Design of the ALPS II Optical System
M. Diaz Ortiz, J. Gleason, H. Grote, A. Hallal, M. T. Hartman, H. Hollis, K. S. Isleif, A. James, K. Karan, T. Kozlowski, A. Lindner, G. Messineo, G. Mueller, J. H. Poeld, R. C. G. Smith, A. D. Spector, D. B. Tanner, L.-W. Wei, B. Willke
DDesign of the ALPS II Optical System
M. T. Hartman, A. Lindner, R. C. G. Smith, A. D. Spector ∗ , and L.-W. WeiDeutsches Elektronen Synchrotron (DESY), 22607 Hamburg, GermanyK. Karan, J. H. P˜old, and B. WillkeMax-Planck-Institut f¨ur Gravitationsphysik (Albert-Einstein-Institut) and LeibnizUniversit¨at Hannover, 30167 Hannover, GermanyM. Diaz Ortiz, J. Gleason, A. Hallal, H. Hollis, T. Kozlowski, G. Messineo,G. Mueller, and D. B. TannerDepartment of Physics, University of Florida, 32611 Gainesville, Florida, USAH. Grote and A. JamesSchool of Physics and Astronomy, Cardiff University, CF24 3AA, Cardiff, UnitedKingdomOctober 16, 2020 Abstract
The Any Light Particle Search II (ALPS II) is an experiment currently being built at DESYin Hamburg, Germany, that will use a light-shining-through-a-wall (LSW) approach to searchfor axion-like particles. ALPS II represents a significant step forward for these types of experi-ments as it will use 24 superconducting dipole magnets, along with dual high-finesse, 122 m longoptical cavities. This paper gives the first comprehensive recipe for the realization of the idea,proposed over 30 years ago, to use optical cavities before and after the wall to increase the powerof the regenerated photon signal. This concept will allow the experiment to achieve a sensitivityto the coupling between axion-like particles and photons down to g αγγ = 2 × − GeV − formasses below 0.1 meV, more than three orders of magnitude beyond the sensitivity of previouslaboratory experiments. The layout and main components that define ALPS II are discussedalong with plans for reaching design sensitivity. A set of top level requirements for the sub-systems is also provided for the first time and includes the requirements on the coherence andspatial mode matching of the cavity eigenmodes. An accompanying paper (Hallal, et al [1]) of-fers a more in-depth description of the heterodyne detection scheme, the first of two independentdetection systems that will be implemented in ALPS II. ∗ [email protected] a r X i v : . [ phy s i c s . op ti c s ] O c t igure 1: Experimental layout of ALPS II. Two 106 m long strings of twelve 5.3 T HERA dipoles areseparated by the COB. The COB also houses the wall which blocks the PC transmitted light fromreaching the RC. Each of the cavities are 122 m long. The power inside the PC should be at least150 kW, while the resonant enhancement of the RC β RC , must be greater than 10,000. The couplingefficiency between the PC and RC, given by η , should be at least 0.9. The Any Light Particle Search II (ALPS II) [2] will soon become the world’s leading light-shining-through-a-wall (LSW) experiment. It will improve on the detection sensitivity to the couplingstrength between photons and axion-like particles by three orders of magnitude compared to earlierexperiments such as ALPS I [3] and OSQAR [4]. Like all LSW experiments, ALPS II will directlyprobe the existence of pseudo-scalar fields whose coupling to electro-magnetic fields is described bythe Lagrangian: L a = g aγγ φ a (cid:126)E · (cid:126)B (1)Here g aγγ is the axion-photon coupling strength, φ a is the axion field, the oscillating electric fieldis given by (cid:126)E , and (cid:126)B represents the static magnetic field. This interaction is typically associatedwith the QCD or Peccei-Quinn axion, which was proposed to solve the strong CP problem [5, 6, 7].In addition to the QCD axion, other ‘axion-like’ particles that can also be described by Equation 1have recently taken centerstage. These particles, with potentially stronger interactions, offer possibleexplanations for a variety of astrophysical phenomena including the transparency of the universe tohighly energetic photons [8] and anomalies in stellar cooling rates [9].ALPS II will also be able to search for scalar fields whose coupling to electro-magnetic fields canbe described by the Lagrangian: L s = g aγγ φ s ( (cid:126)E − (cid:126)B ) (2)Experimentally, this only requires that the polarization of the E-field is orthogonal to the B-field.A signal running in both polarization modes with no observed polarization dependence on theproduction rate could be detected as well. This may indicate the existence of other types of WeaklyInteracting Sub-eV Particles (WISPs) that are produced by kinetic mixing such as millichargedparticles or hidden sector photons which do not require a static magnetic field to interact withphotons [10]. In the following, we refer to particles whose interaction strength depends on (cid:126)B as axion-like particles, however the observation of any such particle would represent a profound discovery asit would be the first detection of an interaction beyond the standard model. If the new particle hasa finite mass, depending on its type and interaction strength, it could also contribute to the totaldark matter in the universe [11].It is worth pointing out that LSW experiments such as ALPS II make no assumptions regardingthe natural prevalence of any of these particles, but merely probe the interactions themselves withoutthe need for an external source. LSW experiments can therefore determine the photon-couplingstrength independent of any astrophysical models, while solar searches and haloscopes, such asCAST [12], IAXO [13], ADMX [14], and MADMAX [15] not only depend on the coupling strength,but also rely on models of the axion-flux.In contrast to these searches, LSW experiments take place entirely in the laboratory using ahigh-power laser (HPL) propagating through a magnetic field. This generates a beam of axion-like2able 1: Top level requirements of the ALPS II science run targeting a sensitivity of g αγγ = 2 . × − GeV − (adapted from [21]).RequirementTLR1 150 kW power circulating in PC (fundamental mode, linearly polarized, 1064 nm)TLR2 Parallel and perpendicular polarization adjustment possibility with respect to the mag-netic fieldTLR3 Coupling between the axion mode and the RC fundamental mode: η >
90% (power ratio)TLR4 RC resonant enhancement β RC >
10 000TLR5 Detector sensitive enough to confirm/exclude a reconverted photon rate of 2 . × − /swith a 95% confidence level within 20 daysTLR6 Magnetic field × length product of 560 T · m for PC and RC magnet stringparticles that travel through a light-tight wall into a second magnetic field region where some ofthese axion-like particles convert back to photons [16].ALPS II is based at DESY in Hamburg, Germany, taking advantage of the tunnels, magnets, andcryogenic infrastructure formerly used by the HERA accelerator. It will also use 122 m long opticalcavities to resonantly enhance the electromagnetic field on both sides of the wall which increases thephoton regeneration rate by twelve orders of magnitude over earlier LSW experiments [17, 18, 19, 20].The entire optical setup including these two cavities has to be tightly controlled to maintain andaccurately calibrate the coupling of the generated axion field to the cavities.This paper demonstrates the progress that has been made in the technical design for ALPS II andLSW experiments in general, as it includes the first detailed plan for maintaining both the coherenceand transversal matching of the cavity eigenmodes. The following text will focus primarily on thecore components that define optical system for the experiment and discuss how we plan to reachthe targeted sensitivity, while also providing a set of top level requirements for the subsystems. Acomplementary paper [1], builds on the work presented here and describes the heterodyne detectionscheme (HET) in more detail. ALPS II will consist of two 122 m long, high-finesse optical cavities whose circulating fields willpropagate through strings of 12 superconducting HERA dipole magnets [22], as shown in figure 1.A current of 5.7 kA will flow through these 8.8 m long dipoles and produce a magnetic field of 5.3 Tgiving a magnetic field times length of B L = 560 T · m on each side of the wall with free aperturesbetween 46 and 51 mm. Inside the production cavity (PC) on the left side of the wall, photons willgenerate axion-like particles with an identical energy and spatial mode. These particles pass throughthe light-tight barrier on the central optical bench (COB) before they enter the regeneration cavity(RC) where they convert back to photons. The regenerated photon rate, n reg = η
16 ( g aγγ F ( qL M ) B o L ) P PC hν β RC , (3)scales with ( g aγγ B L ) and is proportional to the power P PC inside the PC and the resonant en-hancement β RC of the RC [23]. The form factor can be approximated by the following equation with3 M representing the 106 m length of each magnet string. | F ( qL M ) | ≈ (cid:12)(cid:12)(cid:12)(cid:12) qL M sin (cid:18) qL M (cid:19)(cid:12)(cid:12)(cid:12)(cid:12)(cid:18) q = m a (cid:126) ω (cid:19) (4)This is a typical phase matching condition which accounts for the possible mass m a , of the relativisiticaxion-like particles. For masses m a < . η between the relativistic axion field and the eigenmode of the RC takesinto account all transversal and spectral mismatches between the axion mode, which is identicalto the PC eigenmode, and the eigenmode of the RC. Here η is given in terms of axion to photoncoupling and therefore the axion field to electromagnetic field coupling would be given by √ η . Itwill be possible to verify √ η before and after measurement runs by opening a shutter in the lighttight barrier and allowing the PC transmitted field to couple to RC.Table 1 lists the top level requirements (TLR) of ALPS II. While the long magnet string (TLR 6)provides a sensitivity gain of ∼
25 when compared to ALPS I, TLR 1, requiring a PC internalpower of 150 kW, and TLR 4, requiring an RC resonant enhancement β RC >
10 000, togetherincrease the sensitivity of the experiment by a factor of ∼
40, demonstrating the importance of theoptical system to the experiment. Achieving both of these requirements depends on the coatingsand surface roughnesses of the cavity mirrors as well as clipping losses in the magnet strings. Thiswill be discussed further in section 2. It should be noted TLR 4 is not far from the limits of what ispossible for mirrors of these dimensions with state of the art polishing techniques. TLR 3 refers tothe coupling of the axion field to the RC and is discussed in section 3. The current plan is to have ansearch based on the above listed parameters that could set an upper limit of g αγγ = 2 . × − / GeV.This corresponds to a regenerated photon rate of 2 . × − / s or roughly 2.4 photons per 24 h of validdata. This search will be followed by a scalar particle search at the same sensitivity by changing thepolarization (TLR 2). We will then improve the sensitivity by increasing the PC circulating power,the RC resonant enhancement and the duty cycle to aim for g αγγ = 2 × − /GeV or better [21]for pseudo-scalar and scalar particles. ALPS II will have the benefit of using two independent detection systems, each with very differentsystematic uncertainties, to measure the reconverted photons. This will help increase confidence insignals that are observed with the same strength in both detectors. The detectors themselves requiredifferent optical systems in order to be operated and cannot be used in parallel.The first detection scheme to be implemented will be the HET, and its optical system is de-scribed in the accompanying paper in this journal [1]. The HET utilizes an interference beatnotebetween a laser, referred to as the local oscillator (LO), and the regenerated photon field on aphotodetector. Demodulating the electronic signal from this photodetector at the known differencefrequency will create a signal proportional to the regenerated field strength that can be integratedover the measurement time. The regenerated photon signal will thus accumulate proportional to themeasurement time τ while the laser shot noise will sum incoherently proportional to √ τ [24].A transition edge sensor (TES) will be used in the second detection system [25]. The TES consistsof an absorptive tungsten chip which is held at a temperature at the threshold of superconductiv-ity. When a photon is incident on the chip it will be absorbed, leading to a slight increase in itstemperature. This will suddenly raise the resistance of the chip causing a drop in the bias currentthat is flowing through it. This current drop can be measured with a superconducting quantuminterference device. Therefore, the reconverted photons can be individually counted as these pulsesoccur, with an energy resolution of ∼ ± . ± /e ) 6 . /e ) 9 . µ radRC resonant enhancement >
10 000
Both the PC and RC will be plano-concave cavities with g = 0 .
43. The curved mirrors will be locatedat the end stations and the flat mirrors at the central station of the experiment as shown in Figure2. The radius of curvature of the mirrors at the end stations were chosen such that the Rayleighrange of the cavity eigenmodes are equal to the length of the magnet strings. This geometry willhelp minimize aperture losses in the cavities while also avoiding higher order mode degeneracies thatwould occur if they were exactly half-confocal. The configuration also ensures that the eigenmodesof both cavities can have a high spatial overlap as the nominally identical Gaussian beam waistsare located on the flat cavity mirrors on the COB. The distance between the flat cavity mirrors is∆ z ∼
835 mm and much smaller than the Rayleigh range z R of the modes. The resulting mismatchin power for ∆ z (cid:28) z R is on the order of1 − η ∆ z = (cid:18) ∆ z z R (cid:19) ≈ − , (5)which is negligible compared to other contributions to the total mismatch η .The cavity eigenmodes will need to be centered within the beam tube of the magnet string toreduce clipping losses. The diameter of the beam tube is nominally 55 mm, however since the magnetswere originally used to steer protons around the arcs of the HERA accelerator, their central axisfollowed a curvature of 600 m and therefore required straightening. This process was very successful,and free apertures ranging from 46-51 mm were measured after being straightened. The magnetswith the largest free apertures will be used near the end stations where the beam size and risk ofclipping losses is the highest. The survey and magnet installation teams expect that they can placethe magnets and the rest of the vacuum system housing the cavities to within ± µ m and ± µ radof a line defining the theoretical optical axis of the experiment. The optics team then expects tobe able to place the COB and cavity end mirror to within ± ± µ rad of the resultingcentral line of the combined magnet string, sufficient to reduce clipping losses inside the two cavitiesto below 1 ppm. The resonant enhancement provided by the regeneration cavity, β RC ≈ T out ( T RC + T RC + ρ ) , (6)depends on the losses and transmissivities of each mirror. Here T out is the transmissivity of the mirrorlocated nearest to the main regenerated photon detector; this will be RC for the HET ( T out = T RC )5igure 2: Layout of the cavities and control architecture for maintaining the phase lock of the PCin HET (top) and TES optical systems (bottom).and is expected to be RC for the TES scheme ( T out = T RC ). Ideally, the maximum resonantenhancement occurs when the RC has minimal round-trip losses ρ , and the mirror transmissivitiesare as low as possible with the cavity still an impedance matched configuration where 2 T out = T RC + T RC + ρ .Losses in our cavities are expected to be dominated by the surface roughness of the mirrors andthe associated scattering of light. We initially assumed that scatter losses can be kept below a fewppm per surface. Unfortunately, the fairly large beam sizes in relation to the size of the substratestogether with the requirements on minimal wedge angles of the flat mirrors, proved to be a challengefor the polishing companies. After receiving the substrates, we estimated that scatter losses insidethe cavity will likely be between 40 and 60 ppm per round-trip. In addition to these losses, the HETalso requires some transmission through T RC to realize their sensing and control scheme as shownin Figure 2 [1]. To be conservative, we decided to use 100 ppm as the design value for T RC and5 ppm for T RC for the HET. For the TES detection scheme we plan to flip these values such that T RC will be 100 ppm while T RC will be 5 ppm; however, in order to optimize the sensitivity of thethe experiment, the transmissivities of these mirrors for the TES system are subject to change basedon what we learn from commissioning the HET optical system.For the HET optical system the dielectric mirror coatings consist of alternating λ/ ∼
110 ppm and ∼ . β ≈
16 000 ± λ/ .2 Production cavity A consequence of the cavities natural amplification is that using the same mirrors the PC will giveit a power build-up factor of 16 000 ± ∼
300 kHz will maintain the resonanceof the laser with respect to the length of the PC using the standard Pound-Drever-Hall (PDH)technique [27, 28]. The sensing scheme and the loop gain are expected to keep the laser frequencywithin a hundredth of the HWHM of the cavity resonance corresponding to a relative power noiseinside the cavity to a RMS value of approximately 100 ppm.The input optics between the HPL and the PC will also be equipped with an automatic alignmentsystem based on a differential wavefront sensing (DWS) scheme. This system uses a pair of quadrantphotodetectors (QPDs) which measure the lateral shift ∆ x and angular offset ∆ θ between the lasermode and the cavity eigenmode [29]. We expect to reach sensitivities of:∆ x RMS < . · w ∆ θ RMS < . · θ Div (8)These signals are then fed back to a pair of actuators to maintain the alignment into the cavity. Thegoal is to also limit the RMS relative power noise inside the cavity due to alignment fluctuationsto 100 ppm for each degree of freedom. The entire system should guarantee that the total relativepower noise stays below 0.1% RMS, which could be critical to reducing dynamic thermal effects fromeffecting the HET [1]. The input optics for the PC will also employ a half-waveplate before mirrorPC to rotate the polarization of the circulating field with respect to the polarity of the magnetstring. This will satisfy TLR2 and allow the experiment to search for both scalar or pseudo-scalarparticles.This combination of the HPL and cavity finesse may allow powers as high as 1 MW inside thePC, however, the final power level will likely be limited by the absorption in the HR coating layersof the two cavity mirrors. There are a number of ways this absorbed light could lead to thermaleffects that cause higher intracavity losses. For example, point absorbers heating up on the surfaceof the mirror could cause the formation of low spatial frequency features which, in turn, leads to anincrease in the scattering losses [30, 31]. Absorption in the mirror coatings could also cause the sizeof the mode circulating in the PC to change and lead to additional clipping loses from the beamtube [32]. The loss in sensitivity due to the mode mismatch between the cavity eigenmodes as thePC mirrors heat up is expected to be insignificant in comparison. In spite of these effects, we areconfident that 150 kW is achievable. The primary obstacles to optimizing the coupling of the axion field to the RC are related to main-taining the coherence and spatial mode matching between them. Both of these parameters willdepend on the residual changes of the PC eigenmode with respect to the eigenmode of the RC andwe allow each to contribute a 5% loss of the signal to meet the 90% coupling efficiency listed underTLR 3. Admittedly, this rather unsophisticated split is a reflection of our limited understanding ofthe expected mirror motion in the HERA tunnel once the optical tables, the vacuum system, themagnets and the clean rooms are all installed and operational.
Maintaining the coherence between the electromagnetic field regenerated from the axion field andthe RC eigenmode is critical to ALPS II achieving its target sensitivity. Therefore, the regenerated7eld should experience no more than 5% average reduction from its optimal resonant enhancementover the duration of the measurement due to its frequency noise with respect to the length of theRC. This requirement is further divided into one on static frequency offset and one on the dynamicphase noise. As the regenerated field is a replica of the field circulating in the PC, the first challengeis to accurately tune the frequency of the PC transmitted field such that it is resonant with theRC. The second challenge is to precisely control the phase of the PC transmitted field around thisnominal value.
The signal loss in regenerated photons due to a small offset of ∆ f in the frequency of the PCtransmitted light relative to a resonance frequency of the RC is quadratic in the offset and can beapproximated by the following expression.1 − η ∆ f ≈ (cid:18) ∆ f HWHM (cid:19) (9)Here HWHM is the half-width half-max linewidth of the RC. To limit the loss of regenerated photonsto 1%, we require that the detuning is less than 10% of the HWHM or less than 1.5 Hz during thescience run.As Figure 2 shows, in both detection systems the frequency of the PC transmitted field ν PC willbe set via offset phase lock loops relative to a frequency of a reference field which itself is lockedto a resonance frequency ν RC of the RC. The offset frequency, a multiple N of the FSR of theRC, is optimized by maximizing the transmission through the RC with the shutter open and thenmaintained during science runs when the shutter is closed [1]. This approach requires that the sourcefor the offset frequency and the FSR of the RC are both stable.The RF frequency will be derived from a clock that is synchronized to a 10 MHz rubidiumfrequency standard with a yearly frequency drift on the order of mHz, well below our requirement.However, macroscopic changes of the length of the RC will change the optimum offset frequency by:∆ f ∆FSR = N · ∆FSR RC = N · FSR RC ∆ L RC L RC (10)The length changes of the RC then have to be∆ L < ∆ f ∆FSR FSR RC LN = 150 µ m N (11)between retuning measurements to ensure that ∆ f < . (cid:54) = N ) of the FSR [33]. ∆ L will be measured continuously during the science run and if it becomeslarger than µ m N the run will be paused and the length of the RC will be adjusted back to its initialvalue before it is started again. We also are investigating options to actively control the length ofthe RC during a measurement run. The feedback system which reduces the frequency or phase fluctuations φ ( t ) of the PC transmittedfield relative to the offset frequency set by the phase lock loop has to provide the precision necessaryto meet the requirements on the coherence. Phase noise in the PC transmitted field relative to theRC spreads the energy of the ideally monochromatic field over a finite frequency band and only thefrequency components which are resonant in the RC will contribute to the signal. The energy in allfrequency components outside the FWHM line-width of the RC will be attenuated.8e require that the power integrated over all frequency components outside this bandwidth isless than 4% of the total power. This requirement roughly translates into an upper limit for thestandard deviation (SD) of the phase noise evaluated over the storage time T of the cavity of [34]:∆ φ SD ( t ) ≈ (cid:113) (cid:104) δφ ( t ) (cid:105) T < . mirror that sup-ports a control bandwidth of 4 kHz. Based on seismic measurements in the HERA tunnel, thisbandwidth paired with an aggressive gain function is expected to be sufficient to suppress the envi-ronmental noise [34]. Another effect which could lead to a loss in sensitivity is related to the alignment of the axion fieldinto the RC. The spatial mode of the axion field entering the RC is an extension of the spatialmode inside the PC and the loss due to small alignment errors can be calculated from the followingequation: 1 − η TM ≈ (cid:18) δxw (cid:19) + (cid:18) δθθ Div (cid:19) (13)where δx is the transversal shift and δθ is the angular misalignment between the two modes measuredat the waist of the RC. The power loss is quadratic in both terms and required to be less than 5%in total. Like the tuning of PLL offset frequency, the alignment of the cavity eigenmodes will be quantifiedusing the PC transmitted field when the shutter is open. This quantification has a systematicerror due to the refraction in all optical components located between the cavity internal fields. Thesubstrates of the cavity end mirrors have known wedge angles θ W between 3 and 4 µ rad which willrefract the PC transmitted field but not the axion field. By clocking the two substrates correctly,the refraction angles will compensate each other such that the final angular refraction is: δθ refr = ( n − θ W < µ rad (14)The refraction in PC will laterally shift the PC transmitted beam by δx < µ m.Each of the detection systems uses additional beam splitters between the two cavities to directthe various laser beams required to operate the experiment [1]. These beam splitters are also madefrom substrates with known wedge angles between 2 and 5 µ rad and will also be clocked to reducethe overall deflection to below 2 µ rad. The total deflection angle between the beams will thereforebe below a 3 µ rad.Each substrate will laterally shift the beam by: y = d sin( θ − θ )cos θ sin θ = n sin θ (15)where d is the thickness of the substrate, θ the angle of incidence and θ the angle inside thematerial. In both designs, the number of substrates which shift the beam to the left has to equal9igure 3: Control architecture for maintaining spatial overlap. The QPDs on the COB monitor theposition of the cavity eigenmodes on the cavity mirrors PC and RC . These signals are used toalign the cavity mirrors at the end stations PC and RC .the number of substrates which shift the beam to the right, assuming that the substrates are equalin thickness and in material, and that the angle of incidence is the same. For example, the HETdesign uses two substrates that shift the beam left and two that shift it right; all at 35 ◦ angle ofincidence and all made from fused silica. According to the vendor, the substrates are 9.5 mm thickwith a tolerance of [+0 , − . ∼ µ m.Based on these numbers, the uncertainty in the resulting mode mismatch between the PC trans-mitted field and the axion field for both degrees of freedom will be below 0.4% which will allow usto use the PC transmitted field to verify the overall alignment of the axion mode into the RC at the95% level. The central optical bench (COB) is a critical piece of the optical system. Its main role is to ensurethat the two cavities maintain their relative alignment during the science runs. This requires that thesurfaces of the flat cavity mirrors are parallel to each other, and that the positions of the eigenmodesof the two cavities are in line with each other. The COB uses no active alignment system; instead, werely on its passive stability, and control loops that stabilize the spot positions on the COB mirrors.Open shutter measurements will be used to quantify the overall misalignment.The COB is constructed from a single aluminum plate on which all mirrors, beam splitters,and waveplates, as well as position sensors are either mounted directly or through additional ULEbase plates [1] using, in both cases, ultra-stable optical mounts. Tests with an autocollimatorhave shown that a prototype COB was capable of maintaining a long term alignment stability of2 µ rad over one week in air with measured thermal alignment coefficients of ≈ µ rad/K in pitchand ≈ µ rad/K in yaw [35]. The air conditioning system of the cleanroom has been designed tomaintain an 0.1 K absolute temperature stability which would, in principle, eliminate any relevantmisalignment. However, the impact of the heating of PC by the cavity internal field on the alignmentstill needs to be evaluated during the commissioning of the experiment.The alignment process of the COB starts with the two cavity mirrors PC and RC . We willuse two counter propagating laser beams, likely derived from a single HeNe laser, and two positionsensors with µ m resolution about 1 m away from the COB. The sensors will initially mark the forwardpropagating positions of the two beams and then act as references for when the cavity mirrors areinstalled and the reflected beams become available. The transmissivity of the cavity mirrors willallow us to observe the beams in transmission and reflection by simply blocking one of them. Thismethod should be sufficient to achieve an initial alignment of the surface normals of PC and RC of better than δθ < µ rad taking also into account the 1 µ rad residual angular refraction caused bythe wedge angles of the cavity mirrors. 10 .2.3 End Mirror Alignment As Figure 3 shows, the COB will also host two in-vacuum QPDs that will monitor the position ofthe cavity eigenmodes with respect to the COB by making DC differential measurements of the lightincident on their quandrants. These QPDs are optimized to sense the position of the 6 mm radiusbeam with sub 100 µ m precision [36]. Assuming that the components on the COB remain stationary,the positions of the eigenmodes on the flat cavity mirrors PC and RC , and in extension on thetwo QPDs, only depend on the orientations of the curved cavity mirrors PC and RC , respectively.The differential signals from the QPDs will be fed back to active alignment stages that are capableof controlling the pitch and yaw of the curved cavity end mirrors.The transversal shift δx between the two eigenmodes is therefore expected to be below 200 µ m.The resulting mode matching losses due to static cavity misalignments should be1 − η TM ≈ (cid:18) δxw (cid:19) + (cid:18) δθθ Div (cid:19) < . , (16)on the same order as the matching between the axion field and the PC transmitted field aftertraversing the COB optics, leaving significant margin for systematic errors and drifts. This paper describes the core components and the design of the ALPS II experiment and representsthe most detailed plan up to now, to maintain the coherence and spatial overlap of two high finesseoptical cavities for a LSW experiment. Upon reaching design sensitivity ALPS II will become themost sensitive LSW experiment to date by three orders of magnitude, and the innovations in theoptical system alone account for nearly two orders of magnitude in sensitivity gains. Additionalgains in sensitivity will come from the long magnetic field length and improvements in detectortechnologies [22, 25, 1].One of the main challenges for the optical system will be to maintain and verify the coherenceof the axion field with respect to length of the RC, as well as the alignment and mode matchingbetween the spatial modes of the axion field and the RC eigenmode. As described in this paper, wewill take great care that the spatial mode of the transmitted light from the PC that is incident on theRC is an accurate representation of the axion mode. This will allow us to quantify the coherence andmode matching of the axion field with respect to the RC. The length and alignment sensing systemfor the lasers and the cavities is based on PDH and DWS, well established phase sensing schemeswith sufficient sensitivity to monitor all relevant degrees of freedom. Additionally, we developed andtested different actuators which should have enough range and bandwidth to operate ALPS II in theHERA tunnels.We also discussed our plans to employ two different schemes to detect the regenerated photonsignal. The first one is the HET and is described in detail in an accompanying paper. The secondscheme uses a TES, and its optical design is currently being finalized and will be implementedfollowing the HET science runs. The experiment itself is presently under construction and aimingfor a first science run in 2021. Once fully operational, the optical system should allow ALPS II tobe able to detect axions with a coupling constant as low as g aγγ = 2 × − / GeV using 20 days ofvalid science data.
Acknowledgments
The work is supported by the Deutsche Forschungsgemeinschaft through SFB 676 and project grantWI 1643/2-1, by the German Volkswagen Stiftung, the National Science Foundation under grant11802006, the Heising Simons Foundation under award 2015-154, and the Science and TechnologiesFacilities Council.
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