Laser radiation pressure slowing of a molecular beam
aa r X i v : . [ phy s i c s . a t o m - ph ] N ov Laser radiation pressure slowing of a molecular beam
J.F. Barry*, E.S. Shuman, E.B. Norrgard, and D. DeMille
Department of Physics, Yale University, P.O. Box 208120, New Haven, CT 06520, USA (Dated: November 13, 2018)
PACS numbers: 37.10.Pq, 37.10.Mn, 37.10.Vz
There is substantial interest in producing sam-ples of ultracold molecules for possible applica-tions in quantum computation [1, 2], quantumsimulation of condensed matter systems [3, 4],precision measurements [5, 6], controlled chem-istry [7, 8], and high precision spectroscopy [9].A crucial step to obtaining large samples of ultra-cold, trapped molecules is developing a means tobridge the gap between typical molecular sourcevelocities ( ∼ − ms ) and velocities for whichtrap loading or confinement is possible ( . − ms ).Here we show deceleration of a beam of neutralstrontium monofluoride (SrF) molecules using ra-diative force. Under certain conditions, the decel-eration results in a substantial flux of moleculeswith velocities . ms . The observed slowing,from ∼ ms , corresponds to scattering & pho-tons. We also observe longitudinal velocity com-pression under different conditions. Combinedwith molecular laser cooling techniques [10–12],this lays the groundwork to create slow and coldmolecular beams suitable for trap loading. Tremendous advances have been made in the decelera-tion of molecular beams in the past decade. Stark decel-eration [13], Zeeman deceleration [14], and collisional de-celeration [15] have all been demonstrated to slow molec-ular beams. However, only for fairly light species ( ∼ N=1-N=1-N=1- X Σ + X Σ D Σ + D Σ v AD v p v=0 v=1 v=2J=1/2+v=0 v v s v s v v v
00 p v v s N=0+ N=3- N=3,J=5/2- J=1/2+v=0 v=1v=0 f = . f + < . f = . f = x - f + < - f = . N=1- N=2+ v=3
J=3/2+ f = . f = . N=4+ A Π FIG. 1:
Relevant energy levels and transitions in SrF.
Solid red lines denote slowing lasers, while solid green linesdenote probe lasers. Dashed lines denote spontaneous de-cay channels, and FCFs ( f v ′ v ) are labeled if applicable. Bluedashed lines indicate decay fluorescence channels used to de-termine the beam Doppler profile. of species, including some for which current phase-space-conserving slowing methods appear ill-suited; this is use-ful for addressing the needs of the variety of applicationsenvisioned for ultracold molecules [20].Here we experimentally demonstrate deceleration ofa molecular beam using radiation pressure. This workbuilds upon similar results demonstrating deflection [11]and transverse cooling [12] of a molecular beam by radia-tive force. The crucial enabling feature for radiative slow-ing is the ability to scatter & photons without heat-ing the internal degrees of freedom of the molecules. Ourscheme for creating this quasi-cycling transition [11, 12] isrecounted briefly here and depicted in Fig. 1. We employthe X Σ +1 / ( v =0 , N =1) → A Π / ( v ′ =0 , J ′ =1 /
2) electronictransition of SrF, with τ = 24 ns lifetime, for cycling and
660 mm 690 mm P M T P M T v Dichroicv v v AD PBSDichroic v Dichroicv FIG. 2:
Schematic of the apparatus.
Red (green) linesindicate slowing (probe) laser beams. slowing. We denote by v s the main cycling and slowinglaser, with wavelength λ s and detuning from resonance∆ v s . The favorable Franck-Condon factors (FCFs) ofSrF limit vibrational branching [21]. Separate repumplasers, denoted v s and v s , address residual vibrationalleakage. Driving an N =1 → J ′ =1 / & photon scattering cy-cles before the bright state population is reduced by 1 /e [11, 12].We use the Doppler shift of laser-induced fluorescence(LIF) to measure the longitudinal velocity profile (LVP)of the molecular beam, as shown in Fig. 2. Our detectionscheme employs two perpendicular probe lasers, denoted v p and v p , to excite molecules from the X( v =0 , N =1)states (with resolved spin-rotation structure (SRS) andhyperfine structure (HFS)) to the A( v =0 , J = ) state (un-resolved HFS) at a distance L d =1350 mm downstreamfrom the source. A longitudinal probe laser, denoted v pAD , then excites the molecules to the D( v =0 , N =3 , J = )state (unresolved HFS). Monitoring the D → X LIF as afunction of the v pAD laser frequency yields a Doppler-shifted LVP free of SRS/HFS, at a wavelength easily fil-tered from all laser light.The v s , v s , v s , and v pAD lasers are spatially over-lapped counterpropagating to the molecular beam. Toaddress all SRS/HFS levels over a wide velocity range,the v s , v s , and v s lasers have radio-frequency (rf) side-bands with modulation index m = 3 . < f mod <
44 MHz, unless noted oth-erwise. Due to the large frequency extent of the side-bands, we do not expect longitudinal velocity compres-sion [23]. We note that the dark magnetic sublevels ofthe X( N = 1) state prevent use of a Zeeman slower. Theslowing lasers are not chirped [24] due to the temporalextent of the molecular beam pulse ( ∼
10 ms). Magneticfield coils create an approximately uniform field B =9 Gat an angle θ B = 45 ◦ relative to the v s linear polarizationover the length 120 mm . L . L s = 660 mm allows monitoringof the LIF from spontaneously emitted photons duringcycling. SimulationData d L I F a t L ( a r b . un i t s ) a) b) -100-180-260-340-420 Velocity (m/s)
Velocity (m/s)
FIG. 3:
Measured and simulated slowing for differentdetunings of the main slowing laser. a) Measured slowedLVP (solid color), control LVP ( – ), and velocities correspond-ing to the v s rf sideband spectrum (gray, with center N ).The panels are scaled so that all controls have equal heights.b) Simulated slowed LVP (solid color), simulated control LVP( – ), and simulated slowed LVP with transverse cooling the en-tire length of the slowing (dotted color, scaled by 1/21). Thegray shaded area indicates the assumed force versus velocityprofile used in the simulation. The ∆ v s detuning (in MHz)is shown in the centered box for each panel set. The scalingof the simulated LVP with transverse cooling is chosen to ac-curately illustrate how the increased divergence of the slowestmolecules impacts the apparent loss in our slowed LVP data.In particular, the factor 21 is the ratio of the peaks of thesimulated control LVPs with and without transverse cooling.This scaling hence factors out the simple gain in downstreamflux due to transverse cooling; the different shapes of simu-lated slowed LVPs with and without transverse cooling showclearly the increased apparent loss of slow molecules in ourexperimental data, merely due to their increased divergence(since transverse cooling is not applied in these experiments)(Supplementary Discussion 1). Application of the slowing lasers shifts the molecularbeam LVP, as shown in Fig. 3a for various ∆ v s . As∆ v s is tuned towards h v f i /λ s from the red (where h v f i is the mean forward velocity), the LVP is shifted to lowervelocities, until ∆ v s ≈h v f i /λ s ; then, when tuned furtherto the blue, the LVP gradually returns to its unperturbedstate. However, the shift to lower velocities is accompa-nied by an increase in apparent molecule loss, which ismost severe when ∆ v s ≈h v f i /λ s .We argue that this apparent loss is due primarily to in-creased divergence and transverse heating as the beam isslowed. Several other loss mechanisms were ruled outas the dominant cause after investigation. Increasingthe background gas pressure (primarily helium) by 5 × changed the slowed LVPs little, indicating that back-ground gas collisions are not a dominant loss mechanism.We investigated possible loss to other rovibrational stateswhich could arise from various mechanisms. For exam-ple, off-resonant excitation to the A( v = 0 , J = ) stateby the v s laser or HFS mixing in the A( v = 0 , J = )state could transfer population to the dark X( v =0 , N =3)state; stray electric fields could lead to decays from theA( v =0 , J = ) state to the dark X( v =0; N =0 ,
2) states; orthe v pAD laser could off-resonantly excite molecules fromthe A( v =0 , J = ) state to the D( v =0 , N =1) state beforethey reach L d . To investigate such mechanisms, we ex-plicitly probed the populations of the X( v =0; N =0 , , v = 1 , N = 0) states and determined that < v =3 , N =1) state was not directly measured,but was estimated from the observed increase in sponta-neous scattering LIF at L s by adding the v s repumplaser; this indicated that molecules cycled through theX( v =2 , N =1) state ∼ × before reaching L d . Togetherwith the estimated FCFs [11], this yields an estimated ∼
6% loss to the X( v =3 , N =1) state. Overall, our inabil-ity to find evidence of population of dark states, togetherwith the observed LVP shift of ∼
50 m/s, is preliminaryevidence that our quasi-cycling transition is nearly closedfor up to ∼ scattered photons. Additional observa-tions provide more quantitative evidence that corrobo-rates this conclusion (Supplementary Discussion 2).Apparent loss from increased divergence and trans-verse heating was modeled via a Monte Carlo simula-tion (details in Methods section). Typical simulationresults, shown in Fig. 3b, indicate that nearly all ap-parent molecule loss can be attributed to increased di-vergence and transverse heating. According to the sim-ulation, the addition of transverse cooling to counter-act divergence losses can vastly increase the flux of slowmolecules. Other observations (e.g., dependence of theslowed LVP on laser power for various detunings) cor-roborate the basic picture that the observed slowed LVPis highly distorted by loss of slow molecules (Supplemen-tary Discussion 3). Dependence of the slowing on variouscontrol parameters was generally weak over small ranges Velocity (m/s) d -320 -300 L I F a t L ( a r b . un i t s ) Velocity (m/s)
FIG. 4:
Slowing with no applied magnetic field.
The∆ v s detuning (in MHz) is shown in the upper right. Oth-erwise the representation is the same as in Fig. 3. Note thesharp features, in particular the increase in peak height orslope of the LVPs; these indicate longitudinal velocity com-pression within part of the distribution. This should be con-trasted with the smooth LVPs obtained at large B (Fig. 3).Here the v s modulation index is m =2 . around their nominal values (Supplementary Discussion4).Most data was taken with B ≈ − θ B = 45 ◦ .Over this range, the slowed LVPs and LIF at L s werefairly insensitive to the value of B . However, we ob-served that Earth’s magnetic field, B E , on its own al-lows some remixing of the dark Zeeman sublevels. Undercertain conditions when B = B E (Supplementary Dis-cussion 5), qualitatively different behavior was observed;namely, sharp features appeared in the LVP, as shown inFig. 4. Moreover, under these conditions there is clearevidence for longitudinal velocity compression: the peakand slope of the LVP increases under these conditions forcertain detunings ∆ v s . We have been unable to find asimple explanation for these features, and full modelingof the system (including all ∼
33 slowing laser frequencies,44 molecular sublevels, B -field remixing, coherent darkstates [22], etc.) is beyond the scope of this paper. How-ever, this behavior could potentially be used to compressthe molecular beam LVP. Ideally this would be done afterslowing had already removed most of the kinetic energyfrom the beam, e.g., by using an initial region of large B for broadband slowing, followed by a second region ofsmall B for longitudinal velocity compression and furtherslowing. A slow and nearly monoenergetic beam wouldbe ideal for trap loading.In summary, we have demonstrated efficient radiationpressure slowing of an SrF molecular beam. Under cer-tain conditions, we detect ∼
6% of the initial detected fluxat velocities < ms . The dominant loss mechanism atpresent is the increased divergence and transverse heat-ing of the beam due to the slowing. The addition oftransverse cooling should provide a much higher flux ofslow molecules, suitable for loading a trap. It may bepossible to use a low B -field section to compress the ve-locity distribution following the initial slowing. A slowmolecular beam could be directly loaded into either amagneto-optical trap (MOT) [10] or a sufficiently deepconservative trap, using optical pumping as a dissipa-tive loading mechanism [25–28]. Furthermore, the pre-liminary evidence of little loss during cycling, even after & photons have been scattered, invites the possibilityof moderately long lifetimes for SrF in a MOT. METHODS
We use an ablation-loaded cryogenic buffer gas beamsource, which provides relatively low initial forward veloc-ities, low internal temperatures, and high brightness [29,30]. It produces an SrF molecular beam of 1 . × molecules/sr/pulse in the X Σ +1 / ( v =0 , N =0) state. To mit-igate variations of the molecular beam flux, data are takenby chopping the slowing lasers on and off between each abla-tion shot. The background pressure in the beam propagationregion is ∼ × − Torr.With the v s , v s , and v s lasers applied, molecules cy-cle over the three bright ground states: X( v =0 , , N =1).Due to different optical pumping rates into and out of thesestates, the X ( v =0 , N =1) populations are expected to becomparable, while the X( v = 2 , N = 1) population should besignificantly less. We hence employ a scheme to detect pop-ulation in both X( v = 0 , N = 1) states. These states areexcited to the A( v =0 , J =3 /
2) state via the v p and v p probelasers, which are spatially overlapped and intersect the molec-ular beam at L d . Both the v p and v p lasers have f mod =42MHz rf sidebands with m = 2 . v = 0 , N = 1) states [11]; since they intersectthe collimated molecular beam transversely, they are subjectto negligible Doppler shift and broadening. The v p and v p laser powers are set to drive both transitions with the sameRabi frequency. Once excited to the D( v =0 , N =3 , J =5 / v pAD laser, the result-ing LIF at L d , predominantly at 360 nm, is filtered and mea-sured by a photon-counting PMT. By scanning the v pAD laserfrequency and noting the Doppler shift (relative to the reso-nant frequency of a transverse v pAD laser beam), we derive themolecular beam LVP. We verified that the detection efficiencyand measured LVP are independent of whether the moleculeis detected from X( v = 0 , N = 1) or X( v = 1 , N = 1). Powerbroadening from the v pAD laser ( ∼
23 MHz FWHM) and mag-netic field broadening ( ∼
18 MHz FWHM) lead to a measuredbroadening of 42 MHz FWHM for the v pAD detection profile,resulting in all velocity values having an uncertainty of ± ms .The v s , v s , v s , and v pAD lasers are spatially overlappedusing a combination of dichroic mirrors and a polarizingbeamsplitter (PBS) to produce a single beam with e inten-sity waist d =3 . v pAD laser with d =4 . v s , v s , v s and v pAD laser powers are 140 mW, 73 mW, 45 mW,and 70 mW respectively. The v s , v s , and v s laser detuningsfrom resonance, denoted ∆ v s , ∆ v s , and ∆ v s respectively,are first varied iteratively to maximize LIF at L s . For finertuning, the v pAD laser detuning, denoted ∆ v pAD , is set to reso-nantly excite SrF molecules with v f ≈ ms , and ∆ v s , ∆ v s ,and ∆ v s are varied iteratively to maximize the number ofmolecules detected in that Doppler class. Unless explicitlynoted, ∆ v s and ∆ v s remain at these empirically determinedvalues, denoted ∆ v s,opt and ∆ v s,opt respectively.In the Monte Carlo simulation, particles are created at the source with randomized velocity distribution matching themeasured forward and transverse velocity distributions of oursource [29]. We assume equal detection efficiency over the v pAD e beam waist at L = L d . We estimate the force profile using amodel 5-level system consisting of one excited state and fourground states (to match the four SRS/HFS levels). The de-generacy of the SRS/HFS levels and the accompanying levelshifts and remixing within each SRS/HFS level due to theapplied B -field are not included in the simulation. The satu-ration parameter s is calculated for each of the four SRS/HFSlevels assuming an estimated saturation power of 6 mW/cm and the known v s laser rf sideband spectrum. Using τ and s , classical rate equations are solved to determine the equi-librium excited state population fraction, ρ ee , as a functionof the detuning from the center of the SRS/HFS spectrum,∆. The dependence of ρ ee is then fit to a Voigt profile. Thisprocess is repeated for the range of powers dictated by the v s laser’s Gaussian intensity profile. Using the peak values of ρ ee for each intensity, we derive an estimate of how the maximumscattering rate varies with the distance from the center of theslowing beams, r . We finally model the scattering rate R asthe analytic function R (∆ , r ) = R max (cid:20) r/r ) a (cid:21) N ∞ Z −∞ e − t / (2 w G ) ( w L / +(∆ − t ) dt , where the normalization N is chosen so that R (0 , R max .The parameter values r = 1 . a = 3 . w L = 99 MHzand w G =95 MHz are derived from these fits, without refer-ence to the LVP data. The first two parameters control howthe scattering rate varies with the beam intensity, while thelatter two characterize the shape of the estimated scatteringrate as a function of ∆. Finally, the free parameter R max isvaried manually to fit the LVP data for a variety of ∆. Weachieve good agreement with R max =2 . × s − , consistentwith our previous observations [11]. Additional details of thesimulation procedure are in Supplementary Methods.[1] DeMille, D. Quantum computation with trapped polarmolecules. Phys. Rev. Lett. et al.
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Acknowledgements
This material is based upon worksupported by the ARO, the NSF and the AFOSR under theMURI award FA9550-09-1-0588.
Author contributions
J.F.B. constructed the exper-iment, performed the measurements, and analyzed the data.E.S.S. assisted with each phase of the project. E.B.N. as-sisted with the experiment construction and data analysis.D.D. supervised each phase of the project.
Competing financial interests
The authors declarethat they have no competing financial interests
Correspondence
Correspondence and requestsfor materials should be addressed to J.F.B. (email:[email protected]).
SUPPLEMENTARY MATERIALDiscussion 1
The addition of transverse cooling shifts the simulated con-trol LVP to lower velocities by . ms relative to the unper-turbed simulated control LVP. This shift is due to the factthat, with transverse cooling, slower molecules are collimatedcloser to the source than are faster molecules, and the likeli-hood of their passing through the detection region is there-fore greater. Overall, once the difference in scale has beenaccounted for, the shape of the simulated control LVP withtransverse cooling is similar enough to the shape of the simu-lated control LVP without transverse cooling that the formeris not shown in the main text. The simulated control LVPwith and without transverse cooling is shown in Supplemen-tary Fig. 5 to illustrate this effect. Discussion 2
We use the quantity ∆ HM , defined as the shift of the half-maximum point on the leading edge of the observed slowedLVP (versus that of the control LVP), as one simple mea-sure to evaluate the effectiveness of our slowing for differentexperimental parameters. Because slowed molecules are lesslikely to be detected (due to increased divergence, etc.), ∆ HM likely provides an underestimate of the actual slowing. With∆ v s = −
260 MHz, providing resonant excitation for moleculeswith v f =175 ms , we routinely achieve ∆ HM ≈ − ms . Sincethe SrF recoil velocity is v rc =5 . mms , we interpret this as amean number of photons scattered per molecule h N sc i≈ ,roughly an order of magnitude greater than in previous work[12]. Discussion 3
Other behavior corroborates the basic picture that theobserved slowed LVP is highly distorted by loss of slowmolecules. As shown in Supplementary Fig. 6a, LIF at L s peaks at ∆ v s ≈ −
160 MHz, whereas ∆ HM peaks at∆ v s ≈ −
220 MHz. These results are reproduced well bythe simulation as shown in Supplementary Fig 6b. We in-terpret this discrepancy in peak locations to indicate that thegreater scattering rate at ∆ v s = −
160 MHz is producingslower molecules, but these molecules are more likely thanfaster molecules to diverge before reaching the detection re-gion. Further, consider the dependence of ∆ HM versus v s laser power, which is shown for ∆ v s = −
340 MHz, − −
180 MHz in Supplementary Fig. 7. The data foreach detuning are fit to a function of the form∆ HM = c P c P where c and c are fit constants and P is the v laserpower. Note that ∆ HM saturates at lower powers when∆ v s ≈h v f i /λ s , i.e. when the detuning most closely matchesthe Doppler shift of the molecular beam. We interpret thisto suggest that more slowing is likely occurring for near-resonant detuning ( ∼ −
180 MHz) than for further red detun-ing ( ∼ −
260 MHz), but that at higher powers this additional L I F a t L d ( a r b . un i t s ) Supplementary Figure 5:
Impact of transverse coolingon simulated control longitudinal velocity profile.
Thesimulated control without transverse cooling (black solid line)and the simulated control with transverse cooling (blackdashed line, scaled by 1/21) are very similar; the addition oftransverse cooling shifts the simulated control LVP by . ms . Data L I F a t L s ( a r b . un i t s ) Simulationb) v s00 (MHz) H M ( m / s ) a) Supplementary Figure 6:
Dependencies of the half-maximum shift and spontaneous scattering fluores-cence on laser detuning.
Measured (a) and simulated (b)dependence of ∆ HM and LIF at L s versus ∆ v s . The LIFdata is scaled to be the same height as the ∆ HM peak inboth panels.slowing is not apparent in the data due to increased diver-gence and therefore decreased detection probability for theslowest molecules. Discussion 4
Overall, the slowed LVP was less sensitive to the v s and v s laser powers and detunings than to the v s laser power anddetuning. At maximum v s power, ∆ HM was found to be in-sensitive when varying ∆ v s by ∼
20 MHz around ∆ v s,opt . All v s powers & B = 4 − v s sideband modulation index for2 . < m < . v s sideband modulationfrequency for 42 MHz < f mod <
44 MHz. H M ( m / s ) v s00 power (mW) Supplementary Figure 7:
Dependencies of the half-maximum shift on laser power and detuning. ∆ HM versus v s laser power for ∆ v s = -340 MHz ( (cid:4) ), -260 MHz( • ), -180 MHz ( N ) and associated fits. Discussion 5
In our apparatus, B E ≈ . ~B E and the v s laser polarization is ≈ ◦ . The data shownin Fig. 4 of the main text were taken with a v s modulationindex of m =2 .
6, where the sharp features were generally morepronounced than at the typical m = 3 . Supplementary Methods
We found it necessary to adjust the size of the simulatedsource to a value larger than the physical cell exit hole diam-eter in order to obtain a qualitative match to our data. Webelieve this reflects the fact that collisions outside the sourceincrease the effective area from which molecules are emitted.Our measurements show the molecular beam transverse ve-locity increases significantly ( ∼ × ) within ∼∼