Performance-optimized components for quantum technologies via additive manufacturing
S H Madkhaly, L A Coles, C Morley, C D Colquhoun, T M Fromhold, N Cooper, L Hackermüller
PPerformance-optimized components for quantum technologies via additivemanufacturing
S H Madkhaly,
1, 2
L A Coles, C Morley, C D Colquhoun, T M Fromhold, N Cooper, ∗ and L Hackerm¨uller † School of Physics and Astronomy, University of Nottingham, University Park, Nottingham, NG7 2RD, UK Department of Physics, Jazan University, Jazan, Kingdom of Saudi Arabia Added Scientific Ltd, Unit 4, Isaac Newton Centre, Nottingham, NG7 2RH, UK
Novel quantum technologies and devices place unprecedented demands on the performance ofexperimental components, while their widespread deployment beyond the laboratory necessitatesincreased robustness and fast, affordable production. We show how the use of additive manu-facturing, together with mathematical optimization techniques and innovative designs, allows theproduction of compact, lightweight components with greatly enhanced performance. We use suchcomponents to produce a magneto-optical trap that captures ∼ × rubidium atoms, employingfor this purpose a compact and highly stable device for spectroscopy and optical power distribution,optimized neodymium magnet arrays for magnetic field generation and a lightweight, additivelymanufactured ultra-high vacuum chamber. We show how the use of additive manufacturing enablessubstantial weight reduction and stability enhancement, while also illustrating the transferability ofour approach to experiments and devices across the quantum technology sector and beyond. I. INTRODUCTION
While the growing range of quantum technologies of-fers great promise for both fundamental research [1–3]and practical applications [4–10], their realization placesever greater demands on component performance. Inparticular, the production of portable quantum sensors[11–17] will require compact, lightweight components ca-pable of operating in a range of harsh environmentalconditions; compactness, stability and robustness will becritical for such components and conventional, lab-basedsystems are not appropriate [18, 19].The rapid transition of quantum technologies from re-search experiments to commercial devices also opens upspace for innovation and the use of unconventional imple-mentations of known techniques. We show how additivemanufacturing (AM) can be used to create performance-optimized components, unimpeded by the constraints ofconventional manufacturing methods, while at the sametime allowing quick and easy production of customizedcomponents and thus greatly accelerating the prototyp-ing and testing of novel component designs. The ap-proach is generalizable to a wide range of experimen-tal components and will transform applications as di-verse as miniaturized optical devices, vacuum systemsand magnetic field generation. Our work complementsprevious studies of integrated laser sources [20–22] andminiaturized vacuum chambers [23] and expands prelim-inary studies of the utility of additive manufacturing inthe setting of quantum technologies [24, 25]. Specifically,we demonstrate a new approach to experimental designin free-space optics, where the overwhelming majority ofthe adjustable components are eliminated and most ofthe optical elements are mounted in a monolithic, ad- ∗ [email protected] † [email protected] ditively manufactured mount within pre-aligned push-fitslots. This new approach offers improvements in stabil-ity as well as significant reductions in cost and in size,weight and power consumption (SWAP). We apply thistechnique to create a stable mount for an optically iso-lated laser source and a compact and highly stable appa-ratus for optical power distribution and laser frequencystabilization.The described components are combined with an AMultra-high vacuum chamber [26] to form a magneto-optical trap (MOT), which captures 2 × cold Rbatoms. The MOT is the starting point for nearly all cold-atom based experiments and quantum technologies [27].The magnetic fields required for our MOT are producedusing an array of neodymium magnets in a custom-builtAM mount, offering significant SWAP reductions overconventional MOT coils. An optimization algorithm wasdeveloped to determine the placement of the permanentmagnets in order to accurately replicate the conventionalanti-Helmholtz field used in a MOT; the algorithm istransferable to the recreation of other field structures.Our results demonstrate the power of AM to directly im-plement the outcome of an optimization process, withoutreference to traditional manufacturing constraints. Mea-surements of the atomic lifetime within the MOT areused to place an upper limit on the background pres-sure in the AM vacuum chamber of ∼ × − mbar. Anoverview of the MOT system is given in figure 1.The remainder of this paper is organized as follows:the overall setup is explained in Section II, including adescription of the laser sources used (Section II A), fol-lowed by a discussion of the compact AM spectroscopyand power distribution system (Section II B). The place-ment of the ferromagnets used for MOT field generationand corresponding optimization algorithm are described(Section II C) and a brief overview of the AM vacuumchamber is given (Section II D). The performance of theMOT is characterized in Section III. a r X i v : . [ phy s i c s . a t o m - ph ] F e b Laser drivers
Ionpump
DFB ChamberMagnetsCSPD Rb dispenserTo beatlockDFBPowersupply
BCA
FIG. 1. Overview of the complete setup, showing 3D printed and optimized components in the areas marked with dashedboxes A, B, and C. A indicates the distributed feedback lasers (DFBs) used as master light sources, B indicates the compactspectroscopy and power distribution apparatus (CSPD), and C indicates the trapping apparatus including the AM UHVchamber, optimized permanent magnet arrays and a set of self-aligning AM fiber outcoupler mounts. The setup takes up avolume of 0.15 m and the custom parts indicated have a cumulative mass of 3.2 kg. II. SYSTEM ARCHITECTURE ANDCOMPONENTSA. Laser sources
With the atomic structure of alkali metal atoms inmind, in particular Rb - see Fig. 4(a-c), the typicalroles of lasers employed for magneto-optical trapping areused here [27]: ‘reference’ and ‘repumper’ lasers, eachfrequency-stabilized directly to an atomic transition viasaturated absorption spectroscopy [28, 29], and a ‘cooler’laser that is stabilized at a fixed frequency offset fromthe reference laser via an optical beat signal [30].Fig. 1(A) shows the distributed feedback lasers(DFBs) used as our reference and repumper lasers;DFBs were chosen for their stability, large mode-hopfree tuning range and compact size. Specifically anEagleyard laser diode is used with an output power of80 mW at 780 nm. Although this is sufficient to producea MOT, a tapered amplifier (Toptica TA-100, coolerlaser), which provides up to 1 W of output power, isalso used to facilitate further experiments and providesthe ‘cooler’ light for our MOT. The DFB packagesare encased in an AM mount with an optical isolator(Isowave I-780-LM), as seen in Fig. 2. The opticalisolator has an external diameter of 4 mm and a depth of ∼ .
10 mm
FIG. 2. Photograph of a butterfly-packaged DFB laser andoptical isolator (indicated with the dashed rectangle) in anAM mount. heron DRV200-A-200 compact driver board, which pro-vides diode currents of up to 200 mA and allows currentmodulation at up to 6 MHz.
B. Laser spectroscopy and optical powerdistribution
To enhance laser stability, all of the optics required forlaser stabilization via vapor cell spectroscopy [32] andoptical beat locking [30, 33], as well as those neededto distribute the optical power of the cooler and re-pumper lasers appropriately between the MOT beams,were secured in a custom-designed optics mount withfew adjustable elements. This mount, designated the‘compact spectroscopy and power distribution’ apparatus(CSPD), uses fixed beam paths and pre-aligned compo-nents (via push-fitting into specially designed slots in theAM mount) to eliminate the need for adjustment screwsor tunable mirror-mounts. The result is a robust andstable setup — see Fig. 1(B). Like the laser mounts, theCSPD was manufactured from Formlabs ‘Rigid Resin’via an SLA process. The CSPD is shown in Fig. 3 andhas dimensions of 128 × ×
12 mm, and a mass of 84 g.Rigid Resin was selected as its build material based ona thorough assessment of the physical properties of theavailable build materials — see supplementary materialfor more details. The CSPD design uses the fewest op-tical elements possible, in order to enhance stability andreduce cost and SWAP.To improve stability, the optical beam paths in theCSPD are kept as short as possible and the number ofreflections undergone by each beam is also minimized.Each beam that is fiber-coupled for transmission to theMOT undergoes a maximum of 2 reflections in this ar-rangement, as does each of the two beams combined toproduce the optical beat signal. The maximum pathlength for any of these beams is 120 mm. The (lessalignment-sensitive) saturated absorption spectroscopybeams each undergo four reflections, with a maximumoptical path length of 290 mm.To illustrate the importance of this, consider the fol- lowing simple model of a beam path subject to experi-mental imperfections. The expected positional deviationof a beam from its target at the end of an optical beampath is given by∆ r = "X i (2∆ φL i ) / , (1)where the sum is taken over all reflective componentsin the beam path, which are all assumed to have inde-pendent alignment inaccuracies of magnitude ∆ φ . Thevalues of L i are the remaining path lengths between eachcomponent and the end of the optical beam path, and wehave applied the small angle approximation tan θ ≈ θ .We can now compare the CSPD with a more conven-tional setup. In the CSPD, prior to fiber coupling thecooler beam undergoes 2 reflections with L = 30 mmand L = 90 mm, yielding ∆ r = 190∆ φ mm. By con-trast, a more conventional system might involve say tenreflective components, roughly equally spaced along a 1 mpath length. In this case we find that ∆ r = 3920∆ φ mm,more than 20 times the equivalent value for the CSPD.Each of the optics slots within the CSPD was designedto leave clearance in the center of the optical component;this prevents direct contact between the mount and thecentral part of the optical element on which the beamimpinges, thus ensuring that device performance is notdegraded by scuffing of the optical surfaces when com-ponents are inserted. Slots for cube beamsplitters haverounded recesses in each corner (similar to an undercut)— see Fig. 3(d). This improves the accuracy of the push-fit alignment by ensuring that cube position/orientationis controlled via extended contact with defined flat sur-faces that can be built accurately using the SLA pro-cess. This is important because AM methods are notwell-suited to producing sharp, internal features, such asthe corners of the beamsplitter slots.The layout of the optics and optical paths within theCSPD were designed to minimize the number of opti-cal components required. A schematic of the beam pathsused in the CSPD is shown in Fig. 3(c). The cooler beamfirst passes through a λ /2 wave plate that controls thedistribution of the power between the MOT beams andthe spectroscopy setup, which happens at the polariz-ing beamsplitter marked ‘1’. The reflected componentis divided among the three output fiber couplers whichprovide the MOT beams. This happens at the two non-polarizing beamsplitters immediately to the right of po-larizing beamsplitter ‘1’. The first of these has a splittingratio of 67/33, while the second splits the power 50/50.The repumper beam also reaches polarizing beamsplit-ter ‘1’ via a wave plate to control power distribution.In this case, the transmitted polarization component isdistributed among the MOT beams.The reflected component of the repumper beam andthe transmitted component of the cooler beam then passthrough a half wave plate fixed at 45 ◦ relative to the po-larizing beamsplitters. Thus, when they are combined CoolerIn (a) (b)
Fiber couplerHalf wave platePolarizingbeamsplitterAspheric lensLinear polarizerPhotodiodeNon-polarizing beamsplitterRepumper beamCooler beamReference beam
OutOut A B C
321 Vapor cell
ReferenceInRepumperIn Out
Mirror (c)
20 mm 20 mm (d)
FIG. 3. The compact spectroscopy and power distribution apparatus. (a) A 3D render of the mount. The holes that can beused as fiber inputs or outputs are indicated. (b) A photograph of the CSPD with optics, a reference cell and fibers adheredto the appropriate positions. (c) A schematic of the optics layout in the CSPD, and how each input laser beam is directedthrough it. The purple beams represent reference light; the orange beams cooler light and the green beams repumper light. (d)Close-up of a beamsplitter slot. The rounded recesses on the edges/corners are there to prevent scuffing of the optically activesurfaces and to improve push-fit alignment accuracy, respectively. with the reference beam at polarizing beamsplitter ‘2’,the cooler light is reflected and the repumper light trans-mitted. The component of the reference light transmit-ted at beamsplitter ‘2’ is mixed with the cooler light onthe same pathway by the polarizing filter, again fixed at45 ◦ relative to the polarizing beamsplitters, such that anoptical beat signal can be produced on photodiode ‘A’.This is used to stabilize the frequency difference betweenthe cooler and reference lasers via feedback to the diodecurrent of the cooler laser.This leaves the repumper light transmitted at beam-splitter ‘2’ and the component of the reference light re-flected at beamsplitter ‘2’. These enter what is a conven-tional saturated absorption spectroscopy setup for onelaser — the difference here is that two beams overlap onthe same spatial path in orthogonal polarizations. Af-ter re-emerging from the spectroscopy setup, they areultimately separated onto their respective photodiodesby the polarizing beamsplitter ‘3’. To generate an errorsignal suitable for feedback stabilization of the laser fre-quencies, the laser currents are sinusoidally modulatedand the modulation signals are combined with the pho- todiode outputs using analog multipliers — a standardpractice in laser stabilization [34].By sharing the same spatial path in the vapor cellthe reference and repumper beams influence each other’sspectroscopy signals via optical pumping effects [35].Provided that both lasers are to be stabilized simulta-neously this does not prove detrimental to the operationof the device, but rather increases the strength of thelocking signals (see supplementary material for more de-tails).The design of the CSPD allows fixed-focus fiber colli-mators to be inserted directly into the fiber access ports(see Fig. 3) and fixed in place using epoxy once aligned.However, the stability of standard fiber-optic connectorswas found to be insufficient to allow long term opera-tion without adjustable components. This could be fixedby a custom fiber mount. In principle, this device canbe extended to unite the laser source housing with thepower distribution and spectroscopy optics, thus elimi-nating the need for any external optics (or an associatedbaseplate/breadboard) and providing all of the light gen-eration requirements for a MOT in a single, stand-alone, E rr o r S i g n a l ( V ) -0.04-0.0200.020.04 Relative Frequency (MHz) -300 0 300
F’=1F=3F=2F’=2121MHz63MHz29MHz F’=3F’=4 Rb δ δ R e pu m p e r C oo l e r (b)(c)(a) (d) S i g n a l A m p li t ud e ( V ) Relative Frequency (MHz) -60 0 60 120
Relative Frequency (MHz) S i g n a l A m p li t ud e ( V ) FIG. 4. Laser locking frequencies relative to Rb D transitions (a), and the corresponding saturated absorption spectroscopyfeatures of cooler (b) and repumper (c) beams. While (d) shows the corresponding error signal generated from the saturatedabsorption spectroscopy optics in the CSPD for the reference beam, as a function of relative laser frequency. The form of thesignal can be seen to remain consistent and appropriate for feedback stabilization of the laser frequency despite substantialvariations in environmental temperature. A horizontal offset has been added to improve visibility. fiber-coupled device. Thermal stability and resistance tests. - Temperaturefluctuations are a major source of drifts in optical align-ment, even in a temperature-stabilized lab environment;outside the lab these problems become much more sig-nificant. To test the thermal stability of the CSPD, theenvironmental temperature was adjusted between 288 Kand 298 K, while monitoring key parameters of the sys-tem.Figure 4 shows the error signal generated for feedbackstabilization of the reference laser frequency at a rangeof environmental temperatures within this window. Notethat the results for different temperatures are intention-ally offset relative to one another to improve visibility.It can be seen from the figure that the overall form ofthe signal is unaffected by beam misalignment due totemperature variations; it remains appropriate for laserstabilization over the entire temperature window. Thechange in signal amplitude occurs due to an increasedvapor pressure in the reference cell at higher tempera-tures.One experimental parameter that is extremely sensi-tive to beam misalignment is the coupling efficiency oflight into optical fibers. The optical power coupled intothe fibers at the outputs of the CSPD was monitoredand only 10 % power variation was observed over the en-tire 10 K temperature window, with a maximum relativepower variation coefficient of 0.02 K − . This result repre-sents a significant advance over standard lab optics andoptomechanics, where typically a change of ∼ C. Magnetic field generation
The efficient creation of a linear MOT field, prioritizingboth field fidelity and power consumption, is an impor-tant consideration for a portable apparatus. In conven-tional systems, the required fields are generated by coilsdrawing many watts of power. The apparatus developedhere instead utilizes an array of ferromagnets to gener-ate MOT-suitable magnetic fields, thus eliminating thepower consumption of the coils entirely. This techniquehas not traditionally been employed for SWAP reductionbecause many experiments require the magnetic fieldsto be briefly extinguished following the collection of anatomic cloud. However, we show that even in such casesit is still possible to augment MOT coils with permanentmagnet arrays, and that doing so reduces time-averagedpower consumption by a factor of 1 / (1 − T M ), where T M is the fraction of the experimental cycle time for whichthe magnetic field should be present — see Supplemen-tary Material for full details.In order to open up these experimental possibilities itis necessary to design a ferromagnetic array that pro-duces the same field distribution as conventional MOTcoils. This can be done via well established numeri-cal optimization methods [37] and computer science al-gorithms [38] allowing the optimal placement of ferro-magnets to be determined a priori for any given appara-tus, thereby greatly reducing testing and manufacturing FIG. 5. A 3D model of the vacuum chamber seen in FIG. 1,without the lattice structure. The blue rings attached to thetop and bottom of the chamber represent the permanent mag-net arrays. times. Neodymium magnets are manufactured in a va-riety of standardized shapes and strengths. This makesthem an ideal choice for an optimization algorithm de-signed to determine the optimal placement of a set ofmagnetized voxels on a predetermined initial grid to cre-ate a required field profile, allowing multiple magnet con-figurations to be designed and tested to establish theirsuitability before manufacture. Such algorithms are fre-quently used in the context of magnetic resonance imag-ing (MRI) [39] in the process of shimming, which em-ploys optimization algorithms to inform the placement ofpermanent magnets or current carrying wires to removeunwanted spherical harmonic contributions in a given re-gion. These techniques for passive shimming [40] wereexploited in the design of the ferromagnet array. A voxelof volume dV , magnetized entirely along z with strength M z , at a position Q = ( ρ, α, ψ ) produces a scalar poten-tial at a position P = ( r, θ, φ ) given by,Ψ = − d V M z πρ ∞ X n =0 n X m =0 (cid:15) m ( n − m + 1)!( n + m )! P mn +1 (cos α ) (cid:18) rρ (cid:19) n P mn (cos θ )cos( m ( φ − ψ )) (2)where P mn are the associated Legendre polynomials and (cid:15) m is the Neumann factor defined as (cid:15) m =0 = 1 and (cid:15) m> = 2. This can be related to the magnetic fields by B = −∇ Ψ. From this, a matrix equation can be formedrelating the spherical harmonic contributions from eachvoxel and its magnetization to the required overall spher-ical harmonics, A ( z, (1 , . . . A ( z,N ) (1 , A ( z, ( n max , m max ) . . . A ( z,N ) ( n max , m max ) × m ... m N = b z (1 , b z ( n max , m max ) . (3) Here the matrix contains A ( z,i ) ( n, m ), the contributionfrom the i th pixel to the n, m spherical harmonic modeto the magnetic field in the z direction. This is thenmultiplied by the vector containing the magnetization ofeach voxel, m i , to be optimized. The elements of thisvector can take values of either m i = 1, for the mag-netization directed entirely along positive z , m i = − z ,or m i = 0 for no magnetic material required. The re-sult of the matrix equation in (3) is the vector of totalcontributions from each ( n, m ) spherical harmonic mode, b z ( n, m ), which are set by the user to constrain the op-timization. All that remains is therefore to define the b elements. The magnetic field for a MOT is well describedby first order spherical harmonics, therefore these can betargeted to produce the required linear fields. In theorythis technique could be expanded to any required field,provided it can be decomposed into spherical harmoniccomponents. This is then similar to the standard form ofa linear optimization problem [38], as utilized previouslyin [41]. Thus, the method employs the spherical har-monic decomposition from the process of shimming toproduce a linear optimization problem to constrain thefield to the desired form. This is then combined with anoptimization function that seeks to maximize the contri-bution of the magnet strength to the field, resulting in afinal placement of magnets, which produces the desiredfield while acting to reduce the required M z .The voxels are then defined as an assortment of readilyavailable pre-manufactured neodymium magnets. Thechosen magnets can form initial placement grids tailoredto the experimental apparatus, based on their individualsizes and the required spacing between voxels (see Fig. 6).Applying the optimization method then determines therequired magnetization, m i of each voxel, and thereforethe required positions and orientations of the magnets.For this specific setup, the initial grids were designed toallow optical access, though in theory any distributionof voxels could be defined. Examples of initial and op-timized grids are shown in Fig. 6. Figure 6(a) showsthe initial grid for cylindrical voxels of radius 6 mm anddepth 3 mm, while Fig. 6(b) illustrates the initial gridfor cylindrical voxels of radius 6 mm and depth 6 mm.The optimized structures for each case are then shown inFigs 6(c) and (d), respectively.The design shown in Fig. 6(d) was chosen for the mag-netic field generating structure, utilizing N42 strengthgrade neodymium magnets, and AM polymer mountsto position the magnets. The choice of final design wasbased on both the fidelity of the resulting field structureand the practical consideration that this design allowedthe magnet rings to be centered to the CF40 viewportson the vacuum system via a simple push-fit mechanism,thus reducing the likelihood of any misalignment. Therapid prototyping provided by AM methods allows swiftmanufacture and application to the experiment.The resulting fields, calculated using the derivatives ofequation (2) for the optimized magnet arrangement, are O p ti m i s e d G r i d s I n iti a l G r i d s FIG. 6. Grids of the possible positions for two different types of magnetized voxels: (a) diameter of 6 mm, depth of 3 mm and(b) diameter of 6 mm, depth of 6 mm. The optimized arrangements to produce a MOT field are shown in (c) and (d) for theinitial grids of (a) and (b), respectively. The geometry in (d) was used as a basis for the magnet rings shown in Fig. 5, as theincreased distance between the rings and the trapping region was necessary to accommodate the vacuum chamber.FIG. 7. (a) Graph showing the similarities between the numerically calculated fields produced by the optimized magnetstructure (circles and squares) of Fig. 6(d) and target magnetic fields (lines) for B x along the x -direction (blue) and B z alongthe z -direction (red). (b) Comparison between the numerically calculated and the experimentally measured magnetic field atthe center produced by a single ring of magnetic voxels vs. distance from the ring. compared to the target field and experimentally mea-sured fields in Fig. 7. Figure 7(a) illustrates good agree-ment between the target field and the numerically calcu-lated field produced by the optimized structure of 6(d),for the B x and B z components along the x and z axesrespectively. Figure 7(b) then illustrates the agreementbetween the field formed by one ring (measured experi-mentally using a Hall probe system) and the fields pro-duced by the same ring calculated numerically. Figure7(b) shows good agreement between the numerically cal- culated and experimentally obtained fields, with the ex-ception of the region closest to the magnets. This smalldivergence most likely can be attributed to a slight mis-alignment of the Hall probe translation assembly rela-tive to the magnet array. Thus, the algorithm providesa powerful method of determining a magnetic structuretailored to a given apparatus, which is capable of pro-ducing a wide variety of fields accurately. FIG. 8. Fluorescence image of the cloud of cold Rb atomscaptured by our MOT, which was produced using the opti-mized components described herein.
D. Vacuum system
The central component of the vacuum system is an ad-ditively manufactured octagonal chamber carrying eightCF16 ports and two CF40 ports, as shown in Fig. 5.This chamber and its production are fully described in[26]; here we give a brief summary. The mass of thechamber (excluding externally attached components) is245 g, considerably less than that of equivalent commer-cial chambers, which typically weigh ∼ < − mbar was achieved, asmeasured via the ion pump current. III. MAGNETO-OPTICAL TRAPPING
The components described above were used to producea magneto-optical trap (MOT), capturing up to 2.5 × Rb atoms.The light used to form the MOT consists of threeretro-reflected laser beams produced by the DFB laser ×10 A t o m N u m b e r Time (s)
FIG. 9. MOT loading curves based on fluorescence data forvarious values of Rb dispenser current. Colored lines show rawdata and black lines are fits to the data based on equation (4). systems and tapered amplifier. The cooler and the re-pumper beams are equally distributed via the CSPD intothree optical fibers that deliver the light to the cham-ber. Each MOT beam contains 15 mW of cooler lightand 4.5 mW of repumper light, with a beam a diameterof 1.2 cm. The maximum total intensity of the six beamsis ∼
40 mW/cm . The MOT is generated in a magneticfield gradient of 12 G/cm provided by the ferromagnetarray. A. Atom number measurement and pressure limitdetermination
For an estimate of the atom number, fluorescence lightfrom the trapped atoms was collected onto a photodiodeusing a plano-convex lens – see supplementary materialfor details.Fig. 9 shows MOT loading curves obtained for vari-ous values of Rb dispenser current from 2.20 A to 2.75 A.The loading curves enable a direct measurement of thepressure in the trapping region under certain conditions[45, 46]. For each loading curve the atom number withrespect to time, N , is fitted to the form N ( t ) = RL (1 − e − Lt ) (4)where the loading rate R and single-body loss rate L areused as free parameters.This description neglects two-body and higher orderloss processes, and is therefore only valid in the limit oflow density of trapped atoms. In order to remain in thislimit, the loading profile taken with the lowest dispensercurrent (2.2 A) is used to determine an upper limit onour background pressure.A fit to this loading profile, according to equation (4),is shown in Fig. 9. The extracted single-body loss rateis L = (0 . ± − ). This single-body loss rate Species Pressure ( × − mbar)H ± ± ± is the total loss rate resulting from collisions with allthermal background gas species present, including ther-mal Rb atoms. A pressure estimate based on this figuretherefore represents the overall pressure in the trappingregion, including the contribution from the intentionallyintroduced Rb atoms. Since our measurements cannotdistinguish the different partial pressures of individualbackground species, our result represents an upper limiton the pressure of unwanted gas species, rather than adirect measurement of it.The resulting pressure estimate depends on the as-sumed composition of the residual background gas. Theloss coefficients per unit pressure for various commonbackground gases have been measured in Ref. [45]. Weuse these coefficients to estimate the upper bound on thepressure in the trapping region under the assumption ofvarious different dominant background gas species. Theresults are displayed in Table I. The background gas ismost likely a mixture of the species listed, placing theresulting pressure limit somewhere within the range ofvalues presented. These results represent an upper limiton the pressure of non-Rb species in the chamber and aretherefore consistent with the results of the ion pump cur-rent readings. While the pressure limit imposed by thismeasurement is much less stringent than that obtainedvia the ion pump current reading, it nevertheless repre-sents an independent confirmation that the pressure is farinto the high-vacuum regime. The result is particularlyrelevant for the future use of printed vessels in quantumtechnologies, opening the door for future highly complexand compact printed chambers with designs not realiz-able by conventional methods. IV. CONCLUSION
We have demonstrated a fundamentally new approachto experimental component design that exploits the po-tential of AM techniques to offer greatly improved perfor-mance. AM allows direct implementation of simulationresults and optimization processes. Our results illustratethe remarkable potential of AM to facilitate experimentalresearch in all areas currently relying on free-space op-tics, tailored magnetic fields, or high vacuum apparatus. The demonstrated techniques enable rapid prototypingalongside improvements in stability and substantial re-ductions in cost and SWAP parameters — many compo-nent weights are reduced by 70 - 90 % compared to stan-dard equivalents. One important area of application isthe field of cold atom experiments and portable quantumtechnologies based on magneto-optical trapping. AMcomponents will allow widespread use of these technolo-gies, including in field applications and space-borne ex-periments.The use of AM to produce these components opensmany future avenues of research. Optimum thermo-mechanical performance can be achieved via the free-dom AM offers when considering material distribution,for example enabling the use of variable-density latticing[47, 48]; optical frameworks such as the CSPD could bedesigned so that thermal expansion has minimal effecton the key alignment variables of the components. Lat-tice structures can also in principle be designed to iso-late or damp specific frequencies of mechanical vibration[49]; this will be a useful feature in many experiments,as there are generally specific, narrow frequency rangeswithin which an experiment or device is most sensitiveto environmental noise.For AM vacuum apparatus, one promising avenue ispart consolidation, in which a substantial part of a cus-tom vacuum system could be printed as a single piece.This eliminates the overwhelming majority of the vac-uum joints, further reducing SWAP parameters, increas-ing mechanical stability and reducing the susceptibilityof the system to leaks. Another option is to exploit AMto produce high-surface area elements such as small-scalelattices or fractal surfaces. These could be coated in re-active materials to produce enhanced getter pumps forpassive pumping in portable devices.Our demonstrated design of customized ferromagneticarrays paves the way for progress beyond the standardmagnetic field distribution used for magneto-optical trap-ping; systematically tailored magnetic field shapes can beproduced in order to optimize selected experimental pa-rameters, such as the total atom number or loading rate.While AM techniques have only just started to be usedin the context of quantum technologies, they hold thepromise of providing a clear pathway for miniaturizationand expanded functionality.
V. ACKNOWLEDGEMENT
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1, 2
L A Coles, C Morley, C D Colquhoun, T M Fromhold, N Cooper, ∗ and L Hackermüller † School of Physics and Astronomy, University of Nottingham,University Park, Nottingham, NG7 2RD, UK Department of Physics, Jazan University, Jazan, Kingdom of Saudi Arabia Added Scientific Ltd, Unit 4, Isaac Newton Centre, Nottingham, NG7 2RH, UK ∗ [email protected] † [email protected] a r X i v : . [ phy s i c s . a t o m - ph ] F e b aterial Supplier ElasticModulus(GPa) GlasstransitionTemp. ( ◦ C) Thermalexpansioncoefficient( α )( µ m/m)/ ◦ C ReferencePolycarbonate(PC) Ultimaker 2.13 147 69 [1–4]Polylactic Acid(PLA) Ultimaker 2.35 60 68 [1, 2]AcrylonitrileButadieneStyrene (ABS) Ultimaker 1.62 105 90 [1–4]Co-polyester(CPE) Ultimaker 1.54 82 70 [1, 2]Photopolymer(rigid) resin(White) Formlabs 4.1 88(heatdeflection) 53 [5]Photopolymer(tough) resin(Green) Formlabs 2.7 45(heatdeflection) 119.4 [6]
TABLE I. Physical and thermal properties of candidate AM build materials for the CSPD[7–9].
MATERIAL SELECTION
Different 3D printing materials were tested to ensure their relevance and compatibility withoptical systems. Formlabs ‘Rigid Resin’ was chosen as the build material for the DFB hous-ing, lens tubes mounts, and CSPD on the basis of its low coefficient of thermal expansionand high elastic modulus, which offer improved alignment stability when compared to al-ternative build materials. Table I details physical and thermal properties of the selection ofbuild materials considered. The material from which our system parts are 3D printed ‘rigidresin’ is shaded in grey.
OPTICAL PUMPING EFFECTS
As described in Section 2.2 of the main article, the use of overlapping repumper and referencebeams in the spectroscopy cell of the CSPD results in a modification of the spectroscopysignals. This means that accurate frequency stabilization for either laser requires both lasersto be frequency stabilized. However, it also enhances the amplitude of the spectroscopic andstabilization signals generated by the CSPD, improving signal to noise and consequentlyenabling more stable locking — particularly for the repumper laser. Figure 1 shows the‘error signals’ used for feedback stabilization of the laser frequencies, generated by modulat-ing the laser current and then combining the spectroscopic and current modulation signalsvia an analog multiplier. The amplitude enhancement resulting from the presence of thesecond laser on the same spatial path can clearly be seen in each case, and results in morepronounced locking signals and steeper lock-points.2 rr o r S i g n a l ( V ) − − − E rr o r S i g n a l ( V ) Relative Frequency (MHz) -185 0-370 185 370
Relative Frequency (MHz) -90 0-180 90 180 (a) (b)
With referenceRepumper only
RefErr2ErrRef2 -0.01-0.0050
Reference onlyWith repumper
FIG. 1. Error signals resulting from saturated absorption spectroscopy (with laser current mod-ulation and phase-sensitive detection) of the Rb D2 line | F = 2 i → | F = 1 , , i ‘repumper’transition (a) and Rb | F = 3 i → | F = 2 , , i ‘reference’ transition (b). The red curves representthe signals generated when only the laser performing the spectroscopy was present in the vapourcell, while the blue lines represent the signals obtained when a beam resonant with the other tran-sition spatially overlapped with this beam in the same vapour cell. As can be seen from the figures,optical pumping effects result in an enhancement of the error signal amplitude — particularly forthe laser addressing the repumper transition. HYBRID MAGNETIC FIELD GENERATION — DETAILED DERIVATION
In section II C of the main article, we claim that augmentation of coils with permanentmagnets can reduce the time-averaged power requirements for magnetic field generation bya factor equal to / (1 − T M ) compared to using coils alone, where T M is the fraction of theexperimental cycle time for which the magnetic field must be active. Here, we provide a fullderivation of this result.The strength of the magnetic field generated by a coil is proportional to the current throughit, I , while the power dissipated in that coil is equal to I R , with R the coil’s resistance.We neglect inductive effects because in practice experimental cycle times are usually suffi-ciently long to make them negligible as a source of power consumption, while from a purelytheoretical perspective they do not necessarily have to result in a net energy loss from anappropriately designed system. It follows that the power dissipation in a set of coils isequal to RI , and hence also to CB , where B is a scalar proportional to the magnetic fieldstrength produced by the coils and C is a constant coefficient dependent on the exact systemparameters.Let us now define a fraction, F , of the required magnetic field that is to be produced bya ferromagnetic array, with the remaining fraction, − F , being produced by coils. Weassume that the fields are of the same form and consider only their relative magnitudes.The power consumption while the field is to be on is now equal to C (1 − F ) B . However,while the field is required to be off the coils must be used to cancel the field component of thepermanent magnets by running current in the opposite direction. The power consumptionfor this process is clearly now equal to CF B .We now define the fraction of the experimental cycle for which the MOT fields are to beactive as T M . From this we see that the time-averaged power consumption P is given by P = T M C (1 − F ) B + C (1 − T M ) F B . (1)3n order to find the value of F that mimimises time-averaged power consumption, we setthe first derivative of P with respect to F equal to zero. This gives CB [ − T M (1 − F ) + 2 F (1 − T M )] = 0 , (2)the solution to which is F = T M .Using a standard approach where the entire required field is generated by the coils, thetime-averaged power consumption would simply be equal to T M CB . Setting F = T M inequation (1) and dividing through by this value, we find that the use of permanent magnetsto create part of the MOT field reduces time-averaged power consumption by a factor of / (1 − T M ) . ATOM NUMBER ESTIMATION
The MOT atom number N is calculated from the photodiode voltage V PD using: N = 4 πλαV PD hc Ω γ sc s , (3)where γ sc denotes the photon scattering rate of the MOT atoms, α is the magnificationfactor of the lenses used to capture the MOT fluorescence, and s is the sensitivity of thephotodiode to 780 nm light. Loading curves (see FIG.9 in the main paper) were obtainedfor various values of Rb dispenser current from 2.20 A (minimum current value at which anatomic cloud can be formed) to 2.75 A. [1] Ultimaker, The widest material choice on the market, https://ultimaker.com/materials (2011-2020).[2] Simplify3D, Filament properties table, (2021).[3] J. T. Cantrell, S. Rohde, D. Damiani, R. Gurnani, L. DiSandro, J. Anton, A. Young, A. Jerez,D. Steinbach, C. Kroese, and P. G. Ifju, Experimental characterization of the mechanical prop-erties of 3d-printed abs and polycarbonate parts, Rapid prototyping journal , 811 (2017).[4] H. Kim, E. Park, S. Kim, B. Park, N. Kim, and S. Lee, Experimental study on mechanicalproperties of single-and dual-material 3d printed products, Procedia Manufacturing , 887(2017).[5] Rigid photopolymer resin for form 2, material data sheet, https://formlabs-media.formlabs.com/datasheets/Rigid_Technical.pdf (2018).[6] Photopolymer resin for form 1+ and form 2, https://archive-media.formlabs.com/upload/XL-DataSheet.pdf (2019).[7] S. K. Gaggar, Effects of test rate and temperature on fracture behavior of some rubber-modifiedpolymers, in Instrumented Impact Testing of Plastics and Composite Materials (ASTM Inter-national, 1986).[8] D. J. Brunelle and W. E. Smith, Polycarbonate transesterification process (1980), US Patent4,217,438.
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