Multi-state detection and spatial addressing in a microscope for ultracold molecules

Domain: physics
Published: 2025-12-09
Editorial outcome: minor_revision

Abstract
Precisemeasurementoftheparticlenumber,spatialdistributionandinternal stateisfundamentaltoallproposedexperimentswithultracoldmolecules bothinbulkgasesandopticallattices.Here,wedemonstratein-situdetection ofindividualmoleculesinabulksampleof87Rb133Csmolecules.Extending techniquesfromatomicquantumgasmicroscopy,wepinthemoleculesina deeptwo-dimensionalopticallatticeand,followingdissociation,collect fluorescencefromtheconstituentatomsusingahigh-numerical-aperture objective.Thisenablesdetectionofindividualmoleculesuptotheresolution ofthesub-micronlatticespacing.Ourapproachprovidesdirectaccesstothe densitydistributionofsmallsamplesofmolecules,allowingustoobtain precisemeasurementsofdensity-dependentcollisionallosses.Further,by mappingtwointernalstatesofthemoleculetodifferentatomicspecies,we demonstratesimultaneousdetectionofthepositionandrotationalstateof individualmolecules.Finally,weimplementlocaladdressingofthesample usingafocusedbeamtoinduceaspatially-dependentlightshiftontherota- tionaltransitionsofthemolecules.

Introduction
Ultracold polar molecules have many promising applications in quantum science1–3, in part due to the possibility of engineering quantumgaseswithtunable,long-rangeandanisotropicdipole-dipole interactions. These dipole-dipole interactions are intimately con- nectedwithcontrolofmolecularrotationalstates4.Theengineeringof dipolarspin-exchangeinteractionsinparticularrequirestheprepara- tionofmoleculesinmixturesorsuperpositionsofdifferentrotational states.Suchinteractionsareakeycomponentincurrentexperimental realisations of spin-1/2 models of quantum magnetism with polar molecules5–9. For disordered samples, simultaneous read-out of the distributionofdensityandspiniscrucialtoaccuratelydeterminethe state of the system, and therefore enable accurate comparison to theoreticalmodels10–12.

Oneoftheleadingapproachestopreparingultracoldmolecular gasesgeneratesrelativelysmallbutdensesamplesofmoleculesby association from pre-cooled atomic gases2. This approach has allowedtheproductionofquantum-degeneratesamplesoffermio- nic KRb13 and NaK14, and bosonic NaCs15. In these experiments, detection is typically performed by breaking the molecules apart andtakingabsorptionimagesoftheresultingatoms16.Thistechni- quehas advantages; theimaging of alkali-metalatomsis sensitive and straightforward, and, as the dissociation process addresses a singlehyperfineandrotationalstateofthemolecule,thedetection isinherentlystatesensitive.However,thedissociationprocesscan addenergytotheatoms,therebyaffectingthespatialdistribution, and the typical noise floor is of order ~100 molecules. Direct detection via absorption imaging of associated molecules has also been demonstrated17. However, the signal-to-noise for small samplesislimitedduetothemoleculeslackingsufficientlyclosed cycling transitions to scatter many photons. Ultracold molecules mayalsobedetectedviaacombinationofionisationspectroscopy and velocity-map imaging18. This enables flexible detection of atomic and molecular species that can give unique insights into chemical processes19, but requires a purpose-built apparatus and doesnotdirectlyprobethespatialdistributionofmoleculesinthe sample.

In atomic systems, quantum gas microscopy20,21 has enabled experimentsthatcandetectdowntoasingleatom,andhasenabled accesstoanewrangeoflocalobservables22.Thetechniqueusesadeep optical lattice to pin atoms while they fluoresce under illumination withcoolinglight.Thisfluorescenceiscollectedwithahigh-resolution imagingsystem,andthelatticestructureisusedtodeconvolvethe imagetoresolvesingleatoms.Thistechniquecanbeextendedtoallow simultaneousreadoutofatomicdensityandspinstate23,allowingthe studyofmicroscopiccorrelationsofspinandcharge24.Thesetechni- quesarealreadybeingappliedtoexperimentswitharraysofultracold moleculespreparedinopticallattices.PioneeringworkbyChristakis and Rosenberg et al.7,25 hasdemonstrated the resolution of correla- tionsbetweenpairsofmoleculesarisingfromtheirquantumstatistics, andobservedcorrelationsfromdipolarinteractionsbetweennearest- neighboursinthelattice.Theseexperimentscomplementthoseper- formed on molecules in optical tweezer arrays26,27 where a similar detection scheme based upon collecting atomic fluorescence is employed.

Recently, microscopy techniques have been extended beyond lattice-confinedsamplesandappliedtothestudyofbulkatomicgases. That is, the atoms are initially not confined to a lattice until a pinning latticefreezestheatominpositionfordetection.Thiseffectivelytakes asnapshotofthepositionsofatomsinthesampleattheresolutionof thelatticespacing.Thishasenabledtheprecisestudyofcorrelationsin thecontinuumforquantumdegenerateornear-degenerateBoseand Fermisystems28–32.Inourwork,weextendthesetechniquesfurtherby applyingthemtobulkmoleculargases.

Here we demonstrate spatially-resolved detection of single ultracold87Rb133Cs(RbCs)moleculesinathermalbulkgas.Ourtechni- que,summarisedinFig.1,generatesimagesoffluorescencecaptured from single atoms produced by breaking apart molecules that are pinned in place using a 2D optical lattice. We use these images to reconstructthemoleculardensityinthetrap,enablingprecisetracking ofone-andtwo-bodylosses.Wealsoshowthatwecandetectmolecules intwodifferentrotationalstatesinasingleexperimentalcycle.Thisis achievedbymappingtherotationalstatesontotheatomicspeciesleft inthelatticesitefordetection.Finally,weaddalocaladdressingbeam. Thisallowsustotransferachosenareaofthesampleintoadifferent rotationalstate.Thisprovidesanadditionaltestofthespinandspatial resolutionofourimagingtechnique.Weobserveandanalysethetime- of-flight expansion of the selected area as a novel approach to ther- mometryofthemoleculesthatarecapturedinthelattice.

Results
Detectionofsinglemolecules
Oursampleinitiallyconsistsof~1500RbCsmoleculesconfinedtoan optical dipole trap; see Methods for details of the preparation sequence.Thedipoletrapisformedattheintersectionofalightsheet, withatightverticalwaistof7μm,andapairofcircularbeams,withall threebeamspropagatinginthehorizontalxyplane(thecoordinate systems is defined in Fig.1a). We calculate the trap frequencies experiencedbymoleculesintherotationalgroundstate(N=0)tobe (ν x,ν y,ν z)=(100,200,680)Hz.

An overview of our detection scheme is shown in Fig.1b. The firststepistopinthemoleculesinplaceusinga2Dopticallattice, therebypreservingspatialinformationaboutthegas.Thelatticeis formed from a single λ=1064nm beam that is retro-reflected in a bow-tieconfiguration,asillustratedinthelowerpartofFig.1a,with1/ e2waistsof100μmatthelocationofthemolecules.Thisgeometry yieldsasquarelatticewithspacinga =λ= 2= 752nmandaxesthat lat arerotatedby45°withrespecttoxandy33.Topinthemolecules,we ramp on the 2D optical lattice in 0.1ms to a depth of 7.0(1)×103E (expressed in units of lattice recoil energy rec,RbCs E =h2=8ma2 , where m is the mass of RbCs molecules) whilst rec lat simultaneously increasing the light sheet power to provide tight confinementvertically.

WethenbreakaparttheRbCsmoleculesintotheirconstituentRb andCsatoms.Thedissociationprocessisthereverseofthemagne- toassociationandstimulatedRamanadiabaticpassage(STIRAP)steps usedtoformthemolecules34,35,andconvertseachmoleculeintoaRb atomin5S 1/2 (F=1,m F=1)andaCsatomin6S 1/2 (F=3,m F=3).Asthe efficiencyofSTIRAPisreducedwhenthetraplightintensityishigh36, welowerthelatticeintensityto <120E for0.1mstoperform rec,RbCs the return STIRAP to the Feshbach state. With this approach, we achieve a transfer fidelity of 95(1)%, comparable to efficiencies achieved in similar experiments where STIRAP is performed in free space36. There is scope to increase this fidelity using feed-forward suppression of laser phase noise37. The time for which the lattice intensityisreducedisshortcomparedtotheexpectedtimefortrap- pedmoleculestotunnelbetweensites(>5ms),althoughsomemole- cules may occupy highly-excited motional states in the lattice and, therefore,mayberelativelyfreetomove.However,weestimatethat thisleadstominimalblurringofthespatialinformation,ontheorder ofoneortwositesatmost.Toavoidlight-assistedcollisionsbetween theRbandCsatomsduringtheimagingstep,weselectivelyremove oneofthespeciesfromallsitesafterthedissociation.Thisisachieved byashortpulseofresonantlight,asdescribedin“Methods”.

Toperformimaging,wemaketheatomsfluoresceusingpolar- isationgradientcooling(PGC).Thisallowsustoexcitefluorescence whilemaintainingalowenoughtemperaturethattheatomsremain pinnedintheirlatticesites20,21.Bothatomicspeciesexperienceatrap depth>4000E inthepinninglattice.Thefluorescenceiscollected rec using an objective lens with a numericalapertureof 0.7 positioned below the sample and imaged onto a CMOS camera. We typically collect fluorescence for 750ms to clearly resolve the signal from individualatomsabovethebackgroundnoise.In“Methods”wepre- sentestimatesofthedetectionfidelity,signal-to-noiseratio,andthe point-spreadfunctionoftheimagingsystem.Exampleimageswhere wechoosetokeepeitherthedissociatedRborCsatomsareshownin Fig.1c.Usingadeconvolutionalgorithmbasedonasingle-layerneural network38,weareabletoreconstructthelatticeoccupancyandhence determine the spatial distribution of molecules. We estimate the fidelityofsitereconstructionislimitedbythedeconvolutionprocess toaround95%forourmostdensemolecularsamples(see“Methods” andSupplementaryFig.1).

Weobserveabinaryfluorescencehistogramassociatedwiththe occupationofeachlatticesite,withthetwopeaksindicatingthepre- senceof1or0molecules(seeSupplementaryFig.1).Thisisbecause our detection scheme leads to the loss of pairs of molecules that occupythesamesiteofthepinninglattice.Thispairlosslikelyoccurs whenthemoleculesarefirstloadedintothelattice;RbCsmolecules areknowntoundergorapidlossatclosetotheuniversalratedueto optical excitation of two-body collision complexes39,40. Additionally, pairlossmayoccurduringtheimagingstepduetohomonuclearlight- assisted collisions, as observed in atomic gas microscope experiments22. These effects combine to lead to the detection of a single molecule on sites that initially contain an odd number of molecules,whilesitesthatinitiallycontainanevennumberofmole- culeswillappearempty.Wenote,however,thatinallofourexperi- ments,themoleculedensityissufficientlylowthatthereisanegligible probabilityofmorethantwomoleculesoccupyingthesamesiteofthe pinninglattice.

Reconstructionofthemoleculardensity
Our technique effectively captures the molecule distribution at the time that the pinning lattice is ramped on, thus enabling a direct measurement of the molecular density in the trap. Forour densest samples,however,caremustbetakentoproperlyaccountforthepair losstoaccuratelydeterminethetruemoleculardensitydistribution. Wecorrecttheobserveddensityoffilledsitestoreconstructthe truedensityprofile.Wefirstextracttheaverageobservedsiteoccu- pancyn0 byspatiallyaveragingacrossourimageswithasquare(7×7 site site)uniformkernel.Thekernelsizeischosentobesmallcomparedto the observed variations in molecule density within the trap. The moleculesampleisthermallydistributedandatequilibriumpriorto thepinning,suchthatweexpectnostrongdensitycorrelationsonthe scaleofthelatticespacing.Tofindthecorrectedsiteoccupancyn , site weassumethatthenumberofmoleculespinnedtoeachsiteisPoisson distributed.Thus,thepairlossprojectionconvertsn ton0 viathe site site relation n0 site = 2 1(1-e-2n site ), plotted in Fig.2a. By inverting this rela- tionship, we determine the local density to be n site(r)= 2 1 n site(r) , which accounts for the finite STIRAP efficiency. The stages of this process aredepicted in Fig.2b. This approach is valid for our experiments, as the peak occupancyisgenerallylow,n0 site ≤0:3.

Measurement of the in situ column-density distribution, when combinedwiththeknowntrapfrequencies,allowsfulldetermination of the thermodynamic properties of the gas. We fit a 2D Gaussian functiontothisdistributiontofindthermal1/ewidthsofthecloud, σ a=8(1)μmandσ b=30(1)μm,wherethedirectionsaredefinedbythe majorandminoraxesoftheobservedcloudasshowninFig.2b.Given the known trap frequencies, these widths correspond to a sample temperatureof2.3(4)μK.Usingthistemperatureandtheverticaltrap frequency,weestimatethewidthalongtheunseenverticaldirectionto be σ v=5.6(8)μm and convert the peak column density to a mean densityviathefactor4 πσ v.

Weapplyourtechniquetostudycollisionallossesinthethermal gasofmolecules.Here,thedensitydependenceofthelossiscritically importanttoverifythemechanismsatplay.Previousstudiesofcolli- sionsinRbCshavereliedupondetectionofthemoleculenumbervia absorption imaging,whichisthenconvertedtothedensitythrough independently measured temperatures and trap frequencies. Our approach,however,yieldsamoredirectmeasurementofthedensity, inadditiontosignificantlyenhancedprecisionwhenmeasuringsmall numbers of molecules. In Fig.2c, we plot the mean density of the sampleasafunctionofholdtimeinthedipoletrap,withthelongest hold times and therefore lowest densities corresponding to the detectionofapproximately50molecules.Wefittheresultsusingthe solutiontotherateequationn(r,t)= -m k m n(r,t)m,wherem=1,2 correspondingtoone-andtwo-bodylosses,respectively.Wefindrate coefficients of k =0.49(2)s−1 and k =5.1(4)×10−11cm3s−1. Given the 1 2 relativelyhightrapintensityof6kWcm−2,weexpecttoseeaone-body lossrate of0.28s−1 due tophoton scattering,baseduponmeasure- mentsoflossperformedinopticaltweezersatawavelengthwithin1 nmofthevalueusedhere27.Ourobservedone-bodyratecoefficientis withinafactorof2ofthisrate;thedifferencemaybeattributedtothe presenceoftwo-photontransitionstomorehighlyexcitedelectronic states41 thatcause strong wavelength dependencearound 1064nm. Thetwo-bodyratecoefficientwemeasureisafactoroftwolowerthan thethermally-averageduniversalrate,andagreeswellwiththerates previouslymeasuredinbulkgases39.

BychoosingnottoremoveexcessRbatomsafterformationofthe molecules,wecaninvestigateatom-moleculecollisions,asshownin blueinFig.2c.Usingabsorptionimaging,wemeasureaconstantRb numberof2.1(1)×104overaholdtimeof0.5s.Thiscorrespondstoa mean atomic density of 8.6(5)×1011cm−3. Using our technique, we measurerapidlossofRbCsimmersedinthisgas,andmeasureadecay rateofk =13(1)s−1.Fromthis,weextractanatom-moleculecollision 1 rate of 1.5(5)×10−11cm3s−1, in good agreement with previous measurements42.

Multi-statedetection
Weextendourimagingtechniquetoperformsimultaneoustwo-state readout of the molecules. We project the rotational state of the moleculeontothespeciesofatomremainingintheimage,thereby enablingdetectionofthepopulationsoftworotationalstatesineach iteration of the experiment. Mapping the rotational states of the moleculeontothespin-1/2{↓,↑}basis,ourmethodallowscomplete characterisationofadisorderedspinsysteminasingleexperimental instance.Ourapproachissimilartothatproposed in11 andcomple- mentsthespinread-outtechniquesdevelopedformoleculesinoptical tweezer arrays27,43. The process relies on the state specificity of the reverse STIRAP and dissociation sequence, which only converts moleculesinasinglehyperfineleveloftherotationalgroundstateinto atompairs,andontheabilitytoselectivelyremoveatomsbasedontheir hyperfine states. We choose the rotational states |↓⟩ = (N=0,M F=5) and |↑⟩ = (1,6). Here, M F=M N+m Rb +m Cs is the projection of the total angularmomentumalongthequantisationaxis(definedbya181.6G magneticfieldorientedverticallyalongz),M Nistheprojectionofthe rotationalangularmomentum,andm (m )istheprojectionofthe Rb Cs nuclear spin of Rb(Cs). At this magnetic field, N and M Faregenerally the onlygood quantum numbers44. However,our chosen states are alsospinstretchedsuchthattheyalsocorrespondtotheuncoupled basis |N,M N,m Rb,m Cs⟩ = |0,0,3/2,7/2⟩ and |1,1,3/2,7/2⟩. Crucially, the |↓⟩ state is directly addressed with a 1.5μm radiation, while the |↑⟩ state is not. Wecancoherentlydrivethepopu- lationbetween |↓⟩ and |↑⟩ usingresonantmicrowaves.

The sequenceofoperations for spinprojection isillustrated in Fig.3a. In the first step, |↓⟩ moleculesaredissociatedtoatompairs, while |↑⟩ molecules are off-resonant with the STIRAP and are not transferredto the Feshbach state. Amicrowaveπ-pulseisthenapplied toreturnthe |↑⟩ molecules totherecoverableN=0state.Afterthis, theRbatomfromthe |↓⟩ stateistransferredfrom(F=1,m F=1)tothe uppermost hyperfine state (2, 2) using microwave adiabatic rapid passage(ARP)andtheCsatomisthenremoved.The |↑⟩ molecules are then dissociated, and a second Rb ARP is performed. This putstheRb atomfrom |↑⟩ in(2,2)andsimultaneouslyreturnstheRbatomfrom |↓⟩ moleculesbacktothelowerhyperfinestate |1,1⟩.Wethenselec- tivelyremoveRbatomsin(2,2)associatedwith |↑⟩ moleculesusing lightonthecyclingtransition5S 1/2 (2,2)→5P 3/2 (3,3). Attheendofthis process,thesitesthatinitiallycontainedamolecule |↓⟩ aremappedto anRbatom,andthosethatcontainedamolecule |↑⟩ aremappedtoa Csatom.

Detection of both species in a single experimental cycle is per- formedbyaseriesofsequentialimagesoffluorescence.Thankstothe largeseparationoftheimagingwavelengths,wefindthattheatomsare unaffectedbyimagingtheotherspecies.Thus,toreliablydeterminethe relative locations of the atoms, we take three successive images as showninFig.3b,collectingfluorescencefirstfromRbonly,thenCsonly, andfinallyRbandCstogether.Thefinalimageremovesanyambiguity inthepositionofthelatticebetweendifferentimages.Thisallowsusto reconstructacompletepictureofthespindensityasshown.

InFig.3c,wedemonstrateourspindetectiontechniqueusinga simpleRabi oscillation experiment. We drive the σ+ transition between |↓⟩ and |↑⟩ byapplyingresonantmicrowavesforavariableduration andusethemulti-statereadouttodetectbothrotationalstates.Here, thetraplightisswitchedoffduringthemicrowavepulsetoavoidlight shiftsofthetransition41.Fromthefitstothemeasurement,wedeter- mineaRabifrequencyof20.0(1)kHz,whichislowenoughtoavoidoff- resonantcouplingtootherhyperfinestatesduetoimperfectmicro- wave polarisation. Since the microwave drive is performed in free space,thermalexpansionofthecloudleadstolossofmoleculeswhen recaptured by the pinning potential. We model this using an expo- nential decay and fit a 1/e time around 700μs. The average initial moleculenumberdetectedviathetwospin-mappingchannelsagrees within the statistical uncertainty; fits to the Rabi oscillations yield 2.61(16)×102moleculesfromRband2.58(11)×102moleculesfromCs.

From independent measurements characterising each stage of the multi-statedetectionsequence,weexpecttheoverallprobabilityof faithfully mapping the state of an isolated molecule to the correct atomtobearound84(2)%forbothstates.Thisiscurrentlylimitedby technicalfactors, suchasthe ARP fidelity and STIRAP efficiency, as discussedintheMethods.Basedonthebestreportedmeasurements for STIRAP in RbCs37 and state-of-the-art transfer fidelities between atomichyperfinestates45,weexpectthatamappingfidelity>98%is possible.

Spatially resolved addressing of molecules
Wealsodemonstratelocaladdressingoftherotationaltransitionina selected regionofthemoleculargas.Thisisachievedbyilluminating partofthesampletolightshiftthemoleculartransitionoffresonance, asillustratedinFig.4a.Here,weaddressthemoleculeswithlightat 817nm,wheretheanisotropicpolarisabilityislargeandnegative27,46. ThisproducesastronglightshiftofthetransitionsfromN=0tothe hyperfinestatesofN=1 asshownin Fig.4b. Wethenapplyamicro- waveπ-pulseonthetransitionfrom |↓⟩ to |↑⟩ .Inregionswherethe lightshiftisgreaterthan theFourierwidthofthemicrowavepulse, moleculeswillremainin |↓⟩ ,whilemoleculesoutsideofthisregionwill be transferred to |↑⟩ . The addressing beam radius is 14.6μm, and the spin-resolvedimagesinFig.4c,d.Fromtheobservedgradientofthe addressingbeamintensityatthisradius,weexpectablurringofthe edgeofthiscircleontheorderof5μm.

Spatialaddressingalsoallowsustoselectivelyremovemolecules fromthesample.Forexample,wecanremoveallmoleculesoutsideof theaddressingbeambyapplyingthelocal-addressingpulse,pinning the molecules, and then discarding those in |↑⟩ . This final step is achievedbyperformingaglobalπpulseonthe |↑⟩ |↓⟩ transition withtheaddressingbeamswitchedoff,thusexchangingthestate occupied bymoleculesin thetworegions,followed bydissociation andresonantremovaloftheatomsin |↓⟩ thatnowoccupythearea outsidetheaddressingregion.

Wecanmeasurethethermalenergydistributionoftheremaining subsetofpinnedmoleculesbyrampingoffthepinningpotentialand observingexpansionofthesampleasafunctionofthetimeofflight,as showninFig.4e.Todetecttheexpansion,were-pinthecloudaftera variable time of flight and image as before. Each realisation of this sequenceproduces ~100molecules.Buildingup2Dhistogramsfrom manyshotsallowsustomeasuretheexpansionofthecloud.Usinga quadratic fit to the results, we determine the temperature to be 5.0(1)μK.Thetemperatureobservedhereishigherthanfortheinitial moleculesampleduetothenon-adiabaticloadingandunloadingof thepinninglattice.

In a complementary measurement, wequantify the energy dis- tributionoftheinitiallypinnedmoleculesbyexaminingthemovement ofmoleculesbetweensitesasafunctionofthelatticedepth.Starting from the localised sample, we ramp the lattice down to a variable depthandthenobservethemeanradiusofthemoleculesfromthe centreoftheaddressingbeamafter1ms.Weseethatforlatticedepths below1000E the radius growsovertime,indicatingthatthemole- rec cules are no longer pinned, as shown in Fig.4c. We compare these resultstoaMonteCarlomodel(see“Methods”)whereweassumethat moleculesmaintainthebandindexinthelatticewheninitiallypinned. Asthelatticedepthisdecreased,thenumberofbandsbelowthetrap depth decreases, and the highest energy molecules freely diffuse aroundthelattice.Wemodelthisasthermalexpansionwithatem- perature corresponding to that measured in Fig.4e. We find good quantitativeagreementbetweenthismodelandourobservations.We alsonotethatforlatticedepthsabove1000E themoleculecloud rec radiusdoesnotsignificantlyincrease,andwemeasurenochangein thecloudsizeatlongtimesupto1000ms;anexampleimageatthis longholdtimeisshownintheinsetofFig.4d.

Methods
ProductionofultracoldRbCsmolecules
Theexperimentalapparatususedherehasbeendescribedinprevious works55,56,thoughitisdistinctfromthatusedforourpreviouswork withRbCsmoleculesinbulkgases.Weutiliseamulti-chambervacuum design,wheretheatomsarefirsttrappedandcooledinastainlesssteel chamber and then transported to a rectangular glass cell using an opticalconveyor-belt56.Ourprocessforformingtheultracoldmixture is illustrated in Supplementary Fig.2. The two species areprepared sequentiallyandareloadedintotwospatiallyseparatedopticaldipole trapsinthecell.TheRbatomsarepreparedfirst,transportedintothe cellandthenmovedby1mmusingamovableopticaltrappingbeam. Cs is then cooled, transported and loaded into a separate fixed- positiondipoletrap.Withthespeciesseparated,weareabletoeva- porativelycoolbothspeciessimultaneouslyandprepareBose-Einstein condensatesof1×105Rbatomsand4×104Csatoms.

To form molecules, we merge the two atomic gases to form a mixturewithhighphase-spacedensity(PSD).Duetotheimmiscibility oftheatomiccondensatesatmagneticfieldswhereCsisstableagainst three-bodylosses57,weformmoleculesfromathermalmixture.We usetheMovingDimplebeamshowninSupplementaryFig.2tomerge thetrapswhentheatomsarejustabovetheirrespectivecondensation temperatures. This generates a mixture containing ~2×105 of each speciesataPSDof~0.1andatemperatureof~200nK.

Ourschemeformolecularassociationfollowsthatusedin34,35.We first associate molecules into the weakly-bound Feshbach state by ramping the magnetic field over the Feshbach resonance at 197G, continuingtherampto181.6GtoaccessamoredeeplyboundFes- hbach state. We then transfer the molecules to their rovibrational ground state using STIRAP and remove any remaining atoms using resonant light (as described below). As mentioned above, for the measurementshere,weobserveaone-waySTIRAPtransferfidelityof η STIRAP =95(1)%.

Opticaltraplight
Allofthelightusedtotrapthemoleculesisderivedfromthesame source operating at λ=1064.521(4)nm, with different beams detunedby~10MHzfromeachothersothatinterferencesaretime averaged on the scale of the atomic or molecular trapping fre- quencies.Thedipoletrap,whichholdsthegroundstatemolecules beforetheyarepinned,isformedbyalightsheetbeamwithvertical waist7μmandhorizontalwaist150μm,andtwocircularbeamsof waists45μmand100μm.

Atomremovalwithresonantlight
Toselectivelyremoveoneoftheatomicspeciesfromthepinning latticeatouroperatingmagneticfieldof181.6G,weusecircularly polarised resonant light propagating along the quantisation axis. For spin-resolved detection, the Rb light is tuned to address the Zeeman-shifted transitions 5S 1/2 (F=2,m F=2)→5P 3/2 (3, 3). For detection not requiring mapping of the internal state onto the atomic species, an electro-optic modulator (EOM) is used to gen- erateadditionallighttoaddressthe5S 1/2 (1,1)→5P 3/2 (2,2)transition. ThisallowstheremovalofRbatomsinthehyperfinegroundstate thatisoccupiedafterdissociationwithouttheneedforARP.TheCs removallightalsousesanEOM;thecarrierisresonantwith6S 1/2 (4, 4)→6P 3/2 (5, 5) and one of the sidebands is tuned to the 6S 1/2 (3, 3)→6P 3/2 (4,4)transition.

When using the EOM for both species, we observe the mean atomnumberremainingaftertheremovalpulsetobe1.9forRband 1.8forCs,whenstartingfrominitialnumbers~1×105.The1/elife- time during the removal pulse is measured to be around 5μs. Thisismuchfasterthantheexpectedmeantimebetweencollisions of ~1ms, such that pair loss caused by the removal of light will be unlikely. If we omit these removal pulses, we observe pair loss during simultaneous PGC with a 1/e lifetime of on the order of 10ms.

Polarisationgradientcooling(PGC)
Forbothspecies,weperformPGContheatomicD 2 linesusingasingle retro-reflectedbeampath(beamwaist0.5mm),angledoutofthexy planeby8degrees,androtatedbyapproximately10degreesinthexy planefromthedirectionofthelatticebeamthatdefinestheydirec- tion. The polarisation of the PGC light is arranged to give a σ+−σ− coolingconfiguration.Weuse500μWofcoolinglightforeachspecies. This light is red detuned from the free-space cycling transitions by around10Γ,whereΓisthenaturallinewidthoftherelevantatomic transition.Repumplight,addressingthelowerhyperfinestateofeach atom, is provided by a separate beam propagating in the xy plane. DuringthePGC,themagneticfieldmustbenulled,requiringadelayof around15msforeddycurrentsfromthehighfieldcoilstodissipate beforebeginningcooling.Tocollectfluorescencefrombothspecies duringthesamesequence,weeitherilluminatetheatomssequentially orsimultaneouslycooltheatomsanduseafilterwheeltoisolatethe fluorescencefromeachspecies.Wefindneithertheholdtimeinthe pinning lattice nor the presence of the cooling light for the other speciesleadstoasignificantlossofatoms.

Characterisationoftheatomdetection
Toestablish the fidelityand signal-to-noiseratio(SNR)ofouratom detection, we analyse images of dilute clouds58. We compare the detectedsignalfromsummingcountsin8×8pixelregionsofinterest aroundisolatedatomswithbackgroundfromidenticallysizedregions thatarecentredonemptypartsofthelattice.Anexemplarysparse image, and the resulting histograms are shown in Supplementary Fig.1a–c. WedefineSNR=(μ atom-μ bg)/(σ atom+σ bg)whereμ is themeanandσ isthestandarddeviationofthecountdistribu- tionforatomsandbackground,respectively58.WefindSNR Rb =4.6and SNR Cs =5.5. For both species, we determine the mean time for an atomtobelostormovetoadifferentsitetobe>10s.

We determine the point-spread functions (PSFs) associated with ourimagingsystembyaveragingoverthesignalsfrom100isolatedRb andCsatoms.ThePSFAiryradius(r Airy)isfoundtobe1.09(12)μmfor Rb and 1.04(10)μm for Cs. While the lattice spacing is below the Sparrow limit of our imaging system (0.77 r Airy)59, we are able to reconstruct the lattice occupancy using the single-molecule imaging neural network38. We determine the lattice phase by fitting the intensity vectorsfromanalysisofsparselyfilledimages,andassumethesedonot varyshottoshot.Foreachimage,thelatticephaseisdeterminedby maximisingthevarianceofthepixelsclosesttoeachlatticesite,andfor eachsite,a20×20pixelregioncentredonthesiteisfedintotheneural network for reconstruction. The single-layer network is trained on simulatedimagesandcanbeunderstoodasperformingaweightedsum of the counts on each site. This weighted sum is compared to a threshold to determine the site occupancy. Supplementary Fig.1d showsthelearnedweightsweuse.Tominimisetheeffectofvariations in peak fluorescence, the images are normalised before being pro- cessed.AzoomedsampleofthereconstructeddataisshowninSup- plementaryFig.1e.Weestimatethefidelityofdetectionbyperforminga doubleGaussianfittotheneuralnetworkoutput,asshowninSupple- mentaryFig.1f,whichshowsthehistogramforthedataatthehighest densityinFig.2.Fromthis,weestimateanerrorrateoflessthan5%.

Internalstatecontrol
We use a pair of antennas, placed just outside the cell, to drive microwave transitions in the atoms and molecules. We drive the molecule transition between the (N=0,m F=5) and (1,6) states at 181.6G,atafrequencyof980.384MHz44.Aswedonothavecontrolof the microwave polarisation, we use a Rabi frequency that is low enoughtoavoidoff-resonantcouplingtootherhyperfinestates.The Rbhyperfinestateiscontrolledusingadiabaticrapidpassage(ARP)to transferbetween5S 1/2 (F=1,m F=1)and5S 1/2 (2,2).

Addressinglight
Theaddressinglightisformedbyan817nmbeamfocusedontothe moleculesfromabovethecellwitha1/e2waistof14.6μmandapeak intensityofI=3.3kWcm−2.ThelightshiftsplottedinFig.4arecalcu- latedusingmethodsfrom60andapreviousmeasurementoftheani- sotropicpolarisabilityat817nmofα(2)= -2814(12)×4πϵ 0 a30. 27

Fidelityofthespin-mappingprocess
Here, we consider the technical factors that affect the fidelity of mappingtheinternalstateofanisolatedmoleculeinthepinninglat- ticetothecorrecttaggingatom.Thespinmappingprotocolrequires controlofrelativelylargemagneticfieldstodissociatethemolecules, combined with a low-noise magnetic field environment for the microwaveARPtransferbetweentheatomicstates.Additionally,the partofthesequencewheremoleculesarepinnedshouldbeperformed as quickly as possible to avoid spontaneous Raman scattering of moleculesfromtheintenselatticelight.

Intheworkpresentedhere,wedevelopedtwoapproaches.The firstistotransientlyturnoffthehighmagneticfieldtoperformARPat a low field where the magnetic field noise is significantly reduced. Usingthisapproach,wemeasureARPfidelitiesof98(1)%.However,we needtointroduceatimedelayof32ms,largelylimitedbythetime requiredforthefieldtostabilisewhenturningbackon.Thisleadsto lossofthe |↑⟩ molecules,whichmustbeheldinthelatticeforthistime. Wemeasureasurvivalprobabilityofη Hold =86(10)%forthesemole- cules,whichstronglybiasesthedetectionfidelityinfavourofthe |↓⟩ molecules.AnadditionalsourceoflossfortheN=1moleculesisoff- resonantscatteringfromtheStokeslightduringtheSTIRAPtransfer usedtobreakaparttheN=0molecules27.Forthisprocess,wemeasure asurvivalprobabilityofη Stokes =97(1)%.Takingallthesefactors together, we determine the mapping fidelity η j = η ARP η Hold η Stokes η STIRAP = 78(9)% for |↑⟩ and η j = η ARP η Hold η Stokes η STIRAP = 91(2)% for |↓⟩ . We applied this approach tothe data shown in Fig.4.

The second approach involves performing ARP at high field, prioritising the speed of the sequence. Here measure a lower ARP fidelityofη ARP =94(1)%,buthaveanincreasedsurvivalprobabilityof thepinnedmoleculesofη Hold =97(1)%duetothesignificantlyshorter 8msholdtime.Thus,inthissecondapproach,thetransferfidelities are η j = η ARP η Hold η STIRAP = 84(2)% for |↑⟩ and η j = η ARP η Hold η STIRAP = 84(2)% for |↓⟩ , as given in the results. We applied this approach to the data shown in Fig.3.

Modelformoleculemotioninthelattice
To model this evolution, we map the thermal distribution of the molecules onto the bands of the optical lattice at full strength, assumingatemperatureof5.0(1)μKasmeasuredinFig.4e.Theband occupationisassumedtoremainunchangedasthelatticeadiabatically rampsdowntoalowerdepth.Thebandenergiesarecalculatedforthe lowerlatticedepth.Moleculesinbandswithenergieshigherthanthe trapdepthbecomeuntrappedandexpandballisticallywithavelocity correspondingtotheirbandenergy.Foreachiteration,amoleculeis initialised at a random position within the circle of the addressing beam and in a random lattice band sampled from the thermal dis- tribution.Thefinalpositionofthemoleculefollowingthe1msholdis then computed.The simulation isrun for 10,000iterations ateach latticedepth.Wealsoaccountfortheresidualunaddressedmolecules thatexistoutsidetheaddressingbeamradiusduetoπ-pulseimper- fections,byallowingsomeprobabilitythatthemoleculeisinitialisedin an ellipse defined by major and minor radii extracted from a 2D Gaussianfitofthefullcloud,asshowninFig.2b.

Peer review rounds
[{"round": 1, "reviewer_comments": {"reviewer_1": "This work reports two important advances in manipulating and detecting ultracold molecules. To date, ultracold molecular gases produced by assembly from degenerate atom gases have mostly been probed at a coarse level with absorption imaging. A few years ago, a group introduced quantum gas microscopy for detecting individual NaRb molecules in an optical lattice. The RbCs microscope described in this work is only the second such realization, but this paper goes beyond just imaging the molecules with single-site resolution. First, they encode a spin-1/2 in two rotational states of the molecule and show they can read out the spin state with single-site resolution. This is done by mapping the rotational state to whether they have a Rb or Cs atom on a site before imaging. This readout is crucial for studying quantum spin systems of molecules, especially when the lattice is far from unit filling (as is the case for all lattice experiments to date). Second, they demonstrate the ability to locally address the molecules and flip part of the cloud to a different spin state. These are important advances that will have a strong impact on the field of ultracold molecules and AMO more generally. The paper is well-written and the relevant work is properly cited. I recommend publication in this journal.\nI have two suggestions to improve the work. First, one difference from the previous molecule microscopy work is that the molecules are produced in the bulk rather than in a lattice, and the preparation scheme means that the molecules are not in the ground state of the lattice when pinned. It would be interesting to report the average number of vibrational quanta occupied in each direction, and to discuss how this would impact the feasibility of studying quantum magnetism with the system. Second, while I appreciate that this is not a quantum computing type paper, I think the authors can still be a bit more quantitative in some parts of the paper. Both of the key results (state detection and local manipulation) do not have any fidelity associated with them as far as I can tell.\nI believe there might be a typo in Fig. 3a: for the N=1 state (top row), shouldn't the state of the Rb atoms after dissociating the molecule be (1,1) rather than (2,2)? (after the ARP, they become (2,2)).", "reviewer_2": "The manuscript by Mortlock et al. describes the ability to freeze Rb or Cs atoms and/or RbCs molecules in a deep optical lattice and perform dual-species quantum gas microscopy on them. These techniques offer a versatile platform for studying atomic and molecular systems and mixtures in bulk or in an optical lattice. The authors exploit these abilities to study the microscopic distribution of molecules and to study the lifetime of a mixture of molecules and atoms.\nMost importantly, the authors use these techniques to perform state-resolved detection of molecules. Since the occupation of molecules is not known because the creation efficiency of molecules is limited or because of any molecular loss processes, it is generally challenging to fully characterize a molecular system when two rotational “spin” states are used. Crucially, the spin state is detected by mapping it onto occupation. However, this mapping is flawed when occupation is a priori unknown. Therefore, it is crucial in molecular systems (and also recently becoming crucial in atomic quantum computers) to independently measure occupation and spin. The authors present a beautiful demonstration of this technique. The technique, as proposed back in 2018, is based on uniquely mapping each spin state to an atomic species. By independently detecting both atomic species, it is possible to detect both the occupation and the spin state.\nFinally, the authors combine this state-resolved detection tool with local optical control to create a spin pattern in the ensemble. They use a local light shift on the rotational transition such that the light shifted region is off-resonant with the global microwave pulse that flips the atomic spin. They use this ability to demonstrate the power of their microscopic state- resolved detection. By switching between bulk ensembles and pinned molecules in a lattice, the demonstrate some preliminary dynamical behavior. However, the true power of these techniques is in the context of dipolar spin-exchange interactions and interacting spin dynamics, which presumably the authors leave for future work.\nThe paper is well written, the figures are clear, and the authors have thoroughly investigated the dual species microscopy of the Rb/Cs/RbCs system. I believe that the paper is suitable for publication in Nature Communications. I have some questions and comments that the authors should consider upon resubmission.\n1. For the Rb+RbCs mixture lifetime, is it possible to detect RbCs using Cs atoms, thereby uniquely mapping either Rb atoms or molecules to an atomic species? Presumably, this would require a spin-flip of Rb right before the STIRAP back, such that atomic Rb can be differentiated from the molecular Rb, and the latter can be removed with a blast pulse. If so, it should be possible to obtain single-shot “species-resolved” images of the atom-molecule mixture. Do I understand correctly that this was not demonstrated here?\n2. For the two-state detection, the authors should elaborate on what additional information the combined Rb-Cs image provides compared to the Rb-only and Cs-only images. Certainly, it provides information about loss or tunneling probability during detection. Perhaps this could be quantified by a subtraction or correlation plot.\n3. As a related point, it would be interesting to see correlation plots between Rb and Cs events in their respective single-species images. Presumably, events in which a Rb and a Cs are on the detected on the same site are extremely rare due to light assisted collisions, as the authors mention. But I imagine that it could be possible to get a positive detection of the illuminated species in some shots before the pair is lost.\n4. It may be helpful for the authors to briefly describe the reason why they need to ramp to low field for the Rb ARP. The readers recognizes that this is a technical issue that will be solved, but the current situation is a curiosity that may be worth mentioning. Presumably it is related to the resonant bandwidth of the microwave coil or similar.\n5. It may be appropriate to quantify the effect of the STIRAP light on the N=1 “up spin” molecules. Certainly, the effect would be small, but the statement could be more precise than “remain unaffected”. Assuming the STIRAP and detection efficiency may be limited to ~0.99, we might assume that this is a good baseline for any deleterious effect on “up” molecules during the STIRAP step of “down” molecules. This means that the lifetime of “up” molecules while the STIRAP light is on should be ~100x longer than the STIRAP pulse time. The authors should consider measuring the lifetime of “up” molecules while the STIRAP light is on, where presumably the down-leg would be the source of any problem."}, "author_response": "Response to the reviewers’ comments\nWe thank both reviewers for their time and thoughtful comments on the paper. We are\npleased that the reviewers both recommend publication in Nature Communications.\nBoth reviewers raise a small number of minor points that we address below. We are\ngrateful for their suggestions which we believe have improved the clarity of the\nmanuscript considerably.\nReviewer 1. Had two suggestions to improve the work.\n1. “ First, one difference from the previous molecule microscopy work is that the\nmolecules are produced in the bulk rather than in a lattice, and the preparation\nscheme means that the molecules are not in the ground state of the lattice when\npinned. It would be interesting to report the average number of vibrational quanta\noccupied in each direction, and to discuss how this would impact the feasibility\nof studying quantum magnetism with the system.”\nWe thank the reviewer for this question. Below we have done the requested calculation\nand rewritten the final paragraph of the Discussion to clarify how our work fits into\nefforts to study quantum magnetism with highly controlled arrays of molecules.\nWe note first that what we present here is not the correct approach to study spin\ndynamics in a lattice. Our work is specifically targeting the ability to do spin-resolved\nsingle-molecule detection in bulk gases. This is a critical tool to address open questions\nin the field. To study spin dynamics, one would follow the procedure used by\nBakr/Nagerl and prepare the molecules in ground band of an optical lattice. This work is\nongoing in our lab and we highlight this in the outlook of the paper.\nHowever, for completeness we have analysed the prospect of spin dynamics in the\ncurrent setup as requested. Details are given below:\nFrom the temperature we observe in Fig. 4e, and our estimates of the trapping\nfrequency after pinning (~60kHz radial, ~5kHz axial) we estimate mean motional\nquantum numbers after pinning of 1.3 radially and 10 axially. We identify two effects\nthat motional excitation would have on studying quantum magnetism using dipole-\ndipole interactions between pinned molecules. 1. Differential light shifts 2. Variation in\ndipole-dipole interaction strength from the dependence.\nr3\nIn the current setup we expect differential light shifts will dominate. We can estimate\nthis with a simple model: assuming that the trapping potential is from a harmonic\nintensity profile, I = I (1-x2), we can see that for a given harmonic oscillator state the\n0\nℏ\nexpectation value of the intensity goes as I = I (1- (2n+1)). Further algebra\nn 0\n2mω\nallows us to derive the AC stark shift for a given harmonic oscillator state, n, as ℏδ =\nn\nΔα\nℏω(2n+1), with Δα being the difference between the polarizability of the two\n2α\nrotational states.\nΔα\nFor the situation in this work, ~0.2 and so the differential light shifts are on the scale\nα\nof the trapping frequency and thus much stronger than our expected dipole-dipole\ninteractions on the order of 100Hz, such that the interactions will be far off resonant for\nmost pairs of molecules.\nIn future work we could change the trapping light to be at the magic wavelength for\nRbCs, which should eliminate this problem, leaving only spin-motion coupling from the\nradial 1/r3 dependence of the dipole-dipole interaction. Preliminary calculations\nindicate that for the 5uK temperature we measure we should expect significant\nΔJ\nbroadening of the dipole-dipole coupling strength ( > 0.1), mainly due to the weak\nJ\naxial confinement.\nTo make it more clear how our current work relates to quantum magnetism we have re-\nworded the final discussion paragraph, see page 7 and 8 of the resubmitted paper.\n2. Second, while I appreciate that this is not a quantum computing type paper, I\nthink the authors can still be a bit more quantitative in some parts of the paper.\nBoth of the key results (state detection and local manipulation) do not have any\nfidelity associated with them as far as I can tell.\nWe agree with the reviewer that although not essential to the paper, quoting fidelities in\nthe main text would be interesting to some readers. We have therefore quantified the\nfidelity of each stage of the spin-mapping protocols.\nWe have investigated two experimental approaches to spin-mapping, both of which are\nnow presented in the resubmission.\nSequence A: Turning off the high field coils for ARP, at the expense of a longer hold of\nthe N=1 molecules in the lattice\nSequence B: Performing ARP at the STIRAP field to minimise the hold of N=1 molecules\nat the expense of ARP fidelity due to increased magnetic field noise.\nThe breakdown of the fidelities associated with each stage of these sequences are as\nfollows:\n• Rb ARP Fidelity\no We measure a fidelity of Rb ARP transfer of 97(1)% in sequence A and\n94(1)% sequence B.\no We note that N=0 detection relies on two ARP transfers, whereas N=1\ndetection only requires one ARP transfer.\n• Survival of “N=1” molecules in the pinning lattice whilst ARP is performed\no We measure the lifetime of the molecules after pinning, and from this\nestimate the loss for the hold times used in the two sequences. From\nthese measurements we get the estimated survival probabilities of\n86(10)% in sequence A (where the hold is 32ms) and 97(1)% in sequence\nB (where the hold is 8ms).\no The atomic lifetime by contrast is much longer, on the order of seconds,\nand spontaneous scattering to other states is not problematic as all\nstates are imaged by the optical molasses.\n• Fidelity of STIRAP (95(1) % for both states)\no In our experiment the STIRAP fidelity is limited by the amount of laser\npower available. We note that using higher laser power, our group has\ndemonstrated 98.7(1) % transfer fidelity (Maddox et al. PRL 2024) and we\nare in the process of making this upgrade.\n• Fidelity of Blasting of Rb and Cs atoms (>99%)\no As mentioned in the relevant section of the methods, we observe a mean\nof <2 atoms remaining if we don’t recover any molecules with STIRAP. These\nare leftover atoms from the >10,000 atoms used to make the\nmolecules.\n• N=1 -> N=0 Pi pulse fidelity (>99%)\no Measured from the lowest number of detection events when we only\nrecover N=0 after a pi pulse.\nCombining all these factors together we estimate detection fidelities of:\nSequence A: 91(2) % for N=0 molecules and 78(9) % for N=1 molecules\nSequence B: 84(2) % for N=0 molecules and 84(2) % for N=1 molecules\nWe have updated the methods section to include a section Fidelity of the spin-mapping\nprocess (on page 9), detailing the above analysis, and made the description of the spin\nresolution in the results section generic (describing both A and B approaches). The data\nin Figure 3c has been replaced with data taken using method B.\nSpatial addressing\nThe resolution of spatial addressing is limited by the spatial rate of change of the light\nshift at the intensity where the light shift and the Fourier width are nearly equivalent.\nUsing the numbers reported in the paper, we calculate the addressing beam the\ngradient in the light-shift at the cross over point to be 3.2 kHz/µm, which for the\nmicrowave pulse time used in our experiment gives a resolution of around 5µm.\nUltimately this resolution is limited by the resolution of the imaging system. In future we\nplan to add in a SLM system to control addressing light projected through the\nmicroscope objective (rather than focused using a low NA lens above the cell). This will\nallow addressing potentials with significantly sharper edges and will enable a resolution\napproaching the lattice spacing. The spin resolution is also in theory limited by the\nfidelity of the pi pulse, which could be improved with composite pulse schemes.\nWe have added a comment on the resolution of spatial addressing in the results (on\npage 7).\nWe believe these changes help make the paper more quantitative, addressing the\nreviewer’s concern.\nI believe there might be a typo in Fig. 3a: for the N=1 state (top row), shouldn't the state\nof the Rb atoms after dissociating the molecule be (1,1) rather than (2,2)? (after the ARP,\nthey become (2,2)).\nWe thank the reviewer for spotting this typo and have rectified the figure as required.\nReviewer 2. Had the following comments for us to consider\n1. For the Rb+RbCs mixture lifetime, is it possible to detect RbCs using Cs atoms,\nthereby uniquely mapping either Rb atoms or molecules to an atomic species?\nPresumably, this would require a spin-flip of Rb right before the STIRAP back, such that\natomic Rb can be differentiated from the molecular Rb, and the latter can be removed\nwith a blast pulse. If so, it should be possible to obtain single-shot “species-resolved”\nimages of the atom-molecule mixture. Do I understand correctly that this was not\ndemonstrated here?\nIt is indeed possible to image Rb atoms and RbCs in the same sequence, using the\nprotocol outlined by the reviewer, and we thank the referee for this suggestion.\nThe measurement we did was constructed as an example of measuring an impurity of\nRbCs in a bath of Rb, such that the loss of Rb atoms is expected to be small. We chose\nto measure the Rb density using absorption imaging as it was too high for single site\nresolved imaging (with >10,000 Rb atoms in the measurement, comparable to the\nnumber of sites in the lattice, we would expect very large parity projection losses).\nBuilding on the reviewer’s suggestion it would be possible to study a different system\nwhere the densities are comparable by reducing the Rb density, e.g. via a pulse which\ntransfers a finite, calibrated, fraction to the F=2 state followed by removal with F=2-\n>F’=3 light as in the spin resolution sequence.\n2. For the two-state detection, the authors should elaborate on what additional\ninformation the combined Rb-Cs image provides compared to the Rb-only and Cs-only\nimages. Certainly, it provides information about loss or tunneling probability during\ndetection. Perhaps this could be quantified by a subtraction or correlation plot.\nWe agree with the reviewer that the joint Rb-Cs image is not strictly needed to establish\nthe molecular state distribution. It certainly contains information on loss of atoms and\ntunnelling. In practice, it was used to establish the relative positions of the lattice in the\ntwo images. Shifts between the images could arise from chromatic effects in the\nimaging system and/or drift of the lattice position over time. We see that the offset\nbetween the two lattices is smaller than one site, which makes it straightforward to\nassign the detected fluorescence to positions in the same underlying lattice structure.\nTo clarify this point, we have added the text in bold to the quoted section:\n“Thus to reliably determine the relative locations of the atoms we take three successive\nimages as shown in Fig. 3b collecting fluorescence first from Rb only, then Cs only, and\nfinally Rb and Cs together. The final image removes any ambiguity in the position of\nthe lattice between different images. This allows us to reconstruct a complete picture\nof the spin density as shown”\nWe also independently quantify the probability of loss or thermal hopping during\nimaging, as discussed in the methods.\n3. As a related point, it would be interesting to see correlation plots between Rb and Cs\nevents in their respective single-species images. Presumably, events in which a Rb and\na Cs are on the detected on the same site are extremely rare due to light assisted\ncollisions, as the authors mention. But I imagine that it could be possible to get a\npositive detection of the illuminated species in some shots before the pair is lost.\nThe reviewer is correct that events where a Rb and Cs are detected on the same site are\nvery rare. Analysing spin-resolution data, we find that we have around 0.005 events per\ndetected molecule where Rb and Cs are detected on the same site. This is despite the\nfact that the detection protocol begins by breaking apart the molecules to produce an\ninitially highly correlated system with one Rb and one Cs atom in each site where there\nwas a molecule.\nWe attribute the observation of a small but finite number of events where Rb and Cs are\ndetected to the following possible experimental imperfections:\n1. When a molecule is dissociated on a lattice site, there is an error in the ARP such\nthat Rb isn’t blasted away as expected. This leaves an atom pair after spin\nmapping. The Cs atom survives for the duration of the Rb fluorescence imaging\nand fluoresces enough to be detected.\n2. During imaging, a Cs atom hops onto the site occupied by a Rb atom such that it\nis later detected on that site in the Cs image.\n3. The reconstruction algorithm incorrectly assigns a neighbouring site as occupied\ndue to the finite size of the atomic point spread function. These false positives\ncould lead to assigning a single site with two molecules.\nAs the reviewer notes, process 1. is suppressed by light assisted collisions (LACs) of\natoms during fluorescence. It is worth noting, however, that we have observed that there\ncan be a relatively long lifetime (>100ms) of Rb-Cs pairs against LACs when the imaging\nlight for only one species is present, as is the case here. This is remarkably long\ncompared to the homonuclear case.\nFor completeness we include below a plot of the correlations, expressed as the\nprobability of observing a Rb atom given the observation of a Cs atom at a site offset by\na vector of lattice sites, normalised to the total number of molecules.\nThe background probability here (around 0.025) indicates the likelihood that two\nmolecules from the gas would be pinned to the same site. However, we expect these\nmolecules would be rapidly lost with high probability prior to detection due to light-\ninduced loss of the two-molecule collision complex, as observed in many other\nultracold molecule experiments.\n4. It may be helpful for the authors to briefly describe the reason why they need to ramp\nto low field for the Rb ARP. The readers recognizes that this is a technical issue that will\nbe solved, but the current situation is a curiosity that may be worth mentioning.\nPresumably it is related to the resonant bandwidth of the microwave coil or similar.\nThe reviewer is correct that this was linked to the resonant bandwidth of the microwave\nantenna. Since our first submission we have replaced this antenna, and worked to\nreduce high frequency magnetic field noise, such that we can drive the MW transition\nfor ARP near the magnetic field required for STIRAP, as detailed in our response to\nreviewer 1. This allows us to significantly reduce the time required for ARP, leading to\nmuch closer agreement in the total molecule number as measured by the two atoms.\nThe data in Figure 3c has been updated with this method, along with the corresponding\ndiscussions in the Results and Methods sections.\nThe new figure is copied below for convenience.\n5. It may be appropriate to quantify the effect of the STIRAP light on the N=1 “up spin”\nmolecules. Certainly, the effect would be small, but the statement could be more\nprecise than “remain unaffected”. Assuming the STIRAP and detection efficiency may be\nlimited to ~0.99, we might assume that this is a good baseline for any deleterious effect\non “up” molecules during the STIRAP step of “down” molecules. This means that the\nlifetime of “up” molecules while the STIRAP light is on should be ~100x longer than the\nSTIRAP pulse time. The authors should consider measuring the lifetime of “up”\nmolecules while the STIRAP light is on, where presumably the down-leg would be the\nsource of any problem.\nIt is known that the Stokes light can affect the N=1 molecules, due to the presence of\nnearby excited states around 1GHz detuned. The spectroscopy of these states is\ndetailed in the theses of Markus Debatin (Innsbruck 2013) and Peter Molony (Durham\n2016).\nAs suggested by the reviewer, we have now measured the probability of loss of N=1\nmolecules during the STIRAP pulse by comparing two sequences, one where we apply\n10 consecutive STIRAP transfers (pulses which would transfer from N=0 to the\nFeshbach state), and a control measurement in a sequence which is identical but omits\nthe STIRAP light. We found from this measurement that there is indeed measurable loss\n(3(1)%) of the N=1 molecules during the application of STIRAP to N=0 molecules, which\nwe have now noted in the paper in the new section on the Fidelity of the spin-mapping\nprocess in the Methods on page 9."}, {"round": 2, "reviewer_comments": {"reviewer_1": "I am satisfied with the responses of the authors to my questions and the changes made to the manuscript.", "reviewer_2": "The authors have carefully and thoroughly addressed the comments raised by both referees and have taken more data that substantially strengthens the manuscript. The have studied and documented the mapping process fidelity in great detail, following two procedures that have each have pros and cons with respect to the authors' ability to perform a microwave ARP at high field. Additionally, they have taken data to carefully measure the loss probability of \"up\" molecules during the STIRAP transfer process for the \"down molecules\". With these additions to the manuscript, I have no further reservations and suggest publication."}, "author_response": ""}]

Decision letter