Efficient state transfer in an ultracold dense gas of heteronuclear molecules

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1 Efficient stte trnsfer in n ultrcold dense gs of heteronucler molecules S. OSPELKAUS, A. PE ER, K.-K. NI, J. J. ZIRBEL, B. NEYENHUIS, S. KOTOCHIGOVA, P. S. JULIENNE 3, J. YE * AND D. S. JIN * JILA, Ntionl Institute of Stndrds nd Technology nd University of Colordo, Deprtment of Physics, University of Colordo, Boulder, Colordo 39-, USA Physics Deprtment, Temple University, Phildelphi, Pennsylvni 9-6, USA 3 Joint Quntum Institute, Ntionl Institute of Stndrds nd Technology nd University of Mrylnd, Githersurg, Mrylnd 99-3, USA *e-mil: junye@jilu.colordo.edu; jin@jilu.colordo.edu Pulished online: June ; doi:.3/nphys997 Polr molecules hve right prospects for novel quntum gses with long-rnge nd nisotropic interctions, nd could find uses in quntum informtion science nd in precision mesurements 3 5. However, high-density clouds of ultrcold polr molecules hve so fr not een produced. Here, we report key step towrds this gol. We strt from n ultrcold dense gs of loosely ound K 7 R Feshch molecules 6,7 with typicl inding energies of few hundred kilohertz, nd coherently trnsfer these molecules in single trnsfer step into virtionl level of the ground-stte moleculr potentil ound y more thn GHz. Strting with single initil stte prepred with Feshch ssocition, we chieve trnsfer efficiency of %. Given fvourle Frnck Condon fctors 9,, the presented technique cn e extended to ccess much more deeply ound virtionl levels nd those exhiiting significnt dipole moment. Strtegies for the reliztion of n ultrcold dense gs of polr molecules hve generlly followed two different pproches. The first is to directly cool ground-stte polr molecules y mens of uffer gs cooling, Strk decelertion,3 or velocity filtering. However, direct cooling strtegies hve typiclly een restricted to the millikelvin temperture rnge. Photossocition schemes 5, on the other hnd, hve the dvntge of using high-density ultrcold tomic clouds s promising strting point. The comintion of photossocition nd pump dump schemes hs recently resulted in the formtion of ground-stte polr molecules 9. However, the reliztion of n ultrcold dense gs of polr molecules hs so fr not een reported. Photossocition schemes rely on spontneous emission to populte ound moleculr levels in the ground-stte moleculr potentil 9,6. The spontneous processes result in lrge spred of popultion mong severl continuum nd ound moleculr sttes. Two-colour photossocition schemes suffer from the smll wvefunction overlp etween the continuum sttes of colliding toms nd the loclized moleculr sttes, resulting in the necessity of lrge opticl power, which then opens up other loss chnnels 7,. This wvefunction overlp cn e significntly enhnced y strting from wekly ound molecule s compred with the continuum stte of two colliding toms. Wekly ound molecules in well-defined ner-dissocition quntum sttes cn e efficiently creted using mgnetic-field-tunle Feshch resonnces in ultrcold tomic gses. The resulting ensemles of Feshch molecules constitute n excellent lunching stge for the ppliction of coherent opticl trnsfer schemes to produce molecules in deeply ound virtionl levels. The comintion of heteronucler Feshch molecule cretion 6,7,9, with coherent de-excittion schemes might therefore result in the cretion of n ultrcold dense gs of polr molecules. In the homonucler R system, Feshch molecules hve een used s strting point for coherent two-photon trnsfer into stte ound y h 5 MHz (ref. ). In ddition, rdiofrequency mnipultion schemes hve een used in the R system, chieving inding energies of >h 3 GHz (ref. 3). These results represent powerful demonstrtion of the degree of control ville in ultrcold gses. Here, we report on coherent trnsfer of heteronucler Feshch molecules into more deeply ound virtionl level of the ground-stte moleculr potentil (see Tle ). We thus demonstrte key step towrds the reliztion of quntum degenerte ultrcold gs of polr molecules. Using two phse-coherent lser fields to couple the initil Feshch stte i nd the trget stte t to common electroniclly excited stte e (Fig. ), stimulted Rmn ditic pssge (STIRAP) is used to coherently trnsfer the popultion of i to t. Through this trnsfer process, we produce dense ultrcold cloud of heteronucler molecules with inding energy of >h GHz. An essentil prerequisite for the successful demonstrtion of STIRAP in this system hs een creful one-photon spectroscopic investigtion of the so-fr unknown K 7 R excited-stte moleculr potentil elow the S / + 5P / threshold nd precise two-photon spectroscopy of more deeply ound virtionl levels in the ground-stte moleculr potentil of K 7 R. Strting from ner-quntum-degenerte Bose Fermi mixture of 7 R nd K toms confined in single-em opticl dipole trp, we use mgnetic-field rmps cross Feshch resonnce t 56.7 G to crete heteronucler Feshch molecules with density of 5 cm 3 (see the Methods section). At mgnetic field of B = 55. G, the Feshch molecules hve inding energy of h (7 ± 5) khz nd cn e directly, nd selectively, imged y high-field resonnt sorption imging (see the Methods section). The Feshch molecules re in superposition of the open chnnel K F = 9/,m F = 9/ +R F =,m F = nd the diticlly connecting closed chnnel K 7/, 7/ +R, (refs 6,7). Here, F denotes the totl tomic spin nd m F is the spin projection long the mgnetic-field direction. 6 nture physics VOL AUGUST Mcmilln Pulishers Limited. All rights reserved.

2 Δ e S / +5 P / i e Ω Ω δ i λ 795 nm S / +5 S / E /h (GHz) 6 i t t t B (G) c 3 τ = ( 3.9 ±.7 ) 3 ms d 6 7 R K N mol ( ) N mol = ( 6 ± ) 7 s t =...6 N tom ( ) τ = (.9 ±.7 ) ms N tom = ( 3.6 ±. ) 7 s t = 6 Figure Schemtic digrm of the STIRAP scheme., Schemtic digrm of moleculr potentils nd moleculr virtionl levels involved in the coherent two-photon trnsfer scheme. The phse-coherent lsers nd couple the initil stte i nd the trget stte t to the intermedite stte e in the excited-stte moleculr potentil connecting to the S / +5P / threshold. Ω nd Ω denote the corresponding Ri frequencies. δ nd re the two-photon nd single-photon detuning, respectively. x represents the decy rte of stte x., Clculted moleculr energy structure of the K 7 R molecule in the ground-stte moleculr potentil elow the K 9/, 9/ R, tomic threshold. All levels hve totl spin-projection quntum numer M F = 7/. The initil Feshch stte i nd the trget stte t re highlighted y the red old lines. The sttes oserved in drk-resonnce spectroscopy (see the text) re plotted with dshed lue lines. c,d, Comprison of single-photon excittion rtes for the i e trnsition, strting from Feshch molecules (c) s compred with photossocition rtes from free toms (d). The excittion rtes re determined y mesuring loss of popultion in stte i from the trp in ech cse. For this set of dt, e is level in the () v = 9 hyperfine mnifold. In d, the R (K) tom numer is plotted with the red filled (open lue) circles. The red solid nd lue dshed lines re simultneous fits to the decying R nd K tom numers. We ssume tht the loss rte (Ṅ tom) is the sme for oth components t ny time. These dt demonstrte tht the strength of the i e trnsition (the first leg of the STIRAP process) is mrkedly enhnced y strting from Feshch molecules. With n initil molecule density of n molecules 5 cm 3 nd initil tomic densities of n toms 3 cm 3, we oserve n enhncement in the initil loss rte of Ṅ molecules /Ṅ toms = (±6) t mgnetic field close to the Feshch resonnce (B = 56. G) (refs,9). The Feshch molecules re mnipulted with light derived from phse-coherent Rmn lser system. A Ti:spphire lser is offset-locked to temperture-stilized Fry Perot cvity, resulting in linewidth of < khz nd solute long-term frequency stility etter thn MHz. The second lser em is derived from n externl cvity diode lser phse-locked to the Ti:spphire lser. The two ems re π-polrized with respect to the mgnetic field nd propgte collinerly when irrdited onto the moleculr ensemle. In the first step, we crry out one-photon, ound ound spectroscopy of the electroniclly excited K 7 R () nd ( +/ ) moleculr potentils for energies within h GHz elow the S / + 5P / threshold. Strting from the Feshch molecules t B = 55. G, lser is used to couple the molecules to virtionl levels in the excited-stte moleculr potentils. These electroniclly excited molecules susequently decy into multitude of moleculr nd tomic sttes where they re invisile to our detection method. Using loss spectr, we identify virtionl series of different excited-stte moleculr potentils, which will e reported elsewhere. After n extensive serch, we hve chosen the ( + ) v = stte s n intermedite coupling stte e. Here, v denotes the virtionl quntum numer s counted from the S / + 5P / threshold. This stte is locted 3 GHz elow the S / +5P / threshold. Compring one-photon loss rtes nture physics VOL AUGUST 63 Mcmilln Pulishers Limited. All rights reserved.

3 Frction Frction.. I /I mx I /I mx τ I /I mx p δ (MHz) δ (MHz) Frction.6.. Figure Drk resonnce in the moleculr system. In this cse, the trget stte t is the K 7/, 7/ +R, v = 3 stte nd the intermedite stte e is stte in the () v = hyperfine mnifold. We shine µs squre pulse of Rmn light onto the Feshch molecules nd the remining frction of Feshch molecules is detected. For δ =, the loss of Feshch molecules is strongly suppressed owing to the emergence of drk stte. For this prticulr set of dt, π. MHz. The inset shows the centrl drk-resonnce feture. strting from Feshch molecules with photossocition rtes of free toms, we oserve n enhncement in the excittion rte y (±6) (Fig. c,d). An essentil prerequisite for STIRAP is precise knowledge of possile trget sttes. Wheres theoreticl model of the electronic ground-stte potentil hs recently een pulished y Pshov et l. 5, the ground-stte level structure of K 7 R in the ner-threshold regime hs never een proed experimentlly. Using two-photon drk-resonnce spectroscopy 6, we proe the inding energy of virtionl levels in the K 9/, 9/ + R, nd K 7/, 7/ + R, chnnels t B = 55. G. We proe levels with inding energies less thn h.5 GHz, which is ccessile to our phse-locked lser system. Figure shows typicl drk-resonnce spectrum when scnning the frequency difference (δ) of the two phse-coherent lser fields in the vicinity of the frequency splitting etween the two moleculr ground-stte levels. The presence of the ner-resonnt lser dresses the trnsition t e (Fig. ), leding to destructive interference for the sorption proility of lser on the proe trnsition i e for δ =. We oserve one-photon loss of Feshch molecules with width of 6 MHz nd nrrow drk-resonnce feture in the vicinity of δ =. At B = (55. ±.5) G, we mesure inding energy of h 3.5() GHz nd h.93(5) GHz for the K 9/, 9/ + R, v = nd 3 sttes, respectively. For K 7/, 7/ + R, v = 3, we find h 7.35(5) GHz. The mesured inding energies devite y less thn.% from the theoreticl prediction sed on the potentils y Pshov et l. 5. With possile trget sttes nd coupling sttes precisely determined, we use STIRAP to trnsfer the molecules coherently into the.93 GHz ound virtionl level of the groundstte moleculr potentil. STIRAP is known to e roust coherent trnsfer scheme in three-level system. When two-photon resonnce (δ = ) is mintined, the molecules re trnsferred etween i nd t with negligile popultion in the lossy excited stte e throughout the process. Figure 3 shows the counterintuitive STIRAP pulse sequence used in the experiment. In the first step, lser is turned on, coupling the trget stte t to the intermedite stte e. While the intensity of lser is rmped down from I mx to within τ p = µs, the intensity of lser is rmped up to its mximum vlue I mx, therey diticlly trnsferring the 3 3 t pulse ( µs ) Figure 3 Time evolution of the coherent two-photon trnsfer., Counterintuitive STIRAP pulse sequence., Mesured popultion (lck circles) in the initil Feshch stte i during the STIRAP pulse sequence. To mesure the popultion in the Feshch stte i t vrious times t pulse, the phse coherent light fields nd re switched off simultneously nd the Feshch molecules re susequently imged y resonnt sorption imging (see the Methods section). Strting with popultion of in i, the Feshch molecules re coherently trnsferred to the trget stte t y the first pulse sequence (t = τ p to t = ). In the deeply ound trget stte, the molecules re invisile to the detection light. Reversing the pulse sequence, the molecules re trnsferred ck to the initil stte i (t = to t = τ p ). The solid line is fit to the experimentl dt on the sis of eqution (). With e = π 5.7 MHz nd i = π 97 Hz, we otin Ω mx /Ω mx =.7 nd t = π 3 khz. Note tht the thus-determined lifetime of the trget stte of τ t = /(π t ) 33 µs is shorter thn the mesured lifetime of 5 µs (Fig. 5) in the sence of light fields. The extr loss is presumly due to residul popultion of the lossy excited stte during the STIRAP process. The dshed line is the corresponding clculted popultion of the trget-stte popultion during the process. popultion from the Feshch stte into the deeply ound trget stte t. Reversing the pulse sequence reverses the process nd the trnsfer occurs from the deeply ound level t to the initil stte i, s shown for t pulse > in Fig. 3. Figure 3 shows the time dependence of the mesured popultion of the initil Feshch stte i during the pulse sequence. Molecules in the Feshch stte cn e detected y direct high-field resonnt sorption imging, wheres moleculr popultion in the trget stte is invisile to the light. During the pulse sequence, we oserve the hiding of the molecules in the more deeply ound virtionl level nd the trnsfer ck into the initil stte fter reversl of the pulse sequence. We oserve n efficiency of the doule STIRAP sequence of 7%, corresponding to n efficiency of % for single pulse. The trnsfer process cn e descried y n open three-level system in the rotting-wve pproximtion: ( ) ( ) Ψ i (t) δ ii / Ω (t)/ i Ψ e (t) = Ω (t)/ i e / Ω (t)/ Ψ t (t) Ω (t)/ i t / ) ( Ψi (t) Ψ e (t) Ψ t (t). () Here, Ψ x (t) Ψ x (t) nd x re the popultion nd decy rte of stte x, respectively (Fig. ). The time dependence of the 6 nture physics VOL AUGUST Mcmilln Pulishers Limited. All rights reserved.

4 . Doule STIRAP.6 Single STIRAP.6. Frction in i. Frction in i.. δ (khz) δ (khz) Figure STIRAP line shpe., STIRAP line shpe for = π 5 MHz, Ω = π 3.6 MHz nd Ω /Ω =.7 oth for single STIRAP (trnsfer from i to t ) nd doule STIRAP (trnsfer from i to t nd ck). The symmetry in the line shpe is due to the finite single-photon detuning (see Fig. )., Difference etween the doule nd single STIRAP signl s plotted in. The difference corresponds to the frction of Feshch molecules trnsferred into the deeply ound stte nd ck t given δ. Tle Bsic properties of KR molecules in different virtionl levels of the ground-stte moleculr potentil. Comprison of the inding energy, internucler distnce ( size ) nd dipole moment of the Feshch molecules, the current trget stte K 9/, 9/ +R, v = 3 nd the solute ground stte X + (v = 99) in the singlet potentil 3. The current trget stte hs 9.5% triplet chrcter nd is therefore denoted y 3 + (v = 3). v is the virtionl quntum numer s counted from the threshold, with the lest ound level lelled s v =. Moleculr property Feshch molecule 3 + (v = 3) X + (v = 99) Binding energy (GHz) , Internucler distnce ( ) Dipole moment (e ). 5.3 trnsfer is determined y the exct pulse shpe nd the rtio of the mximum Ri frequencies Ω mx nd Ω mx. Given the pulse shpe shown in Fig., we cn extrct the Ri frequency rtio used in the experiment. Given I mx /I mx =.7, we otin Ω mx /Ω mx = (.7 ±.), corresponding to rtio of the effective trnsition dipole moments of (3.3 ±.3). The solute coupling strengths cn e extrcted from n nlysis of the STIRAP efficiency s function of the twophoton detuning δ, s shown in Fig.. We hve mesured the line shpe oth for single STIRAP process ( i t ) nd for doule STIRAP ( i t i ). A comprison etween simultion sed on eqution () with Ω /Ω =.7 ±. nd = π (5 ± 5) MHz nd the experimentl single STIRAP line-shpe dt yields Ω mx = π (3.6 ±.5) MHz nd Ω mx = π (6. ±.9) MHz t I mx = (3.7 ±.5) W cm nd I mx (. ±.) W cm. This trnsltes into effective trnsition dipole moments of d eff = (.5 ±.5) e nd d eff = (.7±.) e. Finlly, we hve mesured the lifetime of the deeply ound molecules in the trget stte. Strting from the molecules in stte i, we pply single STIRAP pulse to trnsfer the molecules into the trget stte t. The deeply ound molecules re held in the opticl dipole trp for vrying times t hold. A second STIRAP pulse Molecule numer ( 3 ) 6 Molecule numer ( 3 ) τ t = 5 () µs τ i =.3 (3) ms t hold (ms) Figure 5 Lifetime of the v = 3 molecules. We oserve lifetime of 5 µs. The inset shows the decy of the initil Feshch molecules, which hve lifetime of.3 ms. then trnsfers the molecules ck to the initil stte, where they cn e detected y high-field resonnt sorption imging. Figure 5 shows the decy of the deeply ound molecules. We oserve lifetime of the molecules in t of (5±) µs s compred with lifetime of the initil stte of (.3±.3) ms. We oserve tht the lifetime of oth Feshch molecules nd deeply ound molecules decreses with incresing tom density. This suggests tht tom molecule collisions limit the molecule lifetime. In summry, we hve demonstrted coherent opticl trnsfer of heteronucler Feshch molecules into GHz ound virtionl level of the ground-stte moleculr potentil. Our experiments show tht the inding energy of the molecules cn e significntly enhnced in single STIRAP step. Given promising Frnck Condon fctors through numer of intermedite sttes 9,, the presented techniques cn e extended to inding energies h GHz y referencing oth lsers to frequency com ridging lmost ritrry frequency gps 7. The production of polr moleculr quntum gs y mens of coherent opticl trnsfer of heteronucler Feshch molecules might hence come within experimentl rech. nture physics VOL AUGUST 65 Mcmilln Pulishers Limited. All rights reserved.

5 METHODS FESHBACH MOLECULE FORMATION After evportion of K nd 7 R in n Ioffe Pritchrd mgnetic trp, R nd 6 K toms re loded into single-em opticl dipole trp operting t,6 nm. At this stge, the temperture of the toms is out 3 µk. In the opticl trp, rdiofrequency ditic rpid pssge is used to prepre K 9/, 9/ nd 7 R, spin mixture. It is in this comintion of Zeemn sttes tht the Feshch resonnce t mgnetic field of 56.7 G occurs etween K nd R. After rmping the mgnetic field to 555 G, we further evporte the mixture in the opticl dipole trp to temperture of T/T c. Here, T c is the criticl temperture for the onset of Bose Einstein condenstion of the R cloud. Strting from the ner-degenerte mixture of 5 K toms nd R toms, we finlly use mgnetic-field rmp cross the 56.7 G Feshch resonnce to couple the open scttering chnnel to the ound moleculr stte, therey ssociting out heteronucler Feshch molecules. The molecules hve temperture of 3 nk nd density of 5 cm 3. To suppress inelstic collisions of the molecules with remining unound toms, we remove out 95% of the left-over toms. DIRECT RESONANT ABSORPTION IMAGING OF HETERONUCLEAR FESHBACH MOLECULES The wekly ound heteronucler Feshch molecules (inding energy of 7 khz) re detected y direct sorption imging. The imging uses light resonnt with cycling trnsition strting from the K 9/, 9/ stte. For smll inding energies of the heteronucler molecules, the tomic cycling trnsition of K is detuned y only few meghertz from the moleculr trnsition. Light resonnt with the tomic trnsition will therefore dissocite the molecules nd then sctter on the resulting K toms. To distinguish the sorption signl of wekly ound Feshch molecules from unound K toms, we flip the spin of residul K 9/, 9/ toms with rdiofrequency π-pulse on the tomic 9/, 9/ 9/, 7/ trnsition efore imging. Note tht direct imging of molecules t high mgnetic field is fvourle for heteronucler Feshch molecules. In the heteronucler cse, oth the ground nd the excited electronic potentils shre /R 6 dependence. The difference in energy etween these two sttes therefore vries more slowly with the internucler seprtion thn in the homonucler cse, where the excited-stte long-rnge potentil vries s /R 3. Received Ferury ; ccepted My ; pulished June. References. Sntos, L., Shlypnikov, G. V., Zoller, P. & Lewenstein, M. Bose Einstein condenstion in trpped dipolr gses. Phys. Rev. Lett. 5, ().. DeMille, D. Quntum computtion with trpped polr molecules. Phys. Rev. Lett., 679 (). 3. Sndrs, P. G. H. Mesurility of the proton electric dipole moment. Phys. Rev. Lett. 9, (967).. Kozlov, M. G. & Lzowsky, L. N. Prity violtion effects in ditomics. J. Phys. B, (995). 5. Hudson, E. R., Lewndowski, H. J., Swyer, B. C. & Ye, J. Cold molecule spectroscopy for constrining the evolution of the fine structure constnt. Phys. Rev. Lett. 96, 3 (6). 6. Zirel, J. J. et l. Collisionl stility of fermionic Feshch molecules. Phys. Rev. Lett., 3 (). 7. Zirel, J. J. et l. Heteronucler molecules in n opticl dipole trp. Preprint t < (7).. Kohler, T., Gorl, K. & Julienne, P. S. Production of cold molecules vi mgneticlly tunle Feshch resonnces. Rev. Mod. Phys. 7, 3 (6). 9. Sge, J. M., Sinis, S., Bergemn, T. & DeMille, D. Opticl production of ultrcold polr molecules. Phys. Rev. Lett. 9, 3 (5).. Stwlley, W. C. Efficient conversion of ultrcold Feshch-resonnce-relted polr molecules into ground stte (X + v =,J = ) molecules. Eur. Phys. J. D 3, 5 ().. Weinstein, J. D., decrvlho, R., Guillet, T., Friedrich, B. & Doyle, J. M. Mgnetic trpping of clcium monohydride molecules t millikelvin tempertures. Nture 395, 5 (99).. Bethlem, H. L., Berden, G. & Meijer, G. Decelerting neutrl dipolr molecules. Phys. Rev. Lett. 3, (999). 3. Swyer, B. C. et l. Mgnetoelectrosttic trpping of ground stte OH molecules. Phys. Rev. Lett. 9, 53 (7).. Rngwl, S. A., Junglen, T., Rieger, T., Pinkse, P. W. & Rempe, G. Continuous source of trnsltionlly cold dipolr molecules. Phys. Rev. A 67, 36 (3). 5. Jones, K. M., Tiesing, E., Lett, P. D. & Julienne, P. S. Ultrcold photossocition spectroscopy: Long-rnge molecules nd tomic scttering. Rev. Mod. Phys. 7, (6). 6. Wng, D. et l. Photossocitive production nd trpping of ultrcold KR molecules. Phys. Rev. Lett. 93, 35 (). 7. Wynr, R., Freelnd, R. S., Hn, D. J., Ryu, C. & Heinzen, D. J. Molecules in Bose Einstein condenste. Science 7, 6 9 ().. Thlhmmer, G., Theis, M., Winkler, K., Grimm, R. & Hecker Denschlg, J. Inducing n opticl Feshch resonnce vi stimulted Rmn coupling. Phys. Rev. A 7, 333 (5). 9. Ospelkus, C. et l. Ultrcold heteronucler molecules in 3D opticl lttice. Phys. Rev. Lett. 97, (6).. Ppp, S. B. & Wiemn, C. E. Oservtion of heteronucler Feshch molecules from 5 R 7 R gs. Phys. Rev. Lett. 97, (6).. Pe er, A., Shpiro, E. A., Stowe, M. C., Shpiro, M. & Ye, J. Precise control of moleculr dynmics with femtosecond frequency com. Phys. Rev. Lett. 9, 3 (7).. Winkler, K. et l. Coherent opticl trnsfer of Feshch molecules to lower virtionl stte. Phys. Rev. Lett. 9, 3 (7). 3. Lng, F. et l. Cruising through moleculr ound-stte mnifolds with rdiofrequency. Nture Phys., 3 6 ().. Bergmnn, K., Theuer, H. & Shore, B. W. Coherent popultion trnsfer mong quntum sttes of toms nd molecules. Rev. Mod. Phys. 7, 3 5 (99). 5. Pshov, A. et l. Coupling of the X + nd 3 + sttes of KR. Phys. Rev. A 76, 5 (7). 6. Arimondo, E. & Orriols, G. Nonsoring tomic coherences y coherent two-photon trnsitions in three-level opticl pumping. Lett. Nuovo Cimento 7, (976). 7. Cundiff, S. T. & Ye, J. Colloquium: Femtosecond opticl frequency coms. Rev. Mod. Phys. 75, 35 3 (3).. Courteille, Ph., Freelnd, R. S., Heinzen, D. J., vn Aeelen, F. A. & Verhr, B. J. Oservtion of Feshch resonnce in cold tom scttering. Phys. Rev. Lett., 69 7 (99). 9. Lurthe Tolr, B. et l. Controlling the formtion of cold molecules vi Feshch resonnce. Europhys. Lett. 6, 7 77 (3). 3. Kotochigov, S., Julienne, P. S. & Tiesing, E. A initio clcultion of the KR dipole moments. Phys. Rev. A 6, 5 (3). Acknowledgements We cknowledge finncil support from NIST, NSF nd DOE. K.-K.N. nd B.N. cknowledge support from the NSF, S.O. from the Alexnder-von-Humoldt Foundtion nd P.S.J. from the ONR. We thnk D. Wng for stimulting discussions nd C. Ospelkus for criticl reding of the mnuscript. Author informtion Reprints nd permission informtion is ville online t Correspondence nd requests for mterils should e ddressed to J.Y. or D.S.J. 66 nture physics VOL AUGUST Mcmilln Pulishers Limited. All rights reserved.