A magneto-optical trap with millimeter ball lenses
Cainan S. Nichols, Leo M. Nofs, Michael A. Viray, Lu Ma, Eric Paradis, Georg Raithel
AA magneto-optical trap with millimeter ball lenses
Cainan S. Nichols, Leo M. Nofs,
1, 2
Michael A. Viray, Lu Ma, Eric Paradis, ∗ and Georg Raithel Department of Physics and Astronomy, Eastern Michigan University, Ypsilanti, Michigan 48197, USA Department of Physics, University of Michigan, Ann Arbor, Michigan 48109, USA (Dated: May 21, 2020)We present a magneto-optical trap (MOT) design based on millimeter ball lenses, contained withina metal cube of 0.75 (cid:48)(cid:48) side length. We present evidence of trapping approximately 4 . × of Rbatoms with a number density of 3 . × atoms / cm and a loading time of 1.3 s. Measurement anda kinetic laser-cooling model are used to characterize the atom trap design. The design providesseveral advantages over other types of MOTs: the laser power requirement is low, the small lensand cube sizes allow for miniaturization of MOT applications, and the lack of large-diameter opticalbeam pathways prevents external blackbody radiation from entering the trapping region. I. INTRODUCTION
The invention of the magneto-optical trap (MOT) [1, 2]ushered in a new wave of physics research, as it al-lowed researchers to cool atoms to previously unattain-able temperatures. Since then multiple groups have cre-ated new MOT designs that use the same tangible prin-ciples but feature different optical configurations, oftenfor the sake of miniaturization, portability, and/or easeof setup. These include grating MOTs [3, 4], pyrami-dal MOTs [5–8], and MOTs with five beams [9], in ad-dition to variations upon the original six-beam config-uration. While the classic six-beam MOT design suf-fices for most cold-atom experiments, numerous precisionmeasurement and atomic-clock experiments require cold-atom systems that are shielded from external perturba-tions [10] such as blackbody radiation. Multiple papershave addressed ways to eliminate blackbody radiation inprecision measurements and atomic clocks [11–13]. Thesix-beam MOT is particularly vulnerable to blackbodyradiation because the beams have large cross-sections andthe necessary optical apertures subtend a large solid an-gle with respect to the trap center. This results in uncer-tainties of the blackbody radiation shift [14]. Precisionmeasurements and atomic clocks may also be sensitiveto external DC electric fields [15], requiring field-zeroingwith electrodes or Faraday shielding. MOT designs withbuilt-in Faraday shielding, including the one describedin the present work, provide immediate reduction of theStark shift. Further applications of such MOTs are foundin research that requires well-defined electrode configura-tions with minimally perturbed symmetry, such as cold-atom-loaded Penning [16, 17] and Paul traps [18].Here we describe a new MOT design that usesmillimeter-sized ball lenses that are held in place in ametal frame of less than 2 cm in diameter, containedinside a vacuum chamber. Ball lenses have well-knownoptical properties [19, 20] and are typically used for opti-cal tweezers [21, 22], but they are not traditionally used ∗ [email protected] in MOTs. In our design, six independent, narrow, colli-mated cooling beams ( w ∼ . π × − steradians. Additionally, the highly di-vergent nature of the light cones behind the ball lensesmakes this MOT operate best at low laser powers. Theseproperties promise great potential for future quantumtechnology applications [23]. In our work we also de-scribe how specific challenges associated with the beamalignment and geometric peculiarities can be addressed.We further discuss how this style of MOT can be imple-mented in future experiments. II. IMPLEMENTATION
In our experimental setup, six 1.5-mm-diameter N-BK7 ball lenses are held in place with a custom-madepart called the ball lens optical box (BLOB). Figure 1ashows a computer rendering of the BLOB, and Fig. 1ba picture of the physical part. The BLOB is a hollowcube with inner side length of 5/8 (cid:48)(cid:48) that is manufacturedfrom six 1/16 (cid:48)(cid:48) thick steel plates. Each ball lens is im-planted in a counterbore at the center of one of the cubefaces, where it is held in place by a metal flap spring.The flaps have 1.3-mm-diameter holes over the lenses tolet light through. The divergent light fields behind thelenses have an approximately Gaussian profile in the di-rections transverse to the beam axes. The counterboreshave inner and outer diameters of 1.3 mm and 2 mm,respectively. The flap springs push the lenses from the a r X i v : . [ phy s i c s . a t o m - ph ] M a y outside of the BLOB against 0.5-mm-deep ledges on theinside of the cube faces, resulting in a simple, secure,and vibration-resistant lens mount. The BLOB cube iswelded onto a piece of steel square tubing that is attachedto the inside of the vacuum chamber used for MOT test-ing. The BLOB has eight extra 4-mm-diameter holes onits edges and faces for optical access. While these ex-tra holes are non-essential for MOT operation, they areuseful for MOT analysis and other applications involvingadditional laser beams.Unlike in standard 6-beam MOTs, in ball-lens MOTsit is not practical to re-cycle the laser beams by retro-reflection because of aberrations caused by the lenses. In-stead, six independent collimated cooling beams (beamwaists w ∼ . ≈ µ m and emerge as conical beams with a numericalaperture N A ≈ .
3, corresponding to an opening angleof the light cones of ∼ ◦ (full width at half maximum(FWHM) of the intensity). A sketch of the fields insidethe BLOB is shown in Fig. 1c.The BLOB is tightly mounted between two large-diameter, re-entrant vacuum windows. The two MOTcoils are placed close to the outsides of the re-entrantwindows, so that the separation between the innermostwindings of the coil pair is only ∼ . (cid:48)(cid:48) . The MOT coilsrun at a current of ∼ Rb. The cool-ing laser is locked to a hyperfine component of the5 S / → P / transition using saturation spectroscopyin a Rb vapor cell [24]. The cooling beam passes throughan acousto-optic modular (AOM) for switching and forfrequency-tuning close to the F = 3 → F (cid:48) = 4 hy-perfine cycling transition. A repumper laser drives the F = 2 → F (cid:48) = 3 hyperfine transition. The power ofeach cooling beam before entering the vacuum chamber is (cid:46) ∼ I sat (the saturation intensity I sat = 1 . for the cy-cling transition [25]). The true intensity is slightly lessdue to reflection and other losses.The setup has a probe laser used for shadow imaging.This laser is on-resonance with the F = 3 → F (cid:48) = 4hyperfine transition and also passes through an AOMfor frequency tuning and switching. The MOT probebeam has a FWHM of 2.5 mm and a center intensity to0.23 mW/cm . The beam is directed through the vacuumchamber, passed through the center of the BLOB, andaligned into a CCD camera (Pixelfly Model 270 XS). Thecamera is used to record shadow images, with the probebeam on and MOT beams off, as well as fluorescenceimages, with the probe beam off and MOT beams on. (a)(b)(c) FIG. 1. (a) Computer rendering of ball lens MOT setup,including the cooling beams. The ball lenses are located at thecenters of the cube faces. The larger holes are for additionaloptical access. (b) Picture of the actual ball lens optical box(BLOB). (c) Cross-sectional sketch of fields in ball lens MOT.Two of the ball lenses are not included in this drawing.
III. MOT ANALYSIS
The main quantities of interest in our experimentalcharacterization of the MOT are atom number, atomdensity, and loading time. The atom number and den-sity are dependent on the design of the MOT and laserparameters, while the loading time is mostly dependenton background pressure and is similar to other MOTs.The atom number, the most important metric in ourcomparison with theory in Sec. IV, and the number den-sity of the MOT are measured using shadow imaging. Inthis configuration, the MOT cooling beams are brieflyturned off, and a probe beam pulse is sent through theMOT and into the Pixelfly camera. The MOT and probebeams are switched with the AOMs. Figure 2a shows anarea-density shadow image for a MOT single-beam in-tensity of I ≈ . , and Fig. 2b shows the corre-sponding timing details. With the probe beam carefullytuned on-resonance with the MOT transition, we find theatom number in our MOT to be N MOT,Exp = 4 . × .The value for N MOT,Exp is found by evaluating N MOT,Exp = (cid:90) σ ln (cid:18) I ( x, y ) − I B ( x, y ) I ( x, y ) − I B ( x, y ) (cid:19) dxdy (1)over the MOT object plane, where I ( x, y ) is the shadowimage with MOT atoms present, I B ( x, y ) is a back-ground image with the probe beam off but all otherlight sources left on, and I ( x, y ) is an image with theprobe beam on but without MOT atoms. Since thelight is unpolarized and the MOT magnetic field is lefton, we use the isotropic absorption cross section σ =1 . × − cm [25]. The integral is evaluated as a dis-crete sum over a two-dimensional array of CCD pixels,with the pixel area given by the CCD pixel area pro-jected into the object (MOT) plane. Assuming that theMOT fills a cubic volume with a side length of 0.5 mm,the typical linear size of the MOT seen from two differ-ent observation angles, the atom density in the MOT isestimated to be 3 . × atoms/cm .The loading time, required for the theoretical atom-number estimate in Sec. IV, is determined with fluores-cence imaging. In this configuration, the MOT light isperiodically switched on for 4 s to allow the trap to ac-cumulate atoms, and then off for 1 s to empty the trap.The camera records images of the atom cloud at 0.25-stime intervals, ranging from 0 s to 3 s of loading time.Figure 3a shows a fluorescence image of the atom cloudafter 3 s of loading, along with a timing diagram inFig. 3b for the fluorescence imaging procedure. In ouranalysis, we plot the background-subtracted fluorescenceprofiles from each of the images and apply Gaussian fitsto these profiles. The atom count is then taken to beproportional to the areas of the fits at the respectivetime steps. This method applies to small MOTs, suchas ours, which are free of radiation trapping effects, andfor which the fluorescence yields an approximately linearmeasure for atom number. Figure 3c represents relativeatom count vs loading time, along with error bars fromthe fits which represent statistical error. Applying an ex-ponential rise time fit to the data, we calculate a timeconstant of 1 . ± . (a)(b) FIG. 2. (a) A shadow image of the MOT showing areadensity (the integrand in Eq. (1)) vs. position in the MOTplane. (b) Timing diagram for the shadow imaging. Whenthe MOT light is turned off, the camera is gated on for 90 µ s.Following a wait time of τ = 20 µ s after the MOT light isturned off, the probe pulse is turned on for a duration of50 µ s. In our performance evaluation we have also studiedthe dependence of atom number on MOT beam intensity.In Fig. 4d we show atom numbers in relative units, ob-tained from MOT fluorescence, vs central beam intensity.The result indicates best performance at an intensity of ∼ I sat ; at higher intensities the atom number dropsquickly. This behavior contrasts with standard six-beamMOTs, in which the atom number keeps increasing toconsiderably higher intensities before leveling off. Ourmodel, presented next, reproduces the observed peculiarintensity dependence of the ball lens MOT. IV. THEORETICAL MODEL OF BALL LENSMOT
The objective of our model is to determine the depen-dence of the number of captured atoms in steady state onball-lens MOT parameters. Further, we study how theatom capture behavior differs from that of a standardsix-beam MOT, and how that translates into differencesin the steady-state trapped-atom number and into guide-lines for best operating conditions for ball-lens MOTs.We first outline our kinetic laser-cooling model. Weassume a spherical MOT cell volume of 1.0 cm radius,which has a volume similar to that of the BLOB used inthe experiment. Thermal atoms are generated at a fixedrate F Sim on the cell wall, at random positions on the
FIG. 3. (a) Inverted fluorescence image of the MOT taken through one of the 4-mm viewports in the BLOB with length scalebar. (b) Timing diagram for the loading curve. The loading time τ is stepped in units of 0 .
25 s, and the camera exposuretime is 10 ms. (c) Atom count (relative scale) vs loading time. Applying an exponential fit to the data yields a time constantof 1 . ± . cell surface with an inward velocity distribution knownfrom gas kinetics. The atomic trajectories are propa-gated with a 4-th order Runge-Kutta routine in whichthe atoms are subjected to the net radiation pressureforce from the six MOT beams. The actual position r ( t )of an atom determines position-dependent beam intensi-ties, beam k -vectors and the local MOT magnetic field.Due to the conical nature of the light fields, the k -vectorsof a given beam depend on position within the beam andcover an angular range that depends on the numericalaperture (NA). Along the optical axis of a beam, thetransverse FWHM increases linearly with distance fromthe ball lens, and the intensity drops off as 1/distance .Further, the polarization of each beam is locally decom-posed into three polarization components (linear, left-handed circular and right-handed circular) relative to thelocal direction of the magnetic field. Hence, the six MOTbeams together give rise to 18 radiation-pressure forcecomponents acting on the atom, where each componenthas the described dependencies on position. Saturationof the assumed J = 0 to J = 1 MOT transition (wave-length 780 nm, saturation intensity 1.6 mW/cm , upper-state decay rate 2 π × /e atom decay time is chosen to be 1.3 s, thevalue observed in our experiment.Other generic MOT parameters for the simulation inFig. 4 include a MOT agnetic field gradient of 15 G/cmalong the field axis and a laser detuning of −
12 MHzfrom the MOT transition, corresponding to a typical RbMOT. We vary the distance d of the ball lenses fromthe MOT center from 7 mm to 50 mm. To study thetransition between a regular and the ball lens MOT, weassume that the transverse intensity distributions of thebeams are Gaussians with a fixed, d -independent FWHMof 6 mm at the MOT center, as measured for the balllenses used in the experiment. The FWHM of the beamsare proportional to distance from their respective focalspots. For large d , the system approaches a regular 6-beam MOT with near-zero-NA, collimated beams. As d is reduced, the MOT gradually transitions into a ball-lensMOT with large-NA beams. The smaller d , the more thedivergence of the MOT-beam light cones affects MOTperformance. Here we restrict ourselves to the case thatall six optical axes pass through the center of the MOT,and that all lenses have the same distance from the MOTcenter.For each set of parameters we evaluate the trajectoriesof 10 to 10 thermal atoms impinging into the MOT FIG. 4. (a) Depiction of three atom trajectories. The relative speeds of the atoms are signified by the thickness of the arrows.Atom 1 is successfully trapped in the MOT. Atom 2 is not trapped because it is moving too slowly, and atom 3 is not trappedbecause its collision parameter b is too large. (b) The number of trapped atoms vs distance d of the ball lenses from the MOTcenter and I/I sat . (c) Root-mean-square (RMS) value of the incident collision parameters b of the captured atoms vs d and I/I sat . (d) RMS value of the incident speed v of the captured atoms vs d and I/I sat . region. Every atom that enters gets tagged with its initialspeed v and collision parameter b relative to the MOTcenter (see Fig. 4a). Most atoms do not become trapped(red trajectories), while some do (blue trajectory). Anyatom whose speed drops below 1 m/s, within 2 mm fromthe MOT center, is considered trapped. We have verifiedthat the exact values of these trapping criteria are notimportant. We log the root-mean-square (RMS) velocityand RMS radius of the trapped-atom cloud in the MOT,the trapped-atom number, the average photon scatteringrate of the atoms, and the RMS values of the initial speed v and collision parameter b of the atoms that becometrapped. V. RESULTS OF THEORETICAL MODELA. Survey of relative performance
In Fig. 4, we present a survey of ball-lens MOT per-formance as a function of d and single-beam intensity I .The simulated loading time is 0.9 s, the half-life for thecollision time constant of 1.3 s measured in the experi-ment. The impingement flux into the MOT cell, F Sim ,is taken to be 50 atoms per µ s. (The trapping resultsare later scaled up to the actual impingement flux.) Fig-ure 4a shows a diagram of typical atom trajectories in theMOT, two of which fail and one is successful in becom-ing trapped. Figure 4b displays the number of capturedatoms N MOT,T h vs d and I/I
Sat . From this simulationit is determined that in the experiment we are operat-ing the MOT near the lower bound in d at which theball lens MOT begins to work. At d (cid:46) d = 50 mm. The numerical data show that at low I/I
Sat our d ≈ d -values theperformance is best at lower intensities and degrades athigh intensities. This accords with the trend measuredin Fig. 3d. For completeness we also report that the tem-perature of the trapped atoms is, universally for all casesin Fig. 4, near the Doppler limit (here, 150 µ K), and thediameter of the trapped-atom cloud near 0.25 mm.In Fig. 4c it is seen that the incident collision parame-ters b of the trapped atoms drops from about 6 mm forthe regular MOT ( d = 50 mm) to about 2 mm for theextreme ball-lens MOT with d = 7 mm, with a minorvariation as a function of intensity. Figure 4d shows thatfor the standard MOT ( d = 50 mm), the RMS capturevelocity ranges between 10 m/s at low and 15 m/s athigh intensity; this range generally is as expected. Inter-estingly, for the extreme ball-lens MOT ( d = 7 mm) theRMS capture velocities increase to about 20 m/s at lowand 30 m/s at high intensity. A closer study, not shown,reveals that the d = 7 mm ball-lens MOT does not cap-ture significant fractions of the slow incident atoms. Atfirst glance this appears counter-intuitive, but we offeran explanation for this in the discussion. B. Quantitative model for the number of trappedatoms
Next we perform an order-of-magnitude comparisonbetween experimentally observed and simulated trapped-atom numbers. The atom flux impinging into the cell isgiven by F Exp = ( A/ n V ¯ v , where A is the surface area ofthe cell that is exposed to impinging thermal atoms, n V is the vapor volume density, and ¯ v = (cid:112) k b T / ( πM ) withcell temperature T = 293 K and atom mass M = 85 amuis the average thermal speed. It is invalid to set n V equalto the room-temperature equilibrium density of Rb, be-cause the MOT cell is not saturated with Rb vapor. Fora good comparison it is essential to perform an in-situreference absorption measurement, from which n V is in-ferred.For the necessary calibration of n V , we have performeda reference absorption measurement with a Gaussian-profile test beam diameter < , tuned to the MOT transition) propagat-ing through a 40-cm-long segment of the MOT cham-ber, with the MOT magnetic field off. The observedabsorption in the vapor cell was 3 . ± . n V . Inthe model, the Gaussian beam is segmented into annularrings with given intensities, radii and radial step sizes.The velocity-averaged absorption coefficient, which de- pends on intensity due to saturation of the transition,is calculated for each ring. The beam power transmit-ted through the 40-cm long sample is then found byintegration over the annular rings. The n V -value inthe calculation is then calibrated to yield the experi-mentally observed 3 . ± .
2% power loss; the result is n V = 6 . × m − . With the average thermal speedof ¯ v = 270 m/s, the impingement flux density then fol-lows to be ¯ vn V / . × m − s − . Multiplicationof this value with the cross-sectional area A of all aper-tures leading into the BLOB (eight 4-mm-diameter holesin our experiment) then yields an experimental impinge-ment flux F Exp = A ¯ vn V / . × s − .In the simulation, the impingement flux into the MOTcell is assumed to be F Sim = 5 × s − . Therefore, if thesimulation shows a trapped-atom number N MOT,Sim , thenumber of trapped atoms expected for our experiment is N MOT,Exp = N MOT,Sim F Exp F Sim = 8600 N MOT,Sim
We have run the simulation for a best estimate of ourexperimental conditions ( d = 7 . I = 2 I sat , where thesteady-state atom number is 131. The theoretically pre-dicted value for the trapped atom number then becomes N MOT,Sim = 1 . × . This number can be comparedwith the number of MOT atoms we have experimentallyobserved under good conditions, N MOT,Exp = 4 . × . VI. DISCUSSION
The picture that emerges from the combined resultsof the survey study is that extreme ball-lens MOTs, i.e.
MOTs with d (cid:46) N A (cid:38) . d = 7 mm ball-lens MOT thereforeonly captures atoms with velocities between 20 m/s and30 m/s and collision parameters less than about 2 mm. Itis particularly noteworthy that atoms slower than about15 m/s and with collision parameters less than about2 mm do not become trapped (trajectory 2 in Fig. 4a).For an atom to become trapped it has to be fast enoughthat its inertia carries it through the outer belt of “bad”radiation pressure, slow enough that it becomes trappedwithin the inner region of “good” radiation pressure, andthe trajectory of the incident atom also has to point atthe center of the MOT to within about 2 mm tolerance.In Fig. 4a only trajectory 1 meets all criteria.The agreement between experimental and simulatedtrapped-atom numbers is within about a factor of three.Considering unknowns such as local versus average ther-mal atom density, the effect of shadowing of half of the4-mm holes in the BLOB, beam aberrations, differencesbetween the assumed J = 0 → J (cid:48) = 1 MOT transitionand the actual Rb J = 3 → J (cid:48) = 4 transition, etc., thislevel of agreement is satisfactory and makes us confidentthat we have captured the essential physical principles ofthe ball lens MOT. VII. CONCLUSION
We have implemented a magneto-optical trap withina small metallic cube using 1.5-mm diameter balllenses, and we have developed a kinetic atom-trappingmodel for the ball-lens MOT. Simulated results are ingood agreement with our experimental observations andparametrize the range over which this MOT should workwell.While this first design of the BLOB was successful informing a MOT, there are several changes that we willimplement for subsequent versions. The simulations in-dicate that our ball lens distance d from the trap centerwas near the lower edge of viability. In view of Fig. 4, forfuture applications d -values in the range of 2 cm appearvery attractive, because they correspond to convenientBLOB box dimensions of about 4 cm side length. Atomnumbers in such a ball-lens MOT should be about 50%of the atom number in a similar-sized regular MOT withcollimated beams.We would be remiss if we did not mention the disad-vantages of this MOT design. Unlike standard designs,it is difficult to counter-align the beams that lie alongthe same axis, making the initial alignment more diffi- cult. Due to the dependence of the central intensity inthe MOT region on the incident angle on the ball lens,the setup has a higher sensitivity to relative beam pow-ers than a standard MOT. Nevertheless, once our firstball-lens MOT was observed, the design provided a siz-able range of stability over both the relative beam powersand angles of incidence for each ball lens.Now that the viability of a ball lens MOT has beendemonstrated, the design may be applied in experiments.The compact BLOB box provides well-defined electro-static boundary conditions and provides a platform to in-stall additional electrodes. This feature makes the BLOBdesign attractive for research on cold plasmas generatedfrom trapped-atom clouds, where uncontrolled DC elec-tric fields can be a problem. The BLOB also provides aneffective shield against radio-frequency, thermal and op-tical radiation entering the box, because the solid anglesubtended by the ball lenses from the center of the boxcan be made less than one-thousands of 4 π and the holesizes for the ball lenses are only about 1 mm in diameter.This aids in controlling AC shifts, which are a limiting ef-fect in optical-lattice optical clocks and have to be consid-ered in high-precision spectroscopy work with Rydbergatoms [10, 26]. Further, recent work has been done else-where on compact ion traps and trapped-ion laser cool-ing [27–29]. The advantages of the ball-lens MOT wouldcoincide well with some requirements of these types ofexperiments. ACKNOWLEDGMENTS
This work was supported by (NSF Grant No.1707377). We thank David Anderson of Rydberg Tech-nologies, Inc. for valuable discussions. [1] H. J. Metcalf and P. van der Straten,Laser cooling and trapping (Springer, 1999).[2] W. D. Phillips, Nobel lecture: Laser cooling and trappingof neutral atoms, Rev. Mod. Phys. , 721 (1998).[3] J. Lee, J. A. Grover, L. A. Orozco, and S. L. Rol-ston, Sub-doppler cooling of neutral atoms in a grat-ing magneto-optical trap, J. Opt. Soc. Am. B , 2869(2013).[4] E. Imhof, B. K. Stuhl, B. Kasch, B. Kroese, S. E. Olson,and M. B. Squires, Two-dimensional grating magneto-optical trap, Phys. Rev. A , 033636 (2017).[5] K. Lee, J. Kim, H. Noh, and W. Jhe, Single-beam atomtrap in a pyramidal and conical hollow mirror, Opt. Lett. , 1177 (1996).[6] J. Arlt, O. Marago, S. Webster, S. Hopkins, and C. Foot,A pyramidal magneto-optical trap as a source of slowatoms, Opt. Commun. , 303 (1998).[7] M. Vangeleyn, P. F. Griffin, E. Riis, and A. S. Arnold,Single-laser, one beam, tetrahedral magneto-optical trap,Opt. Express , 13601 (2009).[8] A. Hinton, M. Perea-Ortiz, J. Winch, J. Briggs, S. Freer, D. Moustoukas, S. Powell-Gill, C. Squire,A. Lamb, C. Rammeloo, B. Stray, G. Voulazeris, L. Zhu,A. Kaushik, Y.-H. Lien, A. Niggebaum, A. Rodgers,A. Stabrawa, D. Boddice, S. R. Plant, G. W. Tuck-well, K. Bongs, N. Metje, and M. Holynski, A portablemagneto-optical trap with prospects for atom interferom-etry in civil engineering, Philos. Trans. R. Soc. London,Ser. A , 20160238 (2016).[9] A. di Stefano, D. Wilkowski, J. M¨uller, and E. Arimondo,Five-beam magneto-optical trap and optical molasses,Applied Physics B , 263 (1999).[10] A. Ramos, K. Moore, and G. Raithel, Measuring therydberg constant using circular rydberg atoms in anintensity-modulated optical lattice, Phys. Rev. A ,032513 (2017).[11] A. Golovizin, E. Fedorova, D. Tregubov, D. Sukachev,K. Khabarova, V. Sorokin, and N. Kolachevsky, Inner-shell clock transition in atomic thulium with a smallblackbody radiation shift, Nat. Commun. , 1724(2019).[12] Y.-L. Xu and X.-Y. Xu, Analysis of the blackbody- radiation shift in an ytterbium optical lattice clock, Chi-nese Physics B , 103202 (2016).[13] I. Ushijima, M. Takamoto, M. Das, T. Ohkubo, andH. Katori, Cryogenic optical lattice clocks, Nature Pho-tonics , 185 (2015).[14] V. V. Flambaum, S. G. Porsev, and M. S. Safronova, En-ergy shift due to anisotropic blackbody radiation, Phys.Rev. A , 022508 (2016).[15] K. Beloy, X. Zhang, W. F. McGrew, N. Hinkley, T. H.Yoon, D. Nicolodi, R. J. Fasano, S. A. Sch¨affer, R. C.Brown, and A. D. Ludlow, Faraday-shielded dc stark-shift-free optical lattice clock, Phys. Rev. Lett. ,183201 (2018).[16] G. Gabrielse, P. Larochelle, D. Le Sage, B. Levitt, W. S.Kolthammer, R. McConnell, P. Richerme, J. Wrubel,A. Speck, M. C. George, D. Grzonka, W. Oelert, T. Se-fzick, Z. Zhang, A. Carew, D. Comeau, E. A. Hessels,C. H. Storry, M. Weel, and J. Walz (ATRAP Collabo-ration), Antihydrogen production within a penning-ioffetrap, Phys. Rev. Lett. , 113001 (2008).[17] J.-H. Choi, B. Knuffman, X. H. Zhang, A. P. Povilus, andG. Raithel, Trapping and evolution dynamics of ultracoldtwo-component plasmas, Phys. Rev. Lett. , 175002(2008).[18] S. Schmid, A. H¨arter, A. Frisch, S. Hoinka, and J. H.Denschlag, An apparatus for immersing trapped ions intoan ultracold gas of neutral atoms, Review of ScientificInstruments , 053108 (2012).[19] EdmundOptics, Understanding ball lenses.[20] M.-S. Kim, T. Scharf, S. M¨uhlig, M. Fruhnert, C. Rock-stuhl, R. Bitterli, W. Noell, R. Voelkel, and H. P. Herzig,Refraction limit of miniaturized optical systems: a ball- lens example, Opt. Express , 6996 (2016).[21] M. Sasaki, T. Kurosawa, and K. Hane, Micro-objectivemanipulated with optical tweezers, Appl. Phys. Lett. ,785 (1997), https://doi.org/10.1063/1.118260.[22] T. Numata, A. Takayanagi, Y. Otani, and N. Umeda,Manipulation of metal nanoparticles using fiber-opticlaser tweezers with a microspherical focusing lens,Japanese Journal of Applied Physics , 359 (2006).[23] V. I. Yudin, A. V. Taichenachev, M. V. Okhapkin, S. N.Bagayev, C. Tamm, E. Peik, N. Huntemann, T. E.Mehlst¨aubler, and F. Riehle, Atomic clocks with sup-pressed blackbody radiation shift, Phys. Rev. Lett. ,030801 (2011).[24] W. Demtr¨oder, Laser Spectroscopy (Springer, 2008).[25] D. A. Steck, Rubidium 85 D line data, Available on-line at http://steck.us/alkalidata (Revision 2.1.6, 20September 2013).[26] J. W. Farley and W. H. Wing, Accurate calculation ofdynamic stark shifts and depopulation rates of rydbergenergy levels induced by blackbody radiation. hydrogen,helium, and alkali-metal atoms, Phys. Rev. A , 2397(1981).[27] B. J. McMahon, C. Volin, W. G. Rellergert, and B. C.Sawyer, Doppler-cooled ions in a compact reconfigurablepenning trap, Phys. Rev. A , 013408 (2020).[28] Z. Andelkovic, R. Cazan, W. N¨ortersh¨auser, S. Bharadia,D. M. Segal, R. C. Thompson, R. J¨ohren, J. Vollbrecht,V. Hannen, and M. Vogel, Laser cooling of externally pro-duced mg ions in a penning trap for sympathetic coolingof highly charged ions, Phys. Rev. A , 033423 (2013).[29] J. F. Goodwin, G. Stutter, R. C. Thompson, and D. M.Segal, Resolved-sideband laser cooling in a penning trap,Phys. Rev. Lett.116