fgur b shows smulaon usng h amlonan. Evn mnor, asmmrc faurs ar rproducd vr wll. W no ha a br quanav mach s achvd whn longr cohrnc ms ar usd n smulaon, mplng chong of som qud cohrncs b h srong hr-on puls whch s no akn no accoun n our smulaon. All smulaons ar don on a s-lvl ssm and confrm ha onl h frs four lvls parcpa n h dnamcs. A larg ampluds, rsuls ar found o dpnd on h rlav phass bwn h hr frqunc componns of h drv. If h dnamcs wr SO4, such phass would onl dfn h subspac of SU4 n whch h qud undrgos SO4

4 roaons, and no ffc of hs rlav phass would b masurd. Th snsv o hs phass ndcas ha h dnamcs n hs rgm ar ndd SU4. Th succss of smulaon wh can also b sn whn comparng o m-doman masurmns. Supplmnar Fgur a shows m-doman voluon of h qud populaon for p=q=.86, Supplmnar Fgur b shows smulaon wh and Supplmnar Fgur c shows smulaon wh h larg-anharmonc amlonan. Th ffc of h fn anharmonc s apparn, and vn small, jaggd faurs n h prmnal daa ar sn o b cohrn, no nos, dnamcs. Supplmnar No As shown n h prvous scon, a mul-on drv n conjuncon wh fn anharmonc rsuls n off-rsonan couplngs,.. h opraor ' of Eq.. An on of h hr componns of ' can b mad m-ndpndn b ransformng o a suabl roang fram, bu hs would lav h ohr componns oscllang a a ba frqunc. Alhough h full amlonan canno b mad m-ndpndn for hs rason, w can undrsand how h fn anharmonc lads o SU4 dnamcs b sudng h group-horcal aspcs of h dund amlonan, whch ar fram-ndpndn. W gnral h Bll-fram analss of a four-lvl ssm o allow dunng bwn h drvs and hr assocad ransons, sarng wh a gnral mndpndn amlonan of h form:, 4

5 whr all h paramrs ar ral-valud.. j j. An on of h componns of ' of Eq. can b brough no hs form, bu no all hr smulanousl. Applng h unar ransformaon B W W, whr W, 5 producs h Bll-fram amlonan B. 6 Ths amlonan can b dcomposd no nsor producs of SU opraors as follows: B I I I I I I I I 7 Th abov s an plc ampl of Caran s dcomposon n SU4, whch sas ha an unar ransformaon n SU4 can b wrn as h produc of hr lmns U K AK, whr K and K ar local manpulaons of qubs and, rspcvl,.. Local qub : I, I, I Local qub : I I, I and A s of h form:,

6 A, whr,, ar non-local opraors ha s n SU4. SU SU Ths dcomposon s also calld h KAK dcomposon and spans h SU4 dnamcal spac. W no ha h off-dagonal couplng rms blong o h local ransformaons, whl h dunngs blong o h non-local ransformaons. Dunng h drv hus swchs h dnamcs bwn SO4 and SU4. Consqunl, our prmnal rsuls and assocad smulaons for hghr-powr drvs ndca h smulanous acon of svral non-commung amlonans, hus ladng o h nrfrnc of Phagoran dnamcs along wh couplng oscllaons, as prsnd n Fg. of h man. j