Ultracold Molecular Assembly

2.6 MB·

by  Lee R. Liu

Ultracold Molecular Assembly
Lee R. Liu,abc Jessie T. Zhang,abc Yichao Yu,abc Nicholas R. Hutzler,abc Yu Liu,abc Till
7 Rosenband,b andKang-KuenNi∗abc
1
0
2
Chemicalreactionscanbesurprisinglyefficientatultracoldtemperatures(<1µK)due
n
to the wave nature of atoms and molecules. The study of reactions in the ultracold
a
J regime is a new research frontier enabled by cooling and trapping techniques devel-

1 oped in atomic and molecular physics. In addition, ultracold molecular gases that offer
1
diversemolecularinternalstatesandlargeelectricdipolarinteractionsaresoughtafter

] forstudiesofstronglyinteractingmany-bodyquantumphysics. Hereweproposeanew
h
approachforproducingultracoldmoleculesintheabsoluteinternalandmotionalquan-
p
- tum ground state, where single molecules are assembled one by one from individual
m
atoms. The scheme involves laser cooling, optical trapping, Raman sideband cooling,
o
andcoherentmolecularstatetransfer. Asacrucialinitialstep,wedemonstratequantum
t
a control of constituent atoms, including 3D ground-state cooling of a single Cs atom, in
.
s a simple apparatus. As laser technology advances to shorter wavelengths, additional
c
i atoms will be amenable to laser-cooling, allowing more diverse, and eventually more
s
y complex,moleculestobeassembledwithfullquantumcontrol.
h
p 1 Introduction
[ eachexperimentalmeasurement,wecouldunambiguously
Ultracoldmoleculesofferexcitingnewopportunitiestoex-
determinethespeciesinvolvedinareaction. Furthermore,
1
plore the fundamental interface of chemistry and physics.
v bycombiningknowledgeoftheinitialquantumstateofthe
1 On the one hand, molecules prepared in a pure internal reactants and the detected quantum states of the reaction
2 and external quantum state allow studies of chemical re-
products, one can learn details of the chemical reactions
1
actions fully in the quantum regime1. Such studies will
3 dynamicsandelucidatetheprocessesofbondbreakingand
0 be of fundamental importance in chemistry. On the other formation. Finally, a growing number of atoms in the pe-
1. hand,therichmolecularinternalstructureandinteractions riodictablecanbelaser-cooled,whichmeansthatthefirst
0 allow building systems that exhibit novel quantum many-
stepintheproposedapproach-lasercoolingofatomstoul-
7 bodyphases2. Understandingandcontrollingfundamental
1 tracoldtemperatures-isbecomingincreasinglyapplicable.
: chemicalprocessesandphysicalinteractionsarecentralto Thisnewwayofperformingchemicalreactionswillenable
v
decipheringcomplexsystems.
i the production and investigation of molecular species that
X
Inspired by scientific and technical advances in the field
wereotherwiseinaccessible.
r of ultracold atomic and molecular physics, we propose a
a
Another motivation for creating a source of single
new approach to assemble ultracold molecules atom-by-
molecules is its built-in individual molecule detection and
atom. The novel source of single gas-phase molecules will
manipulationcapabilitieswhicharecrucialforapplications
provide a new paradigm to study chemical reactions. By
in quantum information processing and quantum simula-
preparing exactly the required number of molecules for
tion. Quantum computers would allow new types of cal-
culations for chemistry3, opening the door to quantum-
computing-based discovery of molecules for medicine, en-
aDepartmentofChemistryandChemicalBiology,HarvardUniversity,Cambridge,Mas-
sachusetts,02138,USA. ergy storage, and other practical uses. Single ultra-
bDepartmentofPhysics,HarvardUniversity,Cambridge,Massachusetts,02138,USA. cold molecules can serve as quantum bits where informa-
cHarvard-MITCenterforUltracoldAtoms,Cambridge,Massachusetts,02138,USA.
∗E-mail:[email protected] tion can be encoded in the long-lived hyperfine or rota-
1–8 |1
sium (Cs) atoms due to their large molecular fixed-frame
dipole moments (4.6 Debye)20,21 and extensive available
1. Trap
spectroscopy22–24. Forultracoldchemicalreactionstudies,
NaCs molecules prepared in different internal states offer
2. Cool distinctenergeticpathwaystoparticipateinchemicalreac-
tionsthatcouldbeswitchedonandoff25.
The first step of the production (Fig. 1) is to prepare
3. Merge
laser-cooled Na and Cs atoms in overlapped magneto-
4. Weakly- optical traps (MOTs) in a single vacuum chamber. A
Bound
schematic of the apparatus is shown in Fig. 2. A more
Molecules
detailed description can be found elsewhere26. The MOT
5. Ground servesasacoldatomreservoirforloadingsingleatomsinto
State tightlyfocusedopticaltweezertraps27. Whenasufficiently
Molecules
confined atom is illuminated with near-resonant light, a
collisional blockade induces parity projection which limits
Fig. 1Step-by-stepprocedureforthe“ultracoldmolecular
the atom number to either zero or one. Loading a single
assembler.” 1. Trapsingleatomsinanarrayofopticaltweezer
traps. 2. Coolatomsintomotionalgroundstate. 3. Mergeapair atom therefore succeeds approximately 50% of the time
oftweezersintoone. 4. Convertatompairsintoweakly-bound duetoitsstochasticnature28. ToindependentlycontrolNa
molecules. 5. Performcoherentinternalstatetransfertobring andCs,wechoosetwodifferentcolortweezers,970nmfor
weakly-boundmoleculestotherovibronicgroundstate. Cs(λ =852nm)and700nmforNa(λ =589nm). The
D2 D2
severe light shifts of Na at the trapping wavelength would
normallypreventatomcooling,andconsequently,efficient
tional states while logic gate operations utilize their long- atomloading. Weeliminatethelightshiftthroughfasttem-
range, tunable, and anisotropic interactions4,5. The single poralalternationoftrapping(tweezer)andcooling26. This
moleculescanalsobeinterfacedwithstrip-linemicrowave technique should enable loading of other species of atoms
cavities for quantum information applications6. Further- and molecules that might otherwise experience large light
more, the same dipole-dipole interactions that give rise to shifts. Subsequently, fluorescence imaging determines if
gate operations can be utilized to study novel quantum asingleatomhasbeensuccessfullyloadedbeforeproceed-
phases once the system is scaled up to many molecules in ing. SimultaneoustrappingofsingleNaandCsatomsside-
aspatialconfigurationofone’schoosing. by-sidehasbeenachieved,asshowninFig. 2.
Many methods for trapping and cooling molecules to To maximize wavefunction overlap between two atoms
cold and ultracold temperatures have been demonstrated so that they can be efficiently converted into a molecule,
or are being pursued7. We follow the general approach we desire atoms trapped in the same tweezer and with
of assembling ultracold molecules from ultracold atoms. the smallest possible wavefunction spread. To achieve
Completeinternalquantum-statecontrolofmoleculeswas this, the second experimental step (Fig. 1) is to cool the
achieved in bulk gases and optical lattices8–15. These ad- atoms into their motional ground state by applying 3D
vances have already opened the door to many research Raman sideband cooling (RSC), a technique first demon-
directions, including ultracold chemistry16 and simula- strated with single ions29 and recently with single neutral
tions of quantum spin models17. Furthermore, interest- Rb atoms30,31. Once Na and Cs atoms are in their 3D mo-
ing strongly interaction phenomena can be explored with tional ground state, the two tweezers will be overlapped
a lower entropy gas and with single molecule addressabil- and merged. The Na tweezer trap will be adiabatically
ity18,19. Themethodproposedhereaimstorealizebothof rampeddowntoensurethatbothCsandNaaretrappedat
thesecapabilities. thesameposition.
Thesmallestwavefunctionspreadachievableinthecon-
2 The steps of single molecule production
finingtweezerquadraticpotentialcorrespondstothezero-
(cid:112)
Here we outline the steps for single molecule production pointlength,z = h¯/(2mω),wheremistheatomicmass,
0
(“ultracold molecular assembler,” see Fig. 1). This ap- h¯ is the reduced Planck’s constant, and ω is the angu-
proach relies heavily on high fidelity internal and exter- lar frequency of the trapped atom. For a representative
nalquantum-statecontrolofatomsandmoleculesandare 2π×70 kHz trap frequency, the zero-point lengths for Na
generallyapplicableforavarietyofspecies. Specifically,we and Cs are z =1059a and z =440a respectively, where
0 0 0 0
choosediatomicmoleculesmadefromsodium(Na)andce- a =0.053 nm is the Bohr radius. Therefore, two atoms
0
2| 1–8
by STImulated Raman Adiabatic Passage (STIRAP)33. To
checkthattheprocessissuccessful, residualatomswillbe
(A) CCD Camera (B) ((CC)) blown out withresonant light, and thesurviving molecule
Na will be coherently converted back into atoms for fluores-
cenceimaging.
Inthefollowingsections,wewilldetailthestepsofmo-
tional and internal state control of molecules with experi-
Atomic mentaldemonstrationsandtheoreticalcalculations.
Fluorescence
3 Controlling the quantized motion of
Optical NA 0.55 atoms
Tweezer
Objective
Beams Using standard MOT and polarization gradient cooling
Dichroic (PGC), we can cool a single Cs or Na atom to the point
Mirror UHV Glass Cell where the discreteness of the trap’s energy levels becomes
important. To further manipulate the atom into the low-
Fig. 2Singleatomtrappingandimagingsetupandresults. (A)
estmotionalstate,itisnecessarytooperateintheresolved
Sketchoftheapparatus. Opticaltweezerbeamsaretransmitted
sidebandregimewherethelinewidthofthecoolingtransi-
throughadichroicandfocusedbytheobjectiveintoaglasscell.
tion is less than the trap frequency (10-100’s of kHz). Ra-
FluorescencefromtrappedNaandCsatomsiscollectedbythe
objective,reflectedbythedichroic,andfocusedbyalensonto man sideband cooling (RSC) has been demonstrated for a
theCCDcamera. (B)Histogramofphotoelectroncountsfrom variety of systems in this regime29,30,34. Here, we demon-
thepixelsintheCCDimageof(C)correspondingtotheNa strate RSC of a single Cs atom to its 3D motional ground
atom. Thedoubly-peakedstructurecorrespondstoatweezer state.
withzerooroneatom. (C)Single-shotfluorescenceimageof TheRSCsequenceconsistsoftwosteps: acoherenttwo-
singleNaandCsatomstrappedinadjacenttweezers.
photon Ramantransition thatconnects two internalstates
whileremovingamotionalquantum,andanopticalpump-
ing (OP) step that re-initializes the internal state of the
cooledtotheirmotionalgroundstatewillstillhaveanex- atom. The two steps are repeated until the atom popu-
tent in one dimension more than a hundred times larger lation reaches the ground state. Although we will discuss
thanatypicalmolecularbondlength,makingefficientcon- cooling of an atom initialized in a single motional state
versionchallenging. ν =n where ν is the motional quantum number, the fol-
FollowingRSC,wewillmergethetwotweezers(Fig.1) lowingmechanismalsoappliestodistributionsofmotional
in order to initialize the Na and Cs atoms in a single in- states,asinthecaseofathermalstatepreparedbyPGC.
ternal and motional quantum state. In a quadratic poten- In our scheme (Fig. 3), the Raman transition is be-
tial, as in the case of the bottom of an optical tweezer, tween Cs ground-state hyperfine levels |F,m (cid:105) = |4,−4(cid:105)
F
two non-interacting particles can be recast into relative and |3,−3(cid:105), which are about 9.2 GHz apart. To drive
and center-of-mass coordinates32. Two atoms prepared in this transition, we phase-lock two diode lasers and set the
their respective motional quantum ground states can then one-photon red detuning ∆ = 2π×44 GHz from the Cs
be viewed as being in a single relative motional state. A D line at 852 nm. To further address the motional de-
2
pair of atoms can then be converted to a molecule in its grees of freedom, the laser beams are arranged as shown
absolute rovibrational ground state with almost unit effi- inFig.3(B)to achievesubstantialtwo-photonmomentum
ciency via quantum state transfer, provided that the entire transfer,∆(cid:126)k=(cid:126)k −(cid:126)k ,whiletheenergydifferenceasso-
F4(i) F3
processiscoherent. ciated with the hyperfine level and motional state change
Toovercometechnicalchallengesassociatedwithbridg- is supplied by the two-photon detuning, δ. If the bottom
ing two quantum states with a large energy difference ofthetrapissufficientlyharmonic,asisthecasehere,this
but small wavefunction overlap, we plan to use two steps resonanceconditionismaintainedforallrelevantmotional
(Fig.1). Asodiumandacesiumatominthesametweezer states,ν.
will be first associated into the most weakly bound molec- The atom is initially prepared in |4,−4(cid:105) by OP. We use
ularstate(vibrationallevelν(cid:48)(cid:48)=24ina3Σ+)byadetuned, σ−-polarized beams resonant with |4,−3(cid:105)→|4(cid:48),−4(cid:105) and
coherent, two-photon Raman pulse. Subsequently, the |3,−3(cid:105)→|4(cid:48),−4(cid:105) transitions, where the primed levels de-
weakly-bound molecule will be transferred into the rota- notesublevelsof6P . DuringthefirststepofRSC,aRa-
3/2
tional,vibrational,andelectronic(rovibronic)groundstate man π-pulse is applied between |F,m ;ν(cid:105)=|4,−4;n(cid:105) and
F
1–8 |3
0.8
(A) 6P3/2 ∆ A B F
0.6
D G
Ω Γ 0.4 C E
52 nm . . .F4 OP pulation 00..02
8 o
P 0.8
|4, –4;n〉 F3 0.6
Ω
F3
|4, –4;n–1〉 0.4
6S . 0.2
(B) 1/2 Raman F4 (2) . . 0.0–150 –100 –50 0 50 100 150
Two–photonRamandetuning δ/2� [kHz]
OP ω
trap |3, –3;n〉
Fig. 43DRamansidebandspectraforCs. [Top]BeforeRSC.
A,B,andCrefertoheatingsidebandsforthetworadialandthe
Raman F4 (1) axialdirections. Dreferstotheaxialcarrier. E,F,andGreferto
δ
Tweezer coolingsidebandsfortheaxial,andthetworadialdirections.
Thetemperatureis9.2µK,correspondingtoa3Dmotional
Raman F3
groundstatepopulationofP =2.5%. [Bottom]AfterRSCis
Raman F4 (3) (0,0,0)
applied. SidebandthermometryindicatesP =84+3%. Solid
(0,0,0) −5
Fig. 3SchematicofRamansidebandcooling(RSC)inCs. (A) linesarefitstoindependentGaussians,andonlyserveto
Energyleveldiagramdepictingthestatesinvolved. Ω ,Rabi extractthecenterofthepeaks.
F3,F4
frequencyofRamanbeams;Γ ,opticalpumpingrate;∆,
OP
one-photondetuning;δ,two-photondetuning,difference
betweentheF3andF4laserfrequenciesminusthehyperfine
temperature of 9.2µK, corresponding to an initial average
splitting;n,initialmotionalquantumnumber. Internaland
motional quantum number n¯ =9 in the loosely confined
externalquantumstatedenotedintheform|F,mF;ν(cid:105). (B) a
axialdirection,leadstosignificantoccupation(i.e.,atleast
Physicalsetupoflaserbeams. Wecoolall3axes(2radial,1
axial)independentlybykeepingRamanF3directionconstant 1%ofthena=0population)oflevelsuptona=40. Some
whiletogglingthedirectionoftheRamanF4beams. OPrefers of these higher-lying levels could not be cooled efficiently
totheopticalpumpingbeam. by only applying RSC pulses for the duration of a ground-
√
state sideband π-pulse due to the n scaling of coupling
of adjacent motional states35. Therefore, we sweep the
|3,−3;n−1(cid:105). Subsequently, OP is pulsed on to cycle the axial pulse duration to address all levels in descending or-
atom back to |4,−4(cid:105). The OP step has a high probabil- der from na =ninit →1. To overcome decoherence, which
ity of preserving the motional state35. Thus, in one RSC reduces the transfer fidelity of each pulse, we repeat the
cycle,ν hasdecreasedbynearlyoneonaverage. Thispro- sweepwithdecreasingninit={41,31,16,11,6}.
cessrepeatsuntiltheatomreachesthedarkstate|4,−4;0(cid:105), Toverifycoolingperformance,wecompareRamanside-
thereby deterministically preparing the internal and the band spectroscopy (Fig. 4) of the single atom with and
motional quantum state of the atom. To address each without cooling. The atom population in the F =3 mani-
axis separately, we toggle the three Raman F4(i) beams foldwasdetectedbyblowingoutatomsintheF =4man-
by repeating the sequence i=3,1,2,1. The linewidth of ifoldwithlightresonantwiththecycling|4,−4(cid:105)→|5(cid:48),−5(cid:105)
the Raman transition is π-time Fourier limited due to the transition. The trap cross section is elliptical giving rise
effective Raman coupling Ω =Ω Ω /2∆=2π×33kHz to different radial trap frequencies. The sidebands fea-
R F3 F4
(2π×7kHz) for radial (axial) trap axes. OP with a rate of ture a main peak and a smaller side peak, the latter of
Γ =2π×83 kHz is applied for 85µs in between cooling which we attribute to interference between the sideband
OP
cycles. FortheentiretyofRSC,thequantizationaxisisde- and the overdriven carrier. Nevertheless, equating the
fined by a 8.6 G magnetic field along the OP propagation ratio of the heights of the main peaks of the two side-
direction. bands to n¯+1 should give the correct n¯. This was ver-
n¯
AllRamanpulsesinthisexperimentforcoolingandspec- ified by simulating sideband spectroscopy on a thermal
troscopyuseaBlackmanwindowtemporalintensityprofile atom using a master equation evolution of the density
toreduceoff-resonantexcitationofthecarrier. Thestarting matrix. By assuming a thermal distribution, we can ex-
4| 1–8
tract a temperature and a ground state probability for parameterregimedistinctfromothermethods.
each axis. For the hot atom, we measure a temperature The two-photon Raman transfer utilizes electronic tran-
of 9.2µK, corresponding to a 3D motional ground state sitions through an intermediate excited state and requires
population of P = 2.5%. After RSC, (n¯ ,n¯ ,n¯ ) = sufficiently large Franck-Condon factors (FCF) between
(0,0,0) a r1 r2
(0.14+0.04,0.03+0.03,0.01+0.04), corresponding to a ground- all relevant levels in order to realize efficient conversion
−0.03 −0.02 −0.01
state population (P ,P ,P )=(87+3,98+2,99+1). (Fig. 5). We calculate all bound states of the ground
na=0 nr1=0 nr2=0 −3 −3 −3
Hence, a 3D ground-state population of P =84+3% is a3Σ+ NaCs potential42 and the excited c3Σ+ and b3Π po-
(0,0,0) −5
reached after 100 cycles of RSC (≈100 ms total cooling tentials22,43 using the mapped Fourier method44. We in-
time). clude the tweezer confinement out to a distance of 2.5µm
The ground-state population achieved following RSC is in our calculations, but make the simplifying assumption
primarily limited due to the fact that the choice of Ω thattheatomshavethesamesphericalharmonictrapping
R
is a trade-off between overcoming decoherence mecha- frequency.∗ ThisassumptionallowstheHamiltonianoftwo
nismswhilemaintainingadequatesidebandresolution. Ef- non-interactingatomstobeseparatedintotheircenter-of-
ficient cooling requires η Ω > 2π, where in our experi- mass (CM) and relative (internuclear separation) coordi-
ment η =0.17(0.14) is tRheRLamTb2-Dicke parameter35 for nates32,R. Becausemolecularconversiondependsonlyon
R
the axial(radial) direction and T = 300µs is the coher- the relative motion of the two atoms, we can neglect the
2
ence time of the Raman transition, limited mainly by ex- CM term and add the tweezer confinement, as 12µωt2rapR2,
ternalmagneticfieldfluctuationsandthephasecoherence whereµ isthereducedmassandωtrapisthetrapfrequency,
of the Raman transition lasers. Future improvement may directlyontothemolecularpotentials.
beachievedbyincreasingtrapfrequency,andthereforethe Tight harmonic confinement gives the wavefunction ap-
upperboundonΩ . preciable amplitude inside the internuclear potential well
R
for the unbound atomic vibrational levels (the lowest one
RSC will also be applied to prepare a single Na atom in
startingatν(cid:48)(cid:48)=25),andisneededtoenhancetheFCFbe-
itsmotionalgroundstate. Asodiumatomhasahigherpho-
tweenlevelsofunboundatomstoexcitedmolecularstates.
ton recoil frequency due to its lighter mass, which means
As an example, the magnitude of the wavefunction over-
that the heating rate due to OP is increased and that the √
lap ( FCF) of the transition between ν(cid:48)(cid:48) =25 to ν(cid:48) =73
atom is initially hotter following preparation by PGC. Ini-
and to ν(cid:48) =0 of the excited molecular state as a function
tial RSC is therefore confounded by motional de-phasing
of trap frequency are shown in Fig. 5(B). Our numerical
ofthehotatomandneedstoovercometheincreasedheat- √
3/4
enhancementscaleswith FCF∝ω ,consistentwithan
ingrateduetoOP.However,thelightmassalsomeansthe trap
analyticalexpressionfoundpreviously46.
atom has a higher oscillation frequency in the trap rela-
Experimentally,wewillcoupletheinitialunboundatom
tive to Cs, giving sidebands that are more highly resolved,
pair(ν(cid:48)(cid:48)=25)totheleastboundmolecularstate(ν(cid:48)(cid:48)=24)
and the larger η allows coupling of significant higher or-
R
in the a3Σ+ potential via a two-photon Raman transition.
der sidebands. Successful RSC of Na will therefore entail
To drive this transition, the two Raman laser beams have
balancingthehigherheatingratesduetoopticalpumping
adifferencefrequencyofω ≈2π×282MHz,thebind-
withhighercoolingratesaffordedbylargesidebandsepa- bound
ing energy of the weakly bound ν(cid:48)(cid:48)=24 state. The choice
rationandhigherordersidebands.
of Raman detuning is critical to avoid excessive sponta-
4 Weakly-bound molecules
neous emission and Stark shifts while maintaining a suf-
Once both Cs and Na atoms are prepared in their mo- ficiently high two-photon Rabi rate47. We show the calcu-
tional ground state, the atoms will be merged into the lated values for these parameters in Fig. 6, together with
same tweezer. The final task in the ultracold molecular the expected operating point, where the Raman lasers are
assembler (Fig. 1) is to convert them into a molecule that tuned several 100’s of GHz below the lowest vibrational
occupies the rovibronic ground state. We plan to achieve state of the excited-state c3Σ+ potential. At this detun-
this goal via two separate coherent two-photon processes: ing, the Raman beams have a wavelength of 1037 nm, in
first, converting atoms into a weakly bound molecule; aregimeconvenientlyaccessiblebyYtterbium-dopedfiber
second, transferring the molecule from a weakly bound lasersandamplifiers.
state to the rovibronic ground state. Many methods have AlthoughtheFCFsthatconnectweakly-boundmolecular
beendemonstratedtoconvertcoldatomstoweakly-bound
molecules36–40, but a coherent method is necessary for
highfidelity conversion. Wenumerically exploremolecule ∗ThisassumptionisroughlytruebecausetheratioofNaandCspolarizabilitiesata
trappingwavelengtharoundλ=1µmtotheirmassesaresimilar45.Thiscondition
formation utilizing a two-photon Raman pulse36,38,41 in a
isnotanexperimentalrequirement.
1–8 |5
A)
. Optimum
.. 104 Prob. spont. emission
v'=73 .. c3Σ+ Δ Na(3s)+Cs(6p3/2) 103 πS−tatirmk es h[mifts m] agnitude [kHz]
.
v'=0
2
10
b3Π B) 101
10-2
0
v'=73 v"=25 10
y CF
g F −1
r 10
e v'=0 v"=25
n 10-4
E Ω Ω −2
2 1 10
−64 −63 −62 −61 −60
101 102 103 Raman beam detuning from Cs D2, ∆/(2π) [THz]
ω / 2π [kHz]
trap
. Fig. 6Probabilityofspontaneousemission(PSE),π-time
.
v''=25 . (transferduration)anddifferentialStarkshiftbetweenthestates
v''=24 Na(3s)+Cs(6s) ν(cid:48)(cid:48)=25andν(cid:48)(cid:48)=24fortheRamanbeams,asafunctionof
. ω 2ω
. bound a3Σ+ trap detuningfromtheCsD2transition(∆/(2π)). Thebeamsare
.
expectedtohaveequalintensity(10mWpower,10µmbeam
waist). Thecalculationincludesvibrationallevelsν(cid:48)(cid:48)=24and25
Internuclear distance [R]
ofthea3Σ+groundstateandacompletebasisofvibrational
Fig. 5Weakly-boundmoleculeformationscheme. (A)Energy eigenstatesderivedfromtheb3Πandc3Σ+excitedstate
leveldiagramdepictingstatesinvolved(nottoscale). Raman molecularpotentialswhichareembeddedinaharmonicwell.
transitionlasers(green)coupletheinitialstateν(cid:48)(cid:48)=25tothe Thedipolematrixelementsareassumedtobe3ea0timesthe
weaklyboundmolecularstateν(cid:48)(cid:48)=24inthea3Σ+potential. To relevantwavefunctionoverlap. MinimumPSE(1.2%)occursat
minimizespontaneousemission,wetunethelasers ∆=2π×−63.468THzwheretheπ-timeis10.7ms. Thebeams
∆=∼2π×(−63)THzbelowtheNa(3s)+Cs(6p )atomic causeatotaldifferentialStarkshiftof15kHz,necessitatinga
3/2
asymptote. (B)Magnitudeofthewavefunctionoverlapfor laserintensitystabilitybetterthan0.5%.
ν(cid:48)(cid:48)=25ina3Σ+toν(cid:48)=73(purple)andtoν(cid:48)=0(blue)inc3Σ+
vs. trapfrequency. Solidlinesshowfitscorrespondingtoa
3/4
scalingofω inbothcases.
trap
favorable FCF’s with the initial and target states, together
withalargespin-orbitcoupling,totransferbetweentriplet
and singlet molecular states. Such a transfer scheme has
statestotheharmonicoscillatorgroundstateareenhanced
beendemonstratedefficiently(≈95%)foranumberoful-
bytheharmonicconfinement,thecalculatedtransitionstill
tracold bi-alkali dimers12–15. In particular, a wise choice
requiresarelativelylongpulsedurationof11msthrough-
ofintermediatemolecularexcitedstatewouldrequireonly
outwhichtheRamanbeamsmuststaycoherent. However,
modest laser powers for the two-photon STIRAP transfer
thecoherencerequirementcaneasilybemetbygenerating
beams. The main challenge of this step lies in the tech-
the two beams from a single laser with an acousto-optic
nical aspect of maintaining coherence of two vastly differ-
modulator (AOM). Because the expected pulse duration is
ent wavelength lasers. Based on prior spectroscopy24, we
significantlylongerthantheharmonicoscillatorperiodsof
expect to use laser wavelengths around 905 nm and 635
the ODT, the Raman beams will not couple to other vibra-
tionallevels(e.g. ν(cid:48)(cid:48)=26)ofthea3Σ+potential. Weexpect nm to drive a coherent STIRAP transition from the initial
to the final state. To maintain their coherence, both lasers
thedominanttermsthatlimittransferfidelitytobesponta-
canbesimultaneouslylockedtoasinglestablehigh-finesse
neousemission(about1%),incompleteground-statecool-
reference cavity48. Thus, single molecule production after
ing,andfluctuatingStarkshifts(seeFig.6).
stochasticloadingofindividualatomsintoopticaltweezers
5 Ground-state molecules
isexpectedwithafidelityof>65%. Toverifythatasingle
Thefinalstepofsinglemoleculecreation(Fig.1)istocon- moleculehasbeenproduced,weplantoreversethecoher-
vertthemoleculefromaweakly-boundtripletgroundstate entproductionstepstoconvertthemoleculebacktoatoms.
to the rovibronic singlet ground state (or potentially any The dissociated atoms will then be separated into individ-
other desired internal quantum state). This step relies on ual tweezers and imaged using fluorescence with 98% fi-
identifying a suitable intermediate excited state that has delity.
6| 1–8
6 Conclusions 4 D.DeMille,Phys.Rev.Lett.,2002,88,067901.
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6 A. Andre, D. DeMille, J. M. Doyle, M. D. Lukin, S. E.
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Maxwell, P. Rabl, R. J. Schoelkopf and P. Zoller, Nat.
We have demonstrated the crucial first steps toward sin-
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glemoleculeproduction,whichincludestrappingthecon-
stituentatoms(CsandNa)side-by-sideinopticaltweezers 7 L.D.Carr,D.DeMille,R.V.KremsandJ.Ye,NewJour-
and motional ground-state cooling of Cs to its 3D ground nalofPhysics,2009,11,055049.
state(84%). Wenumericallyexploreatwo-photonRaman 8 K.-K. Ni, S. Ospelkaus, M. H. G. de Miranda, A. Pe’er,
schemetoconvertatompairstoaweakly-boundmolecule B. Neyenhuis, J. J. Zirbel, S. Kotochigova, P. S. Juli-
byutilizingbothanenhancedFCFduetothetrappingcon- enne,D.S.JinandJ.Ye,Science,2008,322,231–235.
finementandfar-detunedRamanbeamstominimizespon- 9 J. G. Danzl, E. Haller, M. Gustavsson, M. J. Mark,
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and technical requirements to transfer the weakly-bound Nagerl,Science,2008,321,1062–1066.
moleculetoitsrovibronicground-state. 10 F.Lang,K.Winkler,C.Strauss,R.GrimmandJ.H.Den-
Although our initial effort concentrates on producing schlag,Phys.Rev.Lett.,2008,101,133005.
onemolecule,thenumberofsinglemoleculescanbescaled 11 A.Chotia,B.Neyenhuis,S.A.Moses,B.Yan,J.P.Covey,
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astartingpoint. Moleculeswillbeassembledfrompairsof Lett.,2012,108,080405.
atomsinparallelbythesameproductiondescribedabove. 12 T.Takekoshi,L.Reichsöllner,A.Schindewolf,J.M.Hut-
Theopticaltweezerarraycanbegeneratedbyavarietyof son, C. R. Le Sueur, O. Dulieu, F. Ferlaino, R. Grimm
technical tools such as digital mirror devices or by send- andH.-C.Nägerl,Phys.Rev.Lett.,2014,113,205301.
ing a single tweezer through an acousto-optical deflector
13 P.K.Molony,P.D.Gregory,Z.Ji,B.Lu,M.P.Köppinger,
driven by multiple radio-frequency tones. In such a 1D or
C. R. Le Sueur, C. L. Blackley, J. M. Hutson and S. L.
2D tweezer array, unity atom filling can be achieved by
Cornish,Phys.Rev.Lett.,2014,113,255301.
real-time re-arrangement of tweezer locations49,50, which
14 J. W. Park, S. A. Will and M. W. Zwierlein, Phys. Rev.
providesapromisingstartingpointforalarge,flexible,2D
Lett.,2015,114,205302.
arrayofmolecules. Thisultracoldmolecularassemblerfea-
15 M. Guo, B. Zhu, B. Lu, X. Ye, F. Wang, R. Vex-
turesfastcycletime,flexiblegeometry,andindividualcon-
iau, N. Bouloufa-Maafa, G. Quéméner, O. Dulieu and
trol and imaging capabilities, and provides an attractive
D.Wang,Phys.Rev.Lett.,2016,116,205303.
platformforstudiesofultracoldchemistry,quantuminfor-
16 S. Ospelkaus, K.-K. Ni, D. Wang, M. H. G. de Miranda,
mation,andmanybodyphysics.
B. Neyenhuis, G. Quéméner, P. S. Julienne, J. L. Bohn,
Note added: after completion of our work, we became
D.S.JinandJ.Ye,Science,2010,327,853–857.
aware of a related work demonstrating RSC of a single Cs
17 B. Yan, S. A. Moses, B. Gadway, J. P. Covey, K. R. A.
atom51.
Hazzard, A. M. Rey, D. S. Jin and J. Ye, Nature, 2013,
Acknowledgments 501,521–525.
We thank Cindy Regal for inspiring discussions. K.-K. Ni 18 S. A. Moses, J. P. Covey, M. T. Miecnikowski, D. S. Jin
thanks Deborah Jin for encouragement to pursue the re- andJ.Ye,NatPhys,2017,13,13–20.
search presented here. This work is supported by the 19 B. Gadway and B. Yan, Journal of Physics B: Atomic,
NSF through the Harvard-MIT CUA, as well as the AFOSR MolecularandOpticalPhysics,2016,49,152002.
Young Investigator Program, the Arnold and Mabel Beck- 20 J.Deiglmayr,M.Aymar,R.Wester,M.Weidemüllerand
manFoundation,andtheAlfredP.SloanFoundation. O. Dulieu, The Journal of Chemical Physics, 2008, 129,
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