Crossed-Beam slowing to enhance narrow-line Ytterbium Magneto-Optic Traps
Benjamin Plotkin-Swing, Anna Wirth, Daniel Gochnauer, Tahiyat Rahman, Katherine E. McAlpine, Subhadeep Gupta
CCrossed-Beam slowing to enhance narrow-line Ytterbium Magneto-OpticTraps
Benjamin Plotkin-Swing, Anna Wirth, Daniel Gochnauer, Tahiyat Rahman, Katherine E. McAlpine, andSubhadeep Gupta Department of Physics, University of Washington, Seattle WA 98195 (Dated: 23 April 2020)
We demonstrate a method to enhance the atom loading rate of a ytterbium (Yb) magneto-optic trap (MOT)operating on the narrow linewidth S → P intercombination transition. Following traditional Zeemanslowing of an atomic beam, two laser beams in a crossed-beam geometry frequency tuned near the broad S → P transition provide additional atom slowing immediately prior to the MOT. Using this technique,we observe an improvement by a factor of 6 in the atom loading rate of a narrow-line Yb MOT. The relativesimplicity of this approach and its generality make it readily adoptable to other experiments involving narrow-line MOTs. We also present a numerical simulation of this two-stage slowing process which shows goodagreement with the observed dependence on experimental parameters. I. INTRODUCTION
Techniques for laser cooling of alkali atoms developedmore than three decades ago have also been fruitfullyapplied to laser cooling of atomic species beyond alkalisover the last two decades . New scientific pursuits areafforded through the different electronic structure of suchnon-alkali atoms including optical atomic clocks for pre-cision metrology and strong dipolar interactions for ex-plorations of novel many-body phenomena . The dif-ferent electronic structure can also lead to optical cyclingtransitions with linewidths far narrower than their al-kali counterparts, leading to opportunities for narrow-linelaser cooling and magneto-optical traps (MOTs) withcorrespondingly lower temperatures due to the reducedlimiting value of the Doppler temperature.This narrow linewidth however poses a problem forthe atom loading rate of a MOT, since the laser cool-ing force is proportional to this linewidth. This problemcan be circumvented by using a second transition with abroader linewidth as an intermediate “pre-cooling” MOTstage with protection from the correspondingly higherDoppler temperature being furnished by separating thebroad- and narrow-line MOT beams either in time orin space . Such schemes involve Zeeman slowing of anatomic beam on the broad transition together with twosets of six MOT laser beams addressing the two transi-tions at the atom trap.In this work we demonstrate a method to enhance theatom loading rate of a narrow-line Yb MOT fed by aZeeman-slowed atomic beam by introducing only two ad-ditional laser beams on the broad transition. These ad-ditional beams are oriented in a crossed-beam geometryto provide additional cooling immediately prior to theMOT . Using this technique, which is readily adoptableto other atomic species, we observe an improvement bya factor of 6 in the MOT loading rate. We also performa numerical simulation of this two-stage slowing processand find good agreement with the observed dependenceon experimental parameters.The rest of this paper is organized as follows. In Sec- tion II we discuss the basic idea of the cooling schemeand in Section III present its experimental demonstra-tion in our apparatus. We compare our observations tothe results of a numerical simulation of the laser slowingprocess in Section IV and present a summary and outlookin Section V. II. CROSSED-BEAM SLOWING
In order to be captured by a MOT, an atom (i) mustbe located within the volume of the MOT beams (diam-eter D ) and (ii) must be moving slower than the capturevelocity v c of the MOT. A standard method in cold atomphysics is to use the Zeeman slower technique to reducethe forward velocity of atoms in a beam emerging froman oven and bring a large fraction below v c . This methodallows for fine tuning of the exit velocity v f of the slowedatoms using the current flowing through the electromag-net generating the Zeeman slower field. In traversing thedistance d between the end of the Zeeman slower andthe MOT beams, the finite transverse velocity v t of theatoms leads to a transverse displacement v t × d/v f whichneeds to be less than D/ d . The slowing laser beam is set to coun-terpropagate with the atomic beam, which means thatthe beam must pass nearby or through the MOT region.To accommodate this close passage, an increasing fieldZeeman slower is usually used so that the slowing beamdetuning is sufficiently large to not affect the atoms inthe MOT. This scheme requires some distance d for themagnetic field to decay between the end of the Zeemanslower and the MOT region. In addition, the electromag-netic coils at the end of the Zeeman slower are often ofsufficient size that they would block optical access to theMOT unless they are at least several inches away. In ourexperiment d (cid:39)
10 cm, which is a typical value for suchsetups.Even for an atomic beam that is initially perfectly col- a r X i v : . [ phy s i c s . a t o m - ph ] A p r FIG. 1. Schematic top-down view of the vacuum chamberwith MOT and various slower beams superimposed. Thecrossed slower beams intersect just upstream of the MOT andprovide the final stage of slowing down to below the MOTcapture velocity. The distances from the end of the Zeemanslower coils to the MOT center and from the center of thecrossed beams to the MOT center are denoted by d and d M ,respectively. limated, transverse velocity at the end of the Zeemanslower will arise from “blooming” of the atomic beamdue to interactions with the slower beam. This hap-pens because atoms absorb photons from the slower beam(and receive a momentum kick counter to their motion),and then re-emit these photons in a random direction.Summed over many such events, the average momentumchange from emitted photons is zero. However, the distri-bution of net momentum transfer from emission eventshas some width, meaning that many atoms do end upwith non-zero momentum from emission. Modeling theemission in the transverse direction as a random walk,we expect v t to scale as √ N v r , where N is the numberof scattering events in the Zeeman slower and v r is therecoil velocity.We can estimate v c (cid:39) (cid:113) ¯ hk g Γ g Dm , where Γ g = 2 π × S → P
556 nm (green)atomic transition, k g is the corresponding laser wavenum-ber, and m is the mass of ytterbium. It is clear fromthis expression that a narrow-line MOT will feature acorrespondingly small capture velocity v c . For Yb thisis 9 . D = 2 cm. The transverse velocity is v t (cid:39) . v c , this then converts to a transverse displacement whichis larger than D/
2. These estimates already suggest thatloading a narrow-line Yb MOT with a Zeeman slowedatomic beam is less efficient than with a broad-line MOTas in alkali systems. For comparison, in alkali Rubidiumwith a large natural linewidth, v c is an order of magni-tude larger.The dual constraint on v c and transverse position ona conventional Zeeman slower is lifted by the addition ofa second stage of cooling. The crossed beam slower is designed to provide a final stage of slowing immediatelybefore the MOT, so that the Zeeman slower exit velocity v f can be set higher than v c . This allows the condition v t × d/v f < D to be satisfied for larger values of v t . Thecrossed beam slower consists of beams near the strongdipole transition ( S → P at 399 nm) that are set topropagate parallel to two of the MOT beams, intersectingeach other in the atomic beam path just upstream of theMOT, as shown in Fig 1. The transverse forces (verticalin figure) from the crossed slower beams cancel each otherby symmetry, leaving a longitudinal force (horizontal andto the left in figure) that accomplishes the final stage ofslowing down to the MOT capture velocity. III. CROSSED-BEAM SLOWER PERFORMANCE ANDCHARACTERIZATION
We demonstrate the performance of the second-stageslower on an apparatus which can produce
Yb Bose-Einstein condensates of 10 atoms with cycle times asshort as 10 seconds . Details of other aspects of theapparatus relevant to cooling Yb can be found in Ref. 16.We now summarize the details relevant for the second-stage slowing.The magnetic field profile of the slower consists ofan offset field of B o (cid:39)
110 G and an increasing fieldwith the total field reaching a maximum value of B f (cid:39)
475 G at the exit of the slower. The maximum initialforward velocity that can get slowed by the slower isthen µ B ( B f − B o ) / (¯ hk b ) (cid:39)
200 m/s, where µ B is theBohr magneton and k b is the laser wavenumber of the S → P
399 nm (blue) transition. In practice, atomsstarting with even higher forward velocity from the ovencan be slowed by our apparatus due to the slowing laserbeam also interacting with the atoms in the space be-tween the oven and the start of the Zeeman slower. B f is adjustable with the current supplied to the electro-magnet generating the increasing field. The slowing laserbeam addresses the 399 nm transition and is detuned by δ = − π ×
807 MHz ( (cid:39) − µ B B f / ¯ h ) from the transitionwith an average intensity approximately equal to the sat-uration intensity of 59 mW/cm .The two crossed laser beams forming the second-stageslowing (see Fig.1) are positioned to intersect at a dis-tance d = 10 cm beyond the end of the Zeeman slowercoils and d M = 1 cm before the MOT. The crossed beamsare elliptical, with the long axis oriented in and out of thepage with respect to Fig. 1, and with the short axis hav-ing an approximately Gaussian horizontal profile of 1 /e width 1.5 mm. The dimension of the ellipse long axis isset to make the height of the crossed beam slowing regionapproximately match the diameter of the MOT beams.The beam is made narrower on the other axis so thatthe crossed region could be placed as close to the MOTas possible without disturbing the atoms trapped in theMOT. The frequency of the crossed beams was experi-mentally optimized to be δ X = − π ×
42 MHz detunedfrom the 399 nm transition.We assessed the performance of the crossed-beamslower by comparing the MOT loading rates for variousparameters of crossed-beams and slower beam. Repre-sentative “loading curves” are shown in Fig. 2. Suchloading curves were obtained by monitoring the fluores-cence of the MOT using a photomultipler tube and arefitted by a function of the form N ( t ) = N (1 − e − Lt/N ),where L is the initial atom loading rate and N is theequilibrium number at long times. When utilizing thecrossed beams, we see a marked improvement in boththe MOT loading rate and overall MOT population.To further explore the performance of the crossed beamslower, we mapped out the behavior of the loading ratein the two-dimensional parameter space of slower currentand crossed beam intensity s X (see Fig. 3(a)). The suc-cess of the technique is gauged by observing that the peakoccurs at a finite value of s X and that the loading rateat the peak is significantly greater (by a factor of about6) than the largest loading rate along the s X = 0 axis.Furthermore we see that the location of the largest load-ing rate for a given s X moves towards lower currents as s X is increased. This is expected because by increasingthe slowing power of the crossed beams, the atoms mayhave a higher velocity coming out of the Zeeman slowerand still be captured by the MOT. FIG. 2. Fluorescence signals (black lines) showing the atomnumber growth in a narrow-line Yb MOT for optimized ar-rangements with and without the crossed-beams. For eachof the two data curves, the slower current was adjusted tomaximize the loading rate and s X = 0 . IV. NUMERICAL SIMULATION
To provide a theoretical model for our experimental re-sults, we numerically simulate the trajectories of atomssubject to laser cooling forces through the experimental apparatus. Within the Zeeman slower, an atom experi-ences a position- and velocity-dependent average scatter-ing force from the slower beam with acceleration givenby: a S ( v, z ) = − ¯ hk b Γ b m s s + b (cid:16) δ + k b v + µ B B ( z )¯ h (cid:17) (1)where k b = π
399 nm is the wavenumber, Γ b = 2 π ×
29 MHzis the transition linewidth, m is the atomic mass, δ isthe slower beam detuning, s is the saturation parameterof the slower beam (intensity in units of the saturationintensity 59 mW/cm of the transition), and B ( z ) is thevalue of the Zeeman slower magnetic field at position z along the longitudinal direction. B ( z ) is calculated usingthe Biot-Savart law for the coils which compose our Zee-man slower, and it has been verified that the measuredfield is in excellent agreement with the calculated field .It is implicit that v is also a function of z .In the region of the crossed beams, the slower beamis far off resonance with the atoms that are moving slowenough to be eventually captured by the MOT. The rel-evant average scattering force that comes from the two-crossed beams is given by: a X ( v, z ) = − ¯ hk b Γ b m √ s X ( z )1+ s X ( z )+ b (cid:16) δ X + k b v √ (cid:17) (2)where s X ( z ) is the saturation parameter of the crossedbeams at position z and δ X is the detuning of the crossedbeams. The factor of 2 / √ / √ / √ s X arises fromthe Gaussian transverse profile of the crossed beams.In order to simulate the slowing in the cross-beams, wealso need a model of the velocity distribution entering theregion. For this we first simulate the trajectory of atomsthrough the Zeeman slower using Eq. (1). We recordthe longitudinal velocity v center of atoms at the end ofthe Zeeman slowing region for a fixed s and slower cur-rent. This provides a conversion between slower currentand the center of the slowed atom distribution v center en-tering the crossed-beam region. Since the modeled Zee-man slower is ideal, the atoms captured by the sloweremerge with a very narrow longitudinal velocity distri-bution in our simulation. In practice however, the longi-tudinal velocity distribution is broadened by the naturallinewidth Γ b of the transition and non-ideal effects such FIG. 3. Contour map of the MOT loading rate versus saturation intensity of the crossed beams and Zeeman slower current.Color indicates the relative fraction of atoms captured in the MOT. The optimal atom capture occurs for a non-zero crossedbeam intensity. (a) MOT loading rate from fluorescence measurements at various Zeeman slower currents and crossed beamintensities. Map is built up of 97 data points. (b) Simulated results for the fraction of atoms exiting the Zeeman slower whichare captured by the MOT. Map is built up of 117 data points. as the finite laser linewidth, irregularities in the slowingbeam profile, and fluctuations in current to the Zeemanslower coils. We approximate these effects in our simula-tion using a Gaussian distribution with standard devia-tion of 12 m/s, which is the measured value from earlierDoppler spectroscopy characterizing the Zeeman slowerin our apparatus . This value is consistent with Γ b /k b for this transition.To produce the parameter space map, for each s X andslower current value, we simulate the trajectories of 3000atoms with initial longitudinal velocities selected at ran-dom from a normal distribution with mean v center andstandard deviation of 12 m/s to approximate the flux ofslow atoms produced by our Zeeman slower. The atomsbegin with random initial transverse velocities and posi-tions picked from a distribution that is estimated fromthe results of the Zeeman slower simulation. For bothEqs (1) and (2), we use a time step of 20 µ s to model theeffect of the average scattering force from photon absorp-tion in the direction of laser light propagation.To model the effects of spontaneous emission in ran-dom directions, the number of photons scattered during each time step, N ph , is calculated and the atom is numer-ically made to do a 3-dimensional random walk in veloc-ity space of N ph steps of length v rec , the recoil velocityof ytterbium (5 . v tot = (cid:112) v l + v t , where v l is the longitudinal velocity, is less than v c = 9 . s X .Fig. 3 shows how these simulations compare to ourexperimental data. We see that optimal capture for ourexperimental parameters occurs at around slower currentof 30 A and s X = 0 .
3. The simulations demonstrate goodagreement with the experimental results, with the peaklocations differing by less than 3% of the slower current.Our simulations indicate that under optimum condi-tions, 24% of the atoms that are slowed by the Zeemanslower are slowed adequately by the crossed beams to becaptured by the MOT. We also find that of the atomswhich satisfy condition (ii) above, only about 15% donot satisfy condition (i). This indicates that the crossedbeam method has largely solved the blooming problemfor narrow line MOTs. The remaining limiting factor isthe width 12 m/s of the slowed longitudinal velocity dis-tribution, which is larger than the MOT capture velocity v c of 9.7 m/s. With sufficient laser power, this issuecould be addressed by using larger MOT beams and thusincreasing v c . V. SUMMARY AND OUTLOOK
We have described a method to improve the perfor-mance of a narrow-line Yb MOT by a factor of 6 usinga crossed arrangement of two additional slower beamsimmediately prior to the MOT. We have assessed theperformance of our method by observing its effect overa large parameter space of slower magnetic field andcrossed beam intensity. The results of a numerical modelfor the behavior of our system show good agreement withour experimental observations.A notable feature of the method is the relative sim-plicity of the setup, which involves only two additionallaser beams beyond a traditional laser cooling appa-ratus. Our results can be adapted to other exper-imental efforts which use laser cooled Yb, an atomwith various applications in atomic clocks , prepara-tion of quantum degenerate systems , precision atominterferometry , quantum simulation , and quantuminformation processing . The method is also applica-ble to narrow-line MOTs of other elements and has beenvery recently demonstrated in Dy and Er . ACKNOWLEDGMENTS
We thank Alan Jamison for useful discussions. Thiswork was supported by NSF Grant No. PHY-1707575.
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