This content has been downloaded from IOPscience. Please scroll down to see the full text.
Download details:
IP Address: 18.51.1.63
This content was downloaded on 19/05/2017 at 13:22
Please note that terms and conditions apply.
One-dimensional magneto-optical compression of a cold CaF molecular beam
View the table of contents for this issue, or go to the journal homepage for more
2017 New J. Phys. 19 033035
(http://iopscience.iop.org/1367-2630/19/3/033035)
Home Search Collections Journals About Contact us My IOPscience
You may also be interested in:
Laser slowing of CaF molecules to near the capture velocity of a molecular MOT
Boerge Hemmerling, Eunmi Chae, Aakash Ravi et al.
Improved magneto–optical trapping of a diatomic molecule
D J McCarron, E B Norrgard, M H Steinecker et al.
An intense, cold, velocity-controlled molecular beam by frequency-chirped laser slowing
S Truppe, H J Williams, N J Fitch et al.
Magneto-optical trapping forces for atoms and molecules with complex level structures
M R Tarbutt
Optical cooling and trapping of highly magnetic atoms: the benefits of a spontaneous spin
polarization
Davide Dreon, Leonid A Sidorenkov, Chayma Bouazza et al.
A proposed method of efficient laser trapping of neutral radium atoms
Sung Jong Park, Young Jin Kim, Taeksu Shin et al.
BaF radical: A promising candidate for laser cooling and magneto-optical trapping
Liang Xu, Bin Wei, Yong Xia et al.
Preparation of cold molecules for high-precision measurements
T E Wall
Prospects for a narrow line MOT in YO
Alejandra L Collopy, Matthew T Hummon, Mark Yeo et al.
New J. Phys. 19 (2017) 033035 https://doi.org/10.1088/1367-2630/aa6470
PAPER
One-dimensional magneto-optical compression of a cold CaF
molecular beam
EunmiChae1,2,5, Loic Anderegg1,2, Benjamin LAugenbraun1,2, AakashRavi1,2, BoergeHemmerling1,2,6,
Nicholas RHutzler1,2, Alejandra LCollopy3, JunYe3,WolfgangKetterle2,4 and JohnMDoyle1,2
1 Department of Physics, HarvardUniversity, Cambridge,MA02138,United States of America
2 Harvard-MITCenter forUltracold Atoms, Cambridge,MA02138,United States of America
3 JILA,National Institute of Standards andTechnology andUniversity of Colorado, Boulder, CO80309,United States of America
4 Department of Physics,Massachusetts Institute of Technology, Cambridge,MA02139,United States of America
5 Present address: Photon ScienceCenter, School of Engineering, theUniversity of Tokyo, Japan 113-8656.
6 Present address: Department of Physics, University of California, Berkeley, CA 94720,United States of America.
E-mail: eunmi@cua.harvard.edu
Keywords: laser cooling ofmolecules,molecular RFmagneto-optical trap, cryogenicmolecular buffer-gas beam
Abstract
Wedemonstrate the one-dimensional, transversemagneto-optical compression of a cold beamof
calciummonofluoride (CaF). By continually alternating themagnetic field direction and laser
polarizations of themagneto-optical trap (RFMOT), a photon scattering rate of 2 0.4 MHzp ´ is
achieved. A 3Dmodel for this RFMOT, validated by agreement with data, predicts a 3DRFMOT
capture velocity for CaF of 5m s–1.
1. Introduction
Molecules are intriguing candidates for the study of fundamental symmetry violation, quantum simulation of
strongly correlatedHamiltonians, and the creation of new quantum information systems that take advantage of
internalmolecular degrees of freedom [1–10]. In addition, active research is ongoing to create coldmolecules for
new studies in order to understand the full role of quantummechanics in chemical reactions [11, 12]. Themain
difficulty in pursuing these goals is to controllably preparemolecules in single quantum states, and to achieve
long interaction times (typically achieved via trapping). Even the simplestmolecules, diatomicmolecules, have
complex enough internal structure that, at room temperature, typically tens of thousands of states are thermally
populated. Only very recently havemolecular quantum states been controlled in away to allow for quantum
state-dependent chemical reactions [11, 12]. In that work, ultracold bi-alkalimolecules were produced in a
single quantum state by combining two ultracold alkali atoms, taking advantage of themature, powerful tools
for atom cooling [13–18]. However, this technique is so far limited to a specific subset ofmolecules, typically
bialkalis in the 1S state. Extension of thesemethods tomore chemically diverse species is a formidable challenge.
To fully utilize the powerful diversity ofmolecules, newmethods to produce cold and ultracoldmolecules
(e.g. thosewith electron spin degree of freedom) are desirable. A crucial step towards achieving lower
temperatures is trapping, which in itself allows for further coolingmethods to be applied.Major efforts are
currently ongoing to trapmolecules using electric,magnetic, and optical forces [19–31]. One promising option
is amagneto-optical trap (MOT), theworkhorse tool of optical cooling and confinement for atoms. Despite
thorough study and understanding of atomicMOTs, the additional internal structure present inmolecules has
made it difficult to produce amolecularMOT,mostly due to the lack of closed cycling transitions. It is possible
to overcome this difficulty by usingmolecules with sufficiently diagonal Franck–Condon factors (FCFs), as was
proposed in [32, 33]. Recently, 2D and 3DMOTs formolecules have been realizedwith YO and SrF [34–37].
This scheme, although limited tomolecules with strong optical transitions and highly diagonal FCFs, represents
a powerful step toward broadening the scope ofmolecules that can be brought to the ultracold regime, including
manywhich are of interest for new schemes in quantum simulation [6].
OPEN ACCESS
RECEIVED
11 January 2017
REVISED
13 February 2017
ACCEPTED FOR PUBLICATION
3March 2017
PUBLISHED
27March 2017
Original content from this
workmay be used under
the terms of the Creative
CommonsAttribution 3.0
licence.
Any further distribution of
this workmustmaintain
attribution to the
author(s) and the title of
thework, journal citation
andDOI.
© 2017 IOPPublishing Ltd andDeutsche PhysikalischeGesellschaft
CaF is a prototypicalmolecule for cold and ultracold applications and has been studied extensively,
including its collisional properties [38–42]. It has an unpaired outer shell electron, strong laser cooling
transitions, and reasonably diagonal FCFs. Furthermore, its lightmass leads to a larger velocity change per
photon scatter, which, compared to largermass species with all other spectroscopic properties the same,
shortens the slowing distance and increases the capture velocity of aMOT. It is therefore amolecule that is well
suited for laser cooling. Using the X v A v0 0= - ¢ =( ) ( ) transition at 606 nmwith a linewidth of
2 8.29 MHzp ´ [38], about 105 photons can be scatteredwith 2 vibrational repump lasers, before falling into
higher vibrational states [43]. Recent theoretical work indicates that CaF is a good candidate for sympathetic/
evaporative cooling to reach temperatures in themicrokelvin regime, a necessary step toward quantum
degeneracy [41, 42]. Once an ensemble of ultracoldCaFmolecules is prepared, its large electric dipolemoment
and spin degree of freedomwill expand theHamiltonians that can be simulated, including spin-lattice
models [6].
Here we report a demonstration ofmagneto-optical compression of aCaFmolecular beam. This is a key
milestone towards loadingCaF into a 3DMOT. This work verifies all of the processes and technology necessary
formagneto-optical trapping of CaF, identifies an importantMOT-limiting feature of CaF due to level
crossings, and provides crucial data for validating RFMOT loadingmodels. Our results also point towards the
optimal parameters for achieving a RFMOTwith amaximumnumber of trappedCaFmolecules.
2.Methods
Aschematic of the apparatus is depicted infigure1. Inour experiment, a cryogenic two-stage buffer-gas beamsource
is used toproduce a coldCaFmolecular beam [44–47]. CaFmolecules are generatedby ablating ametallicCa target in
anSF6 ice environmentwithin a copper cell, similar to thework in [48]. Themolecules are cooled through collisions
withHegas in a cell held at a temperature of around2K.Coldmolecules and atomicHe exit the cell aperture, forming
abeamwith amean forward velocity of 110±10m s–1, and velocity spreadof 40m s–1. To reduce the amountof
buffer gas reaching the interaction region and to collimate themolecular beam, a 6mm×6mmaperture is placed
41 cm fromthe cell, 9 cmbefore themolecules interactwith theRFMOTmagneticfields and corresponding
transverse laser beams.This aperture sets themolecular beamwidth in thedetection area. In these experiments only a
singleMOTbeam—transverse to themolecular beam—is used toquantitatively study theRFmagneto-optical force
in 1D [34]. Aftermolecules pass through the interaction region, they travel about 30 cm fartherwhere they are
detectedon anEMCCD (Andor, LucaR)usingfluorescence.
The relevant energy levels of CaF are shown infigure 2. The optical transitions in use are from the electronic
ground stateX to thefirst electronic excited stateA. Themeasured FCF for X v A v0 0= - ¢ =( ) ( ) is 0.987 [38]
and one vibrational repump laser from the v=1 state is used, allowing up to 1000 photons to be scattered before
pumping of themolecules to the v=2 state [43]. Loss to other rotational states is prevented by addressing a J to
J J 1¢ = - transition [33]. In this transition, the rotationally excited X N 1=( ) state is excited to the N 0¢ =
state of theA state so that a combination of parity and angularmomentum selection rules results in the
A N 0¢ =( ) statemolecules decaying back to the X N 1=( ) state.
Figure 1.Experimental setup (not to scale). The cell wheremolecules are generated is cooled by a pumped liquid 4He bath. An
aperture of 6mm×6 mm is placed 41 cmdownstream from the cell to collimate themolecular beam and to reduce the remaining
4He buffer-gas. Themolecules interact with the lasers 50 cm from the cell where the in-vacuumRF coils are in place. After the
interaction, themolecules travel 30 cm farther and are detected byfluorescencewith an electronmultiplying charge-coupled device
(EMCCD) camera. All lasers include X v A v0, 1 0= - ¢ =( ) ( ) transitions and their hyperfine splittings.
2
New J. Phys. 19 (2017) 033035 EChae et al
There are 4 hyperfine states that are spaced a few tens ofMHz in the X N 1=( ) statemanifold due to
coupling of the electron’s spin S 1 2=( )with themolecular rotation N 1=( ) andfluorine’s nuclear spin
I 1 2=( ). This hyperfine splitting weakens themagneto-optical force in twoways: reduction of the scattering
rate and level-crossing inweakmagnetic fields at around 10Gauss (figure 2 inset). All states are individually
addressed through frequency sidebands placed on the lasers. One of the hyperfine states (J F1 2, 1= = ) has
an opposite sign of the g factor and the polarization of the lasers addressing this state has opposite handedness
relative to the other states. The intensity of the X v A v0 0= - ¢ =( ) ( ) lasers for all hyperfine states is
150 mW cm−2 in total, and the intensity of the repump lasers for the X v A v1 0= - ¢ =( ) ( ) transition is
100 mW cm−2. The lasers areGaussian beamswith e1 2 diameter of 7 mm.The powers among the hyperfine
states areweighted by the degeneracy of the state. This is due to the fact that scattering rate for theMOTdepends
on the laser intensity for individual states as [37]
R
n
n n I I2 1 4
, 1e
g e j
n
j j j
sc
1
2 2
sat,
gå= G + + + D G=( ) ( ) ( )
whereΓ is a linewidth of the excited states (2 8.29 MHzp ´ [38]), ng(ne) is the number of involved states in the
ground (excited) statemanifold, jD is a laser detuning for the j state, I jsat, is a two-level saturation intensity for
the j state (4.87 mW cm−2 and 4.37 mW cm−2 for the v = 0 and v = 1 states respectively), and Ij is laser
intensity for the j state. The experimental parameters result in the scattering rate R 2 0.43 MHzsc p~ ´ from
equation (1). The hyperfine splitting of the excited stateA is unresolved [38].
One additional complication of amolecularMOT compared to an atomicMOT is that the number of
involved groundmagnetic substates is greater than that of the excited states. Because of this, some of the states
become dark states of the confining lasers. The onlywaymolecules could get out those states in a normalMOT
would be scattering anti-confining photons, destroying theMOT effect. RFMOTs [34, 37] solve this problemby
actively switching themagnetic field gradient and the polarization of the light synchronously at a rate
comparable to the excited state’s lifetime.With this scheme,molecules in all states predominantly scatter
photons that lead to confinement and can be trapped. Switching of the lasers’ polarizations is implemented using
a Pockels cell. To switch the neededmagnetic fields at a rate on the order ofMHz, the coils aremade small and
internal to the vacuumchamber (figure 3). The coils aremade out of a 0.85 mm thick copper sheet cut to a spiral
coil shapewithwirewidth of 1 mmon a 1.5 mm thick alumina substrate. The inner diameter of the coils is about
15 mmand there are 6 turns for each coil. There are 4 coils total, 2 on the upper board and 2 on the lower board
Figure 2. Level diagram forCaFmolecules. Only relevant levels are shown.Quantumnumbers for vibration, rotation, electronic
angularmomentumplus rotation, and themolecule’s total angularmomentum are v,N, J, and F respectively. The parity of the state is
denoted by±. The straight lines indicate lasers used in the experiment andwavy lines show the decay from the excited states. FCFs ( fij)
are also shown. The inset shows the hyperfine states and their Zeeman shift in the ground state X v N0, 1= =( ). The red-detuned
laser frequencies are shown in red broken lines in the inset. The hyperfine splitting and the Zeeman shift of the excited state
A v J0, 1 2¢ = ¢ =( ) is negligible [39].
3
New J. Phys. 19 (2017) 033035 EChae et al
—with the boards spaced by 16 mm.Coils on the same board arewired in aHelmholtz configuration, while the
two boards together provide an anti-Helmholtz field in the space between them.Aluminawas chosen due to its
lowoutgassing rate (necessary for theUHVenvironment of theMOT) and good thermal conductivity (necessary
to carry out the substantial heating producedwhen switching the coils at high frequencies). The alumina boards
aremounted on an aluminumblock, which is itselfmounted to a copper block feedthrough.On the air-side of
the feedthrough, we put a passive heatsink to further increase the cooling power.With this setup, we observe
only a few degrees of temperature increase of the block feedthroughwhen running the coils in RFmode at
830 kHz. The coil assembly is connected to a resonant circuit outside of the chamber.With 1Ampof current run
through the coils, a quadrupolemagnetic field of about 7.3 (3.7)Gauss cm–1 is produced in the axial (radial)
direction.
Themolecules are detected by collecting fluorescent photons using an EMCCDcamera. The excitation
lasers (X v A v0, 1 0= - ¢ =( ) ( )) cross themolecular beam at 90 degrees in the detection region, 80 cm
downstream from the source. Themeasuredwidth of themolecular beam is a convolution of the transverse
velocity of the beam and the initial beam spread.We analyze thismolecular beamwidth to infer the compression
and cooling effect from themagneto-optical force.
3. Results and discussion
Figures 4 and 5 show the compression of themolecular beamby themagneto-optical force. Typicalmolecular
beam signals with red-detuned X v A v0 0= - ¢ =( ) ( ) lasers when themagnetic field and the light polarization
are in phase and out of phase are depicted infigure 4. Themagneto-optical compression narrows themolecular
beamwhen the phase of themagnetic field and the light polarization arematched. In the opposite conditionwith
the relative phase of 180°, themolecular beam experiences an anti-confining force and its width is increased. The
measured beamprofiles arefit using super-Gaussian functions of order 4with their amplitudes, beamwidths as
given by the e1 radius of a fit, and centers as free parameters.
Thefitted beamwidths are plotted infigure 5. Each data point infigure 5 is the average of 350measurements
(molecular pulses) for the red-detunedmagneto-optical compression andDoppler cooling (figure 5(a)), and 200
(800)measurements for the blue-detunedmagneto-optical compression (Doppler heating) (figure 5(b)). The
relative phase between the polarization and themagnetic field is changed between each data point. Error bars
indicate one-standard-deviation statistical uncertainties from fits to beamprofiles. In the absence of the
magnetic field, Doppler cooling (heating) is observedwith red (blue)-detuning of lasers. The direction of the
magneto-optical force is seen to reverse with blue-detuning of the lasers compared to the case with red-detuning
as expected.
We have createdMonte-Carlo simulations of the RFMOT similar to that described in [34]. The results of
these simulations are shown infigure 5 as solid lineswith scattering of 150 photons, corresponding to a photon
scattering rate of 2 0.4p ´ MHz. This agrees with the expected scattering rate based on themeasured laser
powers and transition strengths. Due to the asymmetric hyperfine structure of CaF, aMonte-Carlo simulation
with only one effective detuning gives good agreement for the red-detuning, while results are inworse agreement
for the blue-detuned case. Thewidths of themolecular beam in the detection region for different conditions are
summarized infigure 6.
At a detuning of 7MHz, the optimal compression is achievedwith amagneticfield gradient of 7.3Gauss cm–1.
Several otherfield gradients (3.7, 4.4, 5.8, 12.4, and 18.3Gauss cm–1)were tested but the compression effects are
reduced compared to the optimal gradient. This is due to the small hyperfine splitting ofCaF. Specifically, in a
Figure 3.RFMOTcoils inside the vacuum chamber. The picture was taken before the inside was blackenedwith a non conductive,
low outgassing paint (MH2200 fromAlion) to reduce the background scattered light.
4
New J. Phys. 19 (2017) 033035 EChae et al
magneticfield greater than 5Gauss, the energy difference betweenmagnetic sublevels of different hyperfine states
approaches the natural linewidth. This increases theprobability of scattering anti-confining photons, and thus
weakens the compression effect.
The 1Dmagneto-optical compression demonstrated here provides uswith an improved understanding of
the 3DMOT forCaF.Using the number of scattered photons in 1Dmagneto-optical compression, simple
calculations estimate amaximum (on-axis, perfect conditions) capture velocity of about 13 m s–1 for the 3D
MOT in this experimental setupwith our current geometry and a fairly generic laser configuration for theX–A
transition.We have also performed a full 3DMOTMonte-Carlo simulation of trap loading for both on-axis and
themore realistic set ofmolecular trajectories that include off-axismolecules. Considering the limiting case of
molecules entering theMOT region only directly on-axis with the zeromagnetic field point of theMOT, the
capture velocity is seen in the simulation to be 10 m s–1, which agrees with the simple calculation.However, since
the capture velocity decreases as themolecules travel off axis, wefind that the averaged capture velocity is about
half of the ideal on-axis estimation, resulting in an effective capture velocity (simulating themolecular beam as a
whole, including off-axis trajectories) of about 5 m s–1 for themolecular beam as awhole.White-light slowing of
Figure 4. (a)Typical beamdatawith red-detuned lasers. The transverse beam shape after (anti)magneto-optical compression is
depicted as a (red) blue line. The two configurations are achieved by changing the phase of themagnetic fields by 180°. The integrated
area of the beam is conserved for the both cases. (b)The residuals of thefits to super-Gaussian functions are shown. The vertical unit is
same as in (a). Due to the original beam shape that is skewed to the leftside, the residuals differ from zero on the edges of the beams , as
expected. However, the residuals of theMOT and the anti-MOTdata are equal to a level smaller than the average shift where the
profile ismost sensitive, thewings and peak. This assures that thefitting is a valuable quantitative evaluation of themagneto-optical
compression.
Figure 5.Molecular beamwidths are plotted as a function of the relative phase between themagnetic field and the polarization of the
lasers: red dots in (a) for the X v A v0 0= - =( ) ( ) laser detuning of−7 MHz, and blue dots in (b) for the X v A v0 0= - =( ) ( )
laser detuning of+7 MHz. The black dot in eachfigure indicates the beamwidthwhen theMOT coils were switched off and reflects
the effect of Doppler cooling or heating. Gray area is a guide to eyes, indicating the 1s confidence region of theDopplerwidth. Error
bars are one-standard-deviation statistical uncertainties fromfits to beamprofiles. Lines show theMonte-Carlo simulation results for
each case.
5
New J. Phys. 19 (2017) 033035 EChae et al
aCaFmolecular beamdemonstrated previously in our group [47] resulted in about 5×104molecules at
5±4 m s–1 detected in the capture volume of theMOT.We expect a good fraction of thesemolecules would be
captured in a RFMOTwith current techniques.
4. Conclusion
Magneto-optical compression of a buffer-gas cooledCaF beamhas been achieved. By scattering 150 photons
during the timemolecules spend in the RFMOT region (about 60μs), themolecular beam is compressed, in
good agreement with ourfirst principlesmodel. From the demonstratedmolecular beam compression, we
estimate a RFMOT capture velocity of 5 m s–1 for CaF.
This work provides a deeper understanding of themagneto-optical forces onCaFmolecules and guides the
necessary experimental conditions for effective loading ofmolecularMOTs. It further demonstrates the
generality of the RFMOT scheme formolecules by adding an additional entry to the list ofmolecules onwhich
magneto-optical forces have been demonstrated.
Acknowledgments
Thisworkwas supported by theARO, theCUA, and theNSF. BLA is supported by theNational Science
FoundationGraduate Research Fellowship underNSFGrantNo.DGE1144152.
References
[1] Carr LD,DeMille D, KremsRV andYe J 2009New J. Phys. 11 055049
[2] Baron J et al 2014 Science 343 269
[3] DeMille D, Cahn SB,MurphreeD, RahmlowDAandKozlovMG2008Phys. Rev. Lett. 100 023003
[4] BaranovMA,DalmonteM, Pupillo G andZoller P 2012Chem. Rev. 112 5012
[5] BuchlerHP,Demler E, LukinM,Micheli A, ProkofevN, PupilloG andZoller P 2007Phys. Rev. Lett. 98 060404
[6] Micheli A, BrennenGK andZoller P 2006Nat. Phys. 2 341
[7] YanB,Moses SA, GadwayB, Covey J P,HazzardKRA, ReyAM, JinD S andYe J 2013Nature 501 521
[8] André A,DeMille D,Doyle JM, LukinMD,Maxwell S E, Rabl P, Schoelkopf R J andZoller P 2006Nat. Phys. 2 636
[9] DeMille D 2002Phys. Rev. Lett. 88 067901
[10] Rabl P,DeMille D, Doyle JM, LukinMD, Schoelkopf R J andZoller P 2006Phys. Rev. Lett. 97 033003
[11] NiK-K,Ospelkaus S,WangD,QuéménerG,Neyenhuis B, deMirandaMHG, Bohn J L, Ye J and JinD S 2010Nature 464 1324
[12] Ospelkaus S,Ni K-K,WangD, deMirandaMHG,Neyenhuis B,QuéménerG, Julienne P S, Bohn J L, JinD S andYe J 2010 Science
327 853
[13] NiK-K,Ospelkaus S, deMirandaMHG, Pe’er A,Neyenhuis B, Zirbel J J, Kotochigova S, Julienne P S, JinD S andYe J 2008 Science
322 231
[14] Moses SA, Covey J P,MiecnikowskiMT, YanB, GadwayB, Ye J and JinD S 2015 Science 350 659
[15] Park JW,Will S A andZwierleinMW2015Phys. Rev. Lett. 114 205302
[16] Takekoshi T, Reichsöllner L, Schindewolf A,Hutson JM, Le SueurCR,DulieuO, Ferlaino F, GrimmRandNägerl HC 2014 Phys. Rev.
Lett. 113 205301
[17] Molony PK,Gregory PD, Ji Z, LuB, KöppingerMP, Le Sueur CR, Blackley C L,Hutson JMandCornish S L 2014Phys. Rev. Lett. 113
255301
[18] GuoM,ZhuB, LuB, YeX,Wang F, Vexiau R, Bouloufa-MaafaN,QuéménerG,DulieuO andWangD2016 Phys. Rev. Lett. 116 205303
[19] HummonM,Tscherbul T, Klos J, LuH-I, Tsikata E, CampbellW,DalgarnoA andDoyle JM2011 Phys. Rev. Lett. 106 053201
[20] BethlemHL, BerdenG, Crompvoets FM, JongmaRT, vanRoij A J andMeijer G 2000Nature 406 491
Figure 6. Summary of themolecular beamwidth for each case. Bothmagnetic fields and detuned lasers are applied for the ‘MOT’
cases, while nomagnetic fields are applied for the ‘Doppler’ cases.Molecular beamwidth after themolecules interactingwith resonant
lasers is shown for comparison. The error bars indicate one-standard-deviation statistical uncertainties from fits to beamprofiles.
6
New J. Phys. 19 (2017) 033035 EChae et al
[21] van deMeerakker S, Smeets P, VanhaeckeN, JongmaR andMeijer G 2005Phys. Rev. Lett. 94 023004
[22] Hoekstra S,MetsäläM, Zieger P, Scharfenberg L, Gilijamse J,Meijer G and van deMeerakker S 2007Phys. Rev.A 76 063408
[23] ZeppenfeldM, Englert BGU,Glöckner R, PrehnA,MielenzM, SommerC, van Buuren LD,MotschMandRempeG2012Nature
491 570
[24] PrehnA, IbrüggerM,Glöckner R, RempeG andZeppenfeldM2016Phys. Rev. Lett. 116 063005
[25] Weinstein JD,DeCarvalhoR, Guillet T, Friedrich B andDoyle JM1998Nature 395 148
[26] Sawyer BC, Lev B L,Hudson ER, Stuhl BK, LaraM, Bohn J L andYe J 2007Phys. Rev. Lett. 98 253002
[27] CampbellWC, Tsikata E, LuH-I, van Buuren LD andDoyle JM2007Phys. Rev. Lett. 98 213001
[28] LuH-I, Kozyryev I,Hemmerling B, Piskorski J andDoyle JM2014Phys. Rev. Lett. 112 113006
[29] Stuhl BK,HummonMT, YeoM,QuéménerG, Bohn J L andYe J 2012Nature 492 396
[30] StollM, Bakker J, Steimle T,Meijer G and Peters A 2008Phys. Rev.A 78 032707
[31] Riedel J, Hoekstra S, JägerW,Gilijamse J J,Meerakker S YT andMeijer G 2011Eur. Phys. J.D 65 161
[32] RosaMD2004Eur. Phys. J.D 31 395
[33] Stuhl BK, Sawyer BC,WangD andYe J 2008Phys. Rev. Lett. 101 243002
[34] HummonMT, YeoM, Stuhl BK,Collopy A L, Xia Y andYe J 2013Phys. Rev. Lett. 110 143001
[35] Barry J F,McCarronD J,Norrgard EB, SteineckerMHandDeMille D 2014Nature 512 286
[36] McCarronD J,Norrgard EB, SteineckerMHandDeMille D 2015New J. Phys. 17 035014
[37] Norrgard EB,McCarronD J, SteineckerMH,TarbuttMR andDeMille D 2016Phys. Rev. Lett. 116 063004
[38] Wall T, Kanem J,Hudson J, Sauer B, ChoD, BoshierM,Hinds E andTarbuttMR2008 Phys. Rev.A 78 062509
[39] Devlin J, TarbuttMR, KokkinDL and Steimle TC 2015 J.Mol. Spectrosc. 317 1
[40] MaussangK, EgorovD,Helton J S,Nguyen SV andDoyle JM2005Phys. Rev. Lett. 94 123002
[41] Lim J, FryeMD,Hutson JMandTarbuttMR2015Phys. Rev.A 92 053419
[42] QuéménerG andBohn J L 2016Phys. Rev.A 93 012704
[43] PelegriniM,VivacquaC S, Roberto-NetoO,Ornellas F R andMachado FBC 2005Braz. J. Phys. 35 950
[44] LuH-I, Rasmussen J,WrightM J, PattersonD andDoyle JM2011Phys. Chem. Chem. Phys. 13 18986
[45] HutzlerNR, LuH-I andDoyle JM2012Chem. Rev. 112 4803
[46] Hemmerling B,DraynaGK, Chae E, Ravi A andDoyle JM2014New J. Phys. 16 063070
[47] Hemmerling B, Chae E, Ravi A, Anderegg L, DraynaGK,HutzlerNR, CollopyA L, Ye J, KetterleW andDoyle JM2016 J. Phys. B: At.
Mol. Opt. Phys. 49 174001
[48] WilliamsH, TarbuttMR and Sauer BE 2015 private conversation
7
New J. Phys. 19 (2017) 033035 EChae et al