key: cord-0857968-vo6e4b1s
authors: Liu, Jesse; Dona, Kristin; Hoshino, Gabe; Knirck, Stefan; Kurinsky, Noah; Malaker, Matthew; Miller, David W.; Sonnenschein, Andrew; Awida, Mohamed H.; Barry, Peter S.; Berggren, Karl K.; Bowring, Daniel; Carosi, Gianpaolo; Chang, Clarence; Chou, Aaron; Khatiwada, Rakshya; Lewis, Samantha; Li, Juliang; Nam, Sae Woo; Noroozian, Omid; Zhou, Tony X.
title: Broadband solenoidal haloscope for terahertz axion detection
date: 2021-11-23
journal: Phys Rev Lett
DOI: 10.1103/physrevlett.128.131801
sha: 00b0e57e8f821f136463df148694bde469da30dc
doc_id: 857968
cord_uid: vo6e4b1s

We introduce the Broadband Reflector Experiment for Axion Detection (BREAD) conceptual design and science program. This haloscope plans to search for bosonic dark matter across the [10$^{-3}$, 1] eV ([0.24, 240] THz) mass range. BREAD proposes a cylindrical metal barrel to convert dark matter into photons, which a novel parabolic reflector design focuses onto a photosensor. This unique geometry enables enclosure in standard cryostats and high-field solenoids, overcoming limitations of current dish antennas. A pilot 0.7 m$^{2}$ barrel experiment planned at Fermilab is projected to surpass existing dark photon coupling constraints by over a decade with one-day runtime. Axion sensitivity requires $<10^{-20}$ W/$sqrt{textrm{Hz}}$ sensor noise equivalent power with a 10 T solenoid and 10 m$^{2}$ barrel. We project BREAD sensitivity for various sensor technologies and discuss future prospects.

We introduce the Broadband Reflector Experiment for Axion Detection (BREAD) conceptual design and science program. This haloscope plans to search for bosonic dark matter across the [10 −3 , 1] eV ([0. 24, 240 ] THz) mass range. BREAD proposes a cylindrical metal barrel to convert dark matter into photons, which a novel parabolic reflector design focuses onto a photosensor. This unique geometry enables enclosure in standard cryostats and high-field solenoids, overcoming limitations of current dish antennas. A pilot 0.7 m 2 barrel experiment planned at Fermilab is projected to surpass existing dark photon coupling constraints by over a decade with one-day runtime. Axion sensitivity requires < 10 −20 W/ √ Hz sensor noise equivalent power with a 10 T solenoid and 10 m 2 barrel. We project BREAD sensitivity for various sensor technologies and discuss future prospects.

Astrophysical evidence for dark matter (DM) is unambiguous [1] [2] [3] [4] [5] [6] , but its particle properties remain enigmatic. Recent efforts are expanding bosonic DM searches for m DM 1 eV masses [7] predicted by many extensions of the Standard Model (SM) [8] [9] [10] [11] [12] [13] [14] , complementing higher-mass searches [15] [16] [17] [18] [19] [20] [21] [22] [23] [24] . Notably, the unobserved neutron electric dipole moment [25] [26] [27] [28] motivates the quantum chromodynamics (QCD) axion a predicted by the Peccei-Quinn solution of the strong charge-parity problem [29] [30] [31] . Dark photons A are also soughtafter candidates arising in string theory scenarios [32] [33] [34] [35] . These states have compelling early-Universe production mechanisms and their field oscillations with frequency ν = m DM /2π exhibit DM properties [36] [37] [38] [39] [40] [41] . Nonzero DM-photon couplings enable laboratory detection via electromagnetic (EM) effects.

The most-sensitive detection strategy today is the radio-frequency resonant-cavity haloscope [42] [43] [44] [45] , where ADMX [46] [47] [48] [49] [50] [51] [52] , CAPP [53] [54] [55] , HAYSTAC [56] [57] [58] [59] probe QCD axions within [1.8, 24] µeV masses. However, this strategy has long-standing obstacles from (i) narrow band tuning to unknown m DM and (ii) impractical highmass scaling for m DM 40 µeV. Scan rates fall precipitously with photon frequency R scan ∼ ν −14/3 [59] and the number of required resonators scales unfavorably with effective volume ∼ m 3 DM . Proposed dielectric haloscopes could probe [40, 400] µeV [60] [61] [62] and [0.1, 10] eV [63] masses, while topological insulators target [0.7, 3.5] meV [64] . Significant sensitivity gaps persist across [10 −4 , 1] eV masses, favored by several theoretical scenarios [65] [66] [67] , motivating broadband approaches.

This Letter introduces the Broadband Reflector Experiment for Axion Detection (BREAD) conceptual design to search multiple decades of DM mass without tuning to m DM . BREAD proposes a novel experimental design that optimally realizes dish-antenna haloscopes [68] . Its hallmark is a cylindrical metal barrel for broadband DMto-photon conversion with a coaxial parabolic reflector that focuses signal photons onto a sensor. In contrast to existing dish antennas using spherical or flat surfaces [69] [70] [71] [72] [73] , our geometry is optimized for enclosure in standard cryostats and compact high-field solenoids. This enhances signal to noise, ensures the emitting surface and magnetic field are parallel, and keeps costs practical. We delineate the optical properties of this novel geometry with detailed ray tracing and numerical simulation. While photoconversion is broadband, photosensor performance governs final discovery reach. We assess various state-of-the-art sensors and discuss the advances required in quantum sensing technology for next-generation devices to fulfill BREAD science goals with broad anticipated impact in astronomy and beyond [74] .

Sub-eV-mass bosonic DM behave as classical fields, whose coherent oscillations generate the local halo energy arXiv:2111.12103v2 [physics.ins-det] 24 1. (a) BREAD reflector geometry: rays (yellow lines) emitted from the cylindrical barrel, which is parallel to an external magnetic field Bext from a surrounding solenoid (not shown) and focused at the vertex by a parabolic surface of revolution. (b) Radial intensity distribution rI(r) expected from DM velocity effects in the xy plane at the focal spot using ray tracing, for the BREAD geometry as in (a) with R = 20 cm (blue) and for a conventional plane-parabolic mirror setup used in other experiments [69] [70] [71] [72] [73] with the same emitting surface area (gray). (c) Full field simulation at around 15 GHz including a preliminary coaxial horn design. (d) Electric (blue) and magnetic (orange) field distribution and time-averaged Poynting flux along the z direction in the xy plane at the focal spot. (e) Schematic setup in cryostat for pilot dark photon searches. density ρ DM , which we assume to be 0.45 GeV cm −3 [75] . We consider scenarios where either axions or dark photons exclusively saturate the halo DM. The DM-photon interaction augments the Ampère-Maxwell equation with an effective source current J DM [9] 

A nonzero J DM induces a small EM field that causes a discontinuity at the interface of media with different electric permittivity, such as a conducting dish in vacuum.

To satisfy the E = 0 boundary condition parallel to the dish surface, a compensating EM wave with amplitude |E 0 | must be emitted perpendicular to the surface. These waves transmit P DM = 1 2 |E 0 | 2 A dish of power for dish area A dish . For axions with g aγγ coupling to photons, the current is J a = g aγγ √ 2ρ DM B ext cos(m a t) given an external magnetic field B ext with nonzero component parallel to the plate, resulting in P a = 1 2 ρ DM (B ext g aγγ /m a ) 2 A dish emitted power [68] . QCD axion models [76] [77] [78] [79] [80] relate g aγγ to the mass by g aγγ ∼ 10 −13 (m a /meV) GeV −1 , giving m a -independent power. For dark photons with A -SM kinetic mixing κ and polarizationn, the cur-

The factor α pol = 2/3 averages over A polarizations [68] . P A is m A -independent and persists even when B ext = 0. Signal emission occurs independent of frequency in principle, allowing searches across several mass decades in single runs.

Practically, DM-detection sensitivity also depends on the signal emission-to-detection efficiency s , photosensor noise equivalent power (NEP), and runtime ∆t. NEP is defined as the incident signal power required to achieve unit signal-to-noise ratio (SNR) in a one Hertz bandwidth. We estimate sensitivity to g aγγ and κ (squared) as the SNR exceeding five SNR = ( s P DM √ ∆t)/NEP > 5, where we assume sensors have sufficiently fast readout bandwidth O(100 kHz): 

At high masses, shot noise is relevant due to insufficient signal photons N signal = ( s P DM ∆t)/m DM < 5. For the nominal A dish = 10 m 2 , B ext = 10 T configuration, QCD axions induce a few 1 eV photons week −1 so month-long runtimes render shot noise subdominant for m DM 1 eV. In photon-counting regimes, sensors with dark count rate DCR detect photons emitted at rate R DM = P DM /m DM . We use the counting-statistics significance Z = N signal / √ N noise = ( s R DM ∆t)/ √ DCR∆t > 5 to estimate sensitivity in the background-limited regime. In the background-free photon-counting limit, the coupling sensitivity scales faster g sens aγγ ∝ (∆t) −1/2 . With nominal photoconversion rates down to 1 photon per day, scaling as R γ ≈ 10 −5 (1 eV/m a ) Hz, the photosensors considered are background limited. We thus constrain our projections to this scenario, where appendix 1 discusses requirements of background-free experiments.

BREAD proposes a cylindrical barrel as the emitting surface and a novel reflector geometry comprising a coaxial parabolic surface of rotation around its tangent. This focuses the emitted radiation to a photosensor located on-axis at the parabola's vertex as shown in Fig. 1 (a) . DM-to-photon conversion also occurs at the parabolic surface but is not focused on the vertex. For a barrel with radius R and length L = 2 √ 2R, the effective emitting area is A dish = 2πR L. This aspect ratio suits enclosure in conventional high-field solenoid magnets and ensures B ext is parallel to the emitting surface. Such magnets are widely used in basic or applied applications with fields reaching 10 T or higher [81, 82] .

While photoconversion occurs regardless of m DM , sensitivity is limited at high (low) masses by focusing (diffraction) effects. Both effects broaden the focal spot and reduce the geometric signal efficiency due to finite photosensor size. In the high-mass limit λ dB R, DMto-photon conversion occurs incoherently as the DM de Broglie wavelength λ dB is smaller than the radius of the barrel R ∼ 1 m. Here, the DM-halo velocity v 10 −3 smears out the focal spot size [83] [84] [85] on length scales larger than the signal-photon wavelength λ sig , rendering diffraction effects negligible. The blue line in Fig. 1 (b) shows the expected intensity distribution at the focal spot for the most conservative case where the DM wind points along the least favorable direction. The gray line refers to a planar conversion surface of the same area comparable to other dish-antenna experiments [69] [70] [71] [72] [73] with an on-axis parabolic mirror at 1 m distance. Since rays impinge the focal plane from a larger solid angle, BREAD achieves improved focusing.

In the opposite low-mass limit λ dB R, such defocusing effects are negligible and the signal can be detected coherently. Figure 1 (c) shows the result of a COMSOL simulation at around 15 GHz. Here the full modified Maxwell wave equation is solved to verify that there are no spurious sources or resonances excited that may interfere destructively with the signal. Figure 1 (d) shows the diffraction-limited electromagnetic fields at the focal plane. The electric field polarized along the radial direction can be picked up by coaxial horn antennas [86, 87] . Receiver designs based on microwave and submillimeter astronomy projects could be considered for signal collection. Proof-of-principle pilot experiments near both these limits are in preparation. The radio-frequency pilot targeting 10s of GHz masses, called GigaBREAD, will be detailed in future work. Figure 1 (e) shows the proposed experimental design for the pilot A search at infrared (IR) frequencies, called InfraBREAD. Cooling the conducting surfaces to 4 K suppresses thermal noise and we identified a large cryostat at Fermilab built to test ADMX resonators, which will be available in 2022. The barrel is constructed from aluminum with A dish = 0.7 m 2 (10 m 2 ) for the pilot (upgrade). A 4 K blackbody with 0.7 m 2 area and unit emis-sivity emits ∼ 10 −8 W of power above 1 THz (4 meV). Simulation shows that thermal radiation is evenly distributed across the focal plane and so suppressed by A sens /A dish ∼ 10 −6 for active sensor area A sens . For A dish = 0.7 m 2 , A sens = 0.5 × 0.5 mm 2 yields 50% (25%) signal efficiency s for optimistic (pessimistic) DM-wind alignment; see appendix 3 for further discussion. For absolute alignment of the photosensor in the reflector, we propose a piezoelectric motion stage to fine-tune the sensor position at the focus. Off focus, the signal is not enhanced. This enables in situ noise measurements by moving the single photosensor off axis or installing a second off-axis photosensor. A monochromatic laser or bandpass-filtered blackbody source can inject photons via a small hole in the barrel for absolute calibration of the reflector-photosensor setup. A room-temperature spectrometer at UChicago is available to characterize sources and filters [88] .

Various upgrades and optimizations could be implemented to improve sensitivity of the proposed experimental concept. A small secondary mirror near the focal point could guide the signal toward a low-field region where, e.g. a chopper and/or spectrometer could be installed. The optics may optimize the radiation polarization and incident angle on the photosensors. A detector array or photon imager [89] could also provide spatial resolution to correlate any observed signals with the astrophysical DM distribution. Specifically, the focal point and signal undergo diurnal and annual modulations due to the rotating DM velocity vector in the lab frame [90] and possibly A polarization [91] . The total A dish could be increased within the same available volume by combining the signals from an array of smaller BREAD-like barrels, but this increases complexity significantly. Cosmicray muons are a suggested noise source for photon counters [92] ; in situ vetoes at the sensor or barrel exterior, and/or underground operation are mitigation strategies. Studying these options is deferred to future work.

The expected DM signal rates and optical geometry imply stringent photosensor requirements: broad spectral response ∆E/E > 1, ultralow noise NEP < 10 −20 W Hz −1/2 or DCR < 10 −3 Hz, and millimeter-size active area. Bolometers are promising because they directly measure absorbed photon power, only the absorbing material or structures limit spectral response, and are established technology with diverse applications [93, 94] . They comprise a thermally isolated absorbing element with low heat capacity, sensitive thermometer and weak link to a cold thermal bath. They can measure photon energies from 10 −5 eV [95] to 10 6 eV. Bolometers are typically insensitive to static (DC) radiation due to instrumental low-frequency (1/f ) noise, so input signals must be time-modulated with, e.g. a chopper that shifts the signal to a frequency where 1/f noise is subdominant and SNR increases ∝ (∆t) 1/2 . Photon-counting devices (photocounters) are potentially more sensitive than total-power bolometry, since simple signal-processing techniques, e.g. thresholding and pulse fitting, can suppress noise. Small devices achieve nearly background-free single-photon counting at thresholds 1 eV. For lower energies, numerous devices exploit athermal breaking of Cooper pairs, including kinetic inductance detectors (KID), superconducting nanowire single photon detectors (SNSPD), and quantum capacitance detectors (QCDet) [96] .

We now discuss specific technologies motivating the values in Table I assumed for our projections. We display typical A sens , but later set s = 50% for simplicity assuming sensor development will enable scaling to required sizes. Room-temperature (Gentec pyroelectric [97] ) and cryogenic (IR Labs semiconducting thermistor [98] ) devices exemplify commercial performance.

Superconducting titanium-gold transition edge sensors (TES) [105] [106] [107] report down to 2 × 10 −19 W Hz −1/2 NEP in arrays of 200 × 200 µm 2 pixels [99] . TESs have broad spectral response, where a molybdenum-gold device reporting 4 × 10 −19 W Hz −1/2 NEP covers 1-4 µm to 160-960 µm (eV to meV) [108] . Elsewhere, small 10 µm superconducting-normal-metal junction bolometers report 2 × 10 −20 W Hz −1/2 NEP [109] , which may be promising if active areas are scalable to millimeters [110] .

KIDs [112] [113] [114] are thin-film resonators, whose surface inductance is sensitive to Cooper-pair-breaking photons above the band gap ∆ 0.2 meV. Titanium-nitride KIDs are scalable to 50 × 50 mm 2 kilopixel arrays with 3 × 10 −19 W Hz −1/2 NEP [100] , which are antenna coupled and optimized to [3.4, 12] meV [115] . For cosmic microwave background (CMB) applications (0.2 E 2 meV), KIDs are limited by signal power rather than sensor noise at NEP ∼ 10 −17 W Hz −1/2 [116] , and therefore could have better performance in such frequencies than current sensors targeting CMB science. Given KID and TES devices report similar NEP in each application, we amalgamate their presentation in our projections for simplicity. We extrapolate the 2 × 10 −19 W Hz −1/2 NEP [99] into the [0.2, 125] meV range where we expect KID/TES devices to operate bolometrically, but this will require experimental demonstration.

QCDets [117] [118] [119] recently report 3 × 10 −21 W Hz −1/2 NEP at 1.5 THz (6.2 meV) [101] .

These are scalable to 441 pixel arrays and simulation indicates 1-4×10 −20 W Hz −1/2 NEP for [2, 125] meV [102] , driven by e.g. Origins Space Telescope goals [120] . Such performance is promising, and for simplicity, we assume constant 3 × 10 −21 W Hz −1/2 NEP in our projections. We convert this to DCR = 4 Hz using NEP = (E/η) √ 2 · DCR [121] for E = 6.2 meV and optical efficiency η = 0.9 [101] .

SNSPDs [121] [122] [123] comprise sub-micron-width wires wound across thin-film substrates that count photons above an energy threshold. Superconductivity is momentarily lost upon photon absorption, leading to a measurable voltage pulse. Such devices achieve > 90% efficiency [124] and recently, a 400 × 400 µm 2 tungstensilicide device reports DCR < 10 −4 Hz for 0.8 eV threshold [103] . Using Fermilab refrigerators [125] , we are preparing to test similar SNSPDs fabricated at MIT. Recent advances important for BREAD include extending up to 10 µm (0.12 eV) [104] and developing large 3.1 × 3.1 mm 2 single pixels [126] . Continued research to lower thresholds is motivated given axions with m a 60 meV are disfavored by supernova constraints [127] .

Photocounting is also possible using KIDs [128, 129] and TESs [130] [131] [132] , with the benefit of per-photon energy resolution. With e.g. 10% energy resolution determined by detector resolution, the monochromatic DM signal occupies one energy bin but noise can be spread across 10 bins, improving SNR after sufficient ∆t up to a trials factor. Exploring this in BREAD requires more detailed resolution and noise models, which is deferred to future work.

We project BREAD sensitivity to dark photons in Fig. 2 (left) using Eq. (2) assuming the spectral and noise benchmarks in Table I . Existing constraints following Ref. [91] (blue shading) include stellar astrophysics [133, 134] , cosmology [40, 135, 136] , and γ → A conversion that includes laboratory probes [137, 138] . With just 1 day runtime assuming A dish = 0.7 m 2 , the gray thin line shows the BREAD pilot could surpass existing κ constraints by one decade around 1 meV using the commercial IR Labs sensor. The reach of BREAD is substantially broader compared with two existing dish antennas, SHUKET [139] and Tokyo [71] (dark blue). Importantly, BREAD probes higher masses than existing haloscopes ADMX [47, 48] , CAPP [53] [54] [55] , HAYSTAC [58, 59] , transmon qubit [140] , and WIS-PDMX [141] , whose results are recasted for A following Ref. [91] . Scaling to A dish = 10 m 2 and using KID/TES sensors could open two decades further κ sensitivity, while SNSPDs could achieve three decades gain Table I ) for dark photons A (left) and axions a (right). This assumes signal-to-noise ratio SNR = 5 (significance Z = 5 for photocounters), signal efficiency sig = 0.5, and dish area A dish = 10 m 2 . Blue shading shows existing constraints from Ref. [91] . Benchmark axion predictions include QCD axion models [111] (green band), cogenesis [67] (green dots), KSVZ [78, 79] and DFSZ [76, 77] (green lines). Sensitivity scaling assumes background-limited operation where signal-power limits scale as √ ∆t for runtime ∆t and linearly with improved NEP.

for m A 0.1 eV. Extending runtime to ∆t = 10 3 days enables κ sensitivity to reach six (four) decades beyond existing constraints for m A ∼ 0.4 (200) meV.

Axion sensitivity is illustrated in Fig. 2 (right) . Existing constraints [91] additionally include the CAST helioscope [142, 143] , telescopes [144, 145] , neutron stars [146] [147] [148] , alongside ORGAN [149] QUAX [150, 151] RADES [152] and URF [43] [44] [45] haloscopes. While challenging with commercial devices, 10 day runtimes using KID/TES sensors with NEP ∼ 10 −19 W Hz −1/2 could surpass CAST sensitivity for m a 10 meV. Longer runtimes could test cogenesis predictions for the c aγγ = 1 benchmark [67] . Increasing A dish (B ext ) beyond 10 m 2 (10 T) is financially unfavorable, requiring custom cryostats and magnets. Thus practically probing QCD axion models [111] requires longer runtime and lower sensor noise. Coupling sensitivity scales slowly with runtime g sens aγγ ∼ (∆t) −1/4 , i.e. halving g sens aγγ requires 16× longer runtimes. For ∆t = 10 3 days, reaching KSVZ [78, 79] (DFSZ [76, 77] ) demands 1 (0.2) × 10 −22 W Hz −1/2 NEP. Achieving this NEP for wide spectral ranges is challenging and a key science driver for sensor development. This may be attainable above 0.1 meV for photocounters, e.g. SNSPDs, motivating dedicated measurements in preparation, and next-generation bolometers at lower masses given a recent TES-based device reports 8 × 10 −22 W Hz −1/2 electrical NEP [153] . Maintaining signal efficiency when upgrading A dish = 0.7 → 10 m 2 requires quadrupling the active sensor width. Overcoming these challenges promises significant scientific payoff given the multidecade improvements in search coverage that has long eluded cavity haloscopes. Post discovery, the DM signal will always persist, enabling cross checks with resonant techniques and measurements to elucidate its particle physics and astrophysical properties [70, 91] .

In summary, we proposed BREAD to improve sub-eVmass DM reach by several decades. We introduced the novel coaxial design optimized for embedding in standard solenoids and cryostats, in contrast to existing dish antennas, then detailed numerical optics simulation and examined photosensor candidates. Realizing BREAD into a cornerstone DM experiment will catalyze synergies across quantum technology and astroparticle physics. Valle, Joaquin Viera, and Steven Zoltowski for interesting and helpful discussions. This work is funded in part by the Department of Energy through the program for Quantum Information Science Enabled Discovery 

This appendix first reviews the axion and dark photon signal rate and sensitivity in bolometric and photocounting regimes. Next, we present additional discussion on the cryostat and magnet followed by dark matter velocity effects on the signal spot size. Then, we expand discussion on photosensor performance and noise sources before commenting further on bolometers. Finally, we discuss a potential experimental staging for BREAD.

The interaction Lagrangian coupling SM photons to dark photons A (a spin 1 vector) and axions a (a spin 0 pseudoscalar) is given respectively by [9, 68] 

whereF µν = µνρσ F ρσ with µνρσ being the totally antisymmetric tensor, g aγγ is the axion-photon coupling, κ is the kinetic mixing parameter, and F ( )

is the SM (dark) photon field strength. Upon solving the Lagrangian equations of motion, the consequential modification to SM electrodynamics is an additional effective source current J DM in the Ampère-Maxwell equation [42] 

The nonzero current J DM from the DM-photon interaction Lagrangian of Eq. (3) is given by

where A (t) and a(t) are the dynamical dark photon and axion fields, respectively, and B ext is the external magnetic field applied in the laboratory. In general, one considers wave solutions of the form exp[i(k · x − ωt)], where ω = m DM . As the local DM halo has nonrelativistic velocity v 10 −3 , the momentum wavevector approximately vanishes k → 0 and thus ∇×B in Eq. (4) induced by DM is negligible. From the cosmology of bosonic condensate DM, the local halo energy density ρ DM is related to the DM mass and fields by

Using this in Eq. (5) gives the resulting source current for axions has the form J a = g aγγ √ 2ρ DM B ext cos(m a t).

For dark photons, the source current is J A = κm A √ 2ρ DMn cos(m A t), wheren is the A polarization.

The electric field induced by J DM is then deduced from Eq. (4) and has magnitude where B || ext is the magnetic field component parallel to the emitting barrel surface. This nonzero electric field causes a discontinuity at the interface of a conducting dish in vacuum. To satisfy the E = 0 boundary condition parallel to the dish surface (from Faraday's law ∇ × E + ∂ t B = 0, which remains unchanged), a compensating electromagnetic wave with amplitude E 0 must be emitted perpendicular to the surface. The power per unit area P/A dish of the emitted waves is given by P/A dish = 1 2 |E 0 | 2 and applying this to the axion-induced electric field of Eq. (7) gives P a = 1 2 ρ DM (B ext g aγγ /m a ) 2 A dish for dish area A dish . Normalizing the power to experimental parameters, the power emitted for axion and dark photon DM is, respectively

In photon counting regimes, it is more convenient to consider the DM-induced rate R DM of emitted photons given by P DM /m DM : For counting statistics, the relevant figure-of-merit is the significance Z given a runtime ∆t, which for a photosensor with dark count rate DCR, is estimated as

Formally, N signal / √ N noise holds in the Gaussian regime where N noise 10, below which Poissonian statistics applies. For zero noise counts N noise = 0, one has 95% CL exclusion sensitivity for three or more signal events.

Requiring Z = 5 for DM reach implies the coupling sensitivity is related to the DCR by 

While measuring DCR is more relevant for photosensors operating in photon counting regimes, device physics literature often converts to NEP using NEP = (E/ ) √ 2 · DCR to facilitate comparisons [121] , where is the detection efficiency.

Canonical QCD axion scenarios [80] fix the relation between the axion coupling and mass to g KSVZ aγγ = −3.9 × 10 −13 (m a /meV) GeV −1 and g DFSZ aγγ = 1.5 × 10 −13 (m a /meV) GeV −1 . The prefactor depends on the theoretical details of the ultraviolet completion assumed in the KSVZ and DFSZ models [76] [77] [78] [79] . Using Eq. (9), we find the photon emission rate is

(12) Figure 3 shows the photon emission rate R γ = P DM /m DM for the QCD axion scenarios assuming A dish = 10 m 2 and B ext = 10 T, where the impact of reducing these parameters by a factor of ten is shown.

In this configuration, we estimate on the order of 100 photons per day for 1 THz (4 meV) photons considering the KSVZ scenario. Higher masses m a 1 eV requires longer runtimes ∆t months to overcome shot noise.

The BREAD geometry is advantageous over recent dish antenna designs that use spherical or flat emitting surfaces [69] [70] [71] [72] [73] because the latter are not suited for enclosure in a solenoid and typically require custom magnet designs. Solenoids are the leading magnet design that allows access to large bore sizes and high magnetic fields. An extant large-bore of radius R = 3 m solenoid in particle physics is the CMS experiment at CERN but with modest fields B = 3.8 T, while the ITER project features an R = 1.3 m, B = 13 T magnet [81, 82] . However, these meter-scale magnets cost around three orders of magnitude more than magnets used for state-of-the-art DM experiments e.g. ADMX.

The dish area and magnetic field are two haloscope parameters that bound the instrument dimensions and govern experimental sensitivity of BREAD. The coupling sensitivity improves as ∼ A 1/2 dish B ext . One may consider advances in both existing cryostat and magnets size possible with 10 years of research-and-development. Figure 4 (left) shows how the sensitivity to the axion-photon coupling varies with the product A dish · B 2 ext for 1 and 1000 days runtime. For the proposed aspect ratio where the barrel length L is related to its radius R by L = 2 √ 2R, the radius is fully determined from the dish area A dish

. So as R ∼ A 1/2 for BREAD, coupling sensitivity scales linearly with both bore radius and field strength B ext R.

The radius for the pilot A dish = 0.7 m 2 is R = 0.2 m and the nominal experiment with A dish = 10 m 2 has R = 0.75 m. While a A dish = 100 m 2 barrel that has R = 2.4 m is within engineering feasibility, the financial cost of the large cryostat and magnet required is challenging. The energy stored in the magnetic field in the solenoid is (

, where µ 0 is the vacuum magnetic permeability, which corresponds to 150 MJ for R = 0.75 m, B = 10 T. For comparison, standard medical magnetic-resonance-imaging (MRI) magnets typically have a bore radius of around 0.35 m. Constructing a dedicated solenoid for BREAD is financially impractical. We have identified an available 9.4 T solenoid originally constructed for MRI research at the University of Illinois at Chicago, which we plan to repurpose for next-generation axion DM experiments at Fermilab including BREAD. Given coupling sensitivity scales quickest with the magnetic field, this reinforces the motivation for continued research-and-development into high-field large-bore solenoids. Once the haloscope design parameters A dish , B ext are maximized within engineering and financial feasibility, photosensor performance then governs DM discovery reach.

In principle, the parabolic reflector focuses EM radiation emitted perpendicularly to the barrel onto a point, but in practice, the resulting spot size is smeared. This is due to a nonzero DM velocity causing the direction of photon emission to deviate from the surface normal by a small angle. Therefore, if the photosensor area A sens is smaller than the signal spot area A spot , A sens < A spot , the signal detection efficiency is reduced. Figure 6 shows the impact of DM velocity on the geometric signal efficiency A sens /A spot assuming the sensor has saturated efficiency i.e. each photon that arrives within A sens is absorbed and a detection reported. The upper (lower) axis shows the detector radius assuming the barrel radius is R = 0.75 (0.2) m. The dashed (solid) line shows the most optimistic (pessimistic) scenario for the DM wind velocity aligned in the z (x/y) direction. For the pilot experiment with R = 0.2 m with A dish = 0.7 m 2 , achieving 50% signal efficiency assuming z (x/y) DM-wind alignment requires a 0.25 mm (0.5 mm) sensor radius. The larger nominal radius of R = 0.75 m requires a 1 mm (2 mm) radius sensor. As discussed in the main text, such sensor dimensions are readily fabricated for commercial bolometers but state-of-the-art superconducting photosensors are typically on the order of ∼ 0.1 mm in size or smaller. Figure 4 (center) shows how the sensitivity varies with detection efficiency, showing the modest √ s dependence in Eq. (2) . Indeed, the main text sets an efficiency of s = 50% for simplicity. Because the coupling sensitivity from Eq. (11) only scales as √ s , if instead s = 5%, the sensitivity is only reduced by a factor of around three. Nonetheless, this sets an important BREAD physics-driven instrumentation goal of scaling the candidate sensors to millimeter dimensions while maintaining low noise.

The main text identifies various candidate technologies that could meet the stringent requirements of BREAD. The values reported in the literature are often optimized to certain spectral bands or optical configurations, and while the sensor technologies typically have broadband response, this requires experimental demonstration. Photosensors are also typically fabricated as a flat plane for perpendicular illumination, whereas the photons in BREAD can arrive at steep incidence angles. As the photons are emitted perpendicularly to the surface (and magnetic field), they also have specific polarization. Specifically for BREAD, it is important to characterize how both signal efficiency and noise (dark count) performance scales with not only frequency but also angle-of-incidence and polarization. Many of these photosensor properties are challenging to simulate, therefore dedicated insitu measurements of candidate photosensor technologies are required and under preparation. Ensuring signal efficiency and noise performance are demonstrated while scaling sensor active area to millimeter-sized pixels and/or arrays are key research goals for BREAD.

The noise budget and sources can be categorized by: intrinsic to sensor such as readout, internal thermal fluctuations; extrinsic to sensor such as environmental thermal emission and cosmic rays. Devices that act like bolometers are limited by intrinsic sources such as thermal fluctuations in TESs, and generation-recombination noise of pairs in KIDs. Single photon counters such as SNSPDs are reaching very low noise that they are limited by extrinsic sources. Carefully understanding these noise sources experimentally for BREAD could help design strategies for their mitigation.

Environmental conditions that would affect long-term low-background measurements are challenges not unique to BREAD but also other DM experiments. Cosmicray backgrounds are stochastic, are not expected to have long-term variations, and can be actively rejected with in situ veto systems. The alignment of the barrel-reflectorsensor setup could be subject to time-dependent environmental variations such as temperature and humidity or mechanical vibrations. These can be rejected by correlation with active monitoring systems, and further accommodated with regular dedicated calibration and alignment runs. Detailed studies of this requires in situ data of the experimental site that is the subject of future work.

To provide concrete targets driven by BREAD for photosensor noise, we can estimate the required NEP for sensitivity to the KSVZ and DFSZ axion assuming different runtimes in Figure 4 (right) following Eq. (2). The state-of-the-art NEP today is around 3×10 −21 W Hz −1/2 for quantum capacitance detectors [101] . There are also recent claims TES-based device could achieve 8 × 10 −22 W Hz −1/2 electrical NEP [153] . With this noise performance, it remains challenging to probe the KSVZ scenario assuming 1000 days runtime, which requires 1 × 10 −22 W Hz −1/2 . Probing DFSZ requires an order of magnitude improvement in NEP to 2 × 10 −23 W Hz −1/2 , which is very challenging but motivates a target for sensor research-and-development. Figure 5 shows the projected reach for dark photons and axions in the coupling vs. mass plane for generic bolometric photosensors or photocounters, assuming various NEP and DCR for ∆t = 1000 days runtime. Experimentally demonstrating that the required NEP is achievable across several decades of frequency with high efficiency is a challenging requirement for BREAD to probe QCD axion models. The scientific potential for realizing this is significant, given the multidecade mass sensitivity without needing to tune the experiment to an unknown DM mass. Photocounters such as SNSPDs have promising dark count rates, but their low-mass (longer wavelength) reach are currently limited to E > 125 meV photon energies (λ < 10 µm wavelengths) [104] . Lowering these photon energy thresholds is a key sensor research-anddevelopment target that would have a significant payoff in BREAD.

We expand on details related to bolometers. For the SNR calculation with bolometers, the bandwidth of the sensor does not enter directly. A chopper or moving mirror modulates the signal, allowing noise mitigation by rejecting DC power components. Thus the bandwidth appearing in the signal-to-noise calculation is the bandwidth of the modulated signal, which becomes narrower with integration time, giving an SNR that improves with √ ∆t. The sensor bandwidth of a bolometer is measured with pulse rise and decay time. This is only relevant in that it restricts the speed that the signal can be modulated with a chopper. For example, the chopper acquired with the IR Labs bolometer operates at 100 Hz implying a 10 millisecond or faster bolometer response is required.

The noise equivalent power NEP is related to the thermal relaxation time of a bolometer. Therefore, the design goals of NEP and large bandwidth are in tension and the lowest noise bolometers will be slow. Bolometers need to have sufficiently fast response such that a chopper can modulate the signal at a frequency that makes 1/f components of the system noise subdominant. We anticipate this does depend on the specific device technology, and characterizing this for candidate sensors with experimental measurements is an important part of the BREAD research program. Table II summarizes benchmark experimental parameters for a staged approach to BREAD. The corresponding sensitivity to the axion g aγγ and dark photon κ couplings are normalized to benchmark targets. We consider the prototypical pilot dark photon search with 10 days runtime. This demonstrator forms a nearer-term science goal that will give valuable experimental experience, already provide meaningful physics results, and serve as a proofof-principle for BREAD. Longer term, stage 1 shows the nominal experiment with the full-scale experiment inside a 10 T magnet assuming only a 10 −18 W Hz −1/2 NEP photosensor can be installed and demonstrated, which can start to probe currently unconstrained axion parameter space. The planned stage 2a (2b) considers 1000 days runtime and experimental work to successfully develop and couple a 10 −20 (10 −22 ) W Hz −1/2 NEP photosensor. This could probe QCD axion scenarios assuming ongoing research-and-development can demonstrate multiple order-of-magnitude improvements in sensor NEP.

Rotation of the Andromeda Nebula from a Spectroscopic Survey of Emission Regions

Detailed mass map of CL0024+1654 from strong lensing

Cosmological parameters from SDSS and WMAP

A direct empirical proof of the existence of dark matter

Planck 2018 results. I. Overview and the cosmological legacy of Planck

Particle dark matter: Evidence, candidates and constraints

Natural units are used, where the (reduced) Planck's constant , speed of light c, vacuum permittivity ε0 and permeability µ0 are set to unity = c = ε0 = µ0 = 1

String Axiverse

The Low-Energy Frontier of Particle Physics

Working Group Report: New Light Weakly Coupled Particles

The quest for axions and other new light particles

New Ideas in Dark Matter 2017: Community Report

Quantum Sensing for High Energy Physics

New experimental approaches in the search for axion-like particles

Results from a search for dark matter in the complete LUX exposure

Dark Matter Results from First 98.7 Days of Data from the PandaX-II Experiment

Dark Matter Search Results from a One Ton-Year Exposure of XENON1T

First Dark Matter Constraints from a SuperCDMS Single-Charge Sensitive Detector

Results on Low-Mass Weakly Interacting Massive Particles from an 11 kg d Target Exposure of DAMIC at SNOLAB

Analyzing the Discovery Potential for Light Dark Matter

Dark Matter Searches at Colliders

Searches for electroweak production of supersymmetric particles with compressed mass spectra in √ s = 13 TeV pp collisions with the ATLAS detector

Combination of Searches for Invisible Higgs Boson Decays with the ATLAS Experiment

Search for new phenomena in events with an energetic jet and missing transverse momentum in pp collisions at √ s =13 TeV with the ATLAS detector

New Experimental Limit on the Electric Dipole Moment of the Neutron

Improved Experimental Limit on the Electric Dipole Moment of the Neutron

Revised experimental upper limit on the electric dipole moment of the neutron

Measurement of the Permanent Electric Dipole Moment of the Neutron

CP Conservation in the Presence of Instantons

Problem of Strong P and T Invariance in the Presence of Instantons

A New Light Boson?

Two U(1)'s and Epsilon Charge Shifts

Kinetic mixing and the supersymmetric gauge hierarchy

Secluded U(1) below the weak scale

Naturally Light Hidden Photons in LARGE Volume String Compactifications

Cosmology of the Invisible Axion

A Cosmological Bound on the Invisible Axion

The Not So Harmless Axion

Dark Light, Dark Matter and the Misalignment Mechanism

WISPy Cold Dark Matter

Axion dark matter: What is it and why now?

Experimental Tests of the Invisible Axion

Limits on the Abundance and Coupling of Cosmic Axions at 4.5 < ma < 5.0 µeV

Results of a Laboratory Search for Cosmic Axions and Other Weakly Coupled Light Particles

Results from a search for cosmic axions

Large scale microwave cavity search for dark matter axions

Experimental constraints on the axion dark matter halo density

SQUID-Based Microwave Cavity Search for Dark-Matter Axions

A Search for Hidden Sector Photons with ADMX

A Search for Invisible Axion Dark Matter with the Axion Dark Matter Experiment

Extended search for the invisible axion with the axion dark matter experiment

Search for Invisible Axion Dark Matter in the 3.3-4.2 µeV Mass Range

Axion Dark Matter Search around 6.7 µeV

Search for Invisible Axion Dark Matter with a Multiple-Cell Haloscope

First Results from an Axion Haloscope at CAPP around 10.7 µeV

Design and operational experience of a microwave cavity axion detector for the 20-100 µeV range

First Results from a Microwave Cavity Axion Search at 24 µeV

Results from phase 1 of the HAYSTAC microwave cavity axion experiment

HAYSTAC), "A quantum-enhanced search for dark matter axions

Dielectric Haloscopes: A New Way to Detect Axion Dark Matter

Dielectric Haloscopes to Search for Axion Dark Matter: Theoretical Foundations

A new experimental approach to probe QCD axion dark matter in the mass range above 40 µeV

Axion and hidden photon dark matter detection with multilayer optical haloscopes

Proposal to Detect Dark Matter using Axionic Topological Antiferromagnets

Vector Dark Matter from Inflationary Fluctuations

More Axions from Strings

Predictions for Axion Couplings from ALP Cogenesis

Searching for WISPy Cold Dark Matter with a Dish Antenna

Experimental Search for Hidden Photon CDM in the eV mass range with a Dish Antenna

First results from a hidden photon dark matter search in the meV sector using a plane-parabolic mirror system

Search for hidden-photon cold dark matter using a K-band cryogenic receiver

Limits from the Funk Experiment on the Mixing Strength of Hidden-Photon Dark Matter in the Visible and Near-Ultraviolet Wavelength Range

Brass website

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This value of ρDM is typically adopted in axion haloscope literature [50], but we note its significant uncertainties that range from

A Simple Solution to the Strong CP Problem with a Harmless Axion

On Possible Suppression of the Axion Hadron Interactions

Weak Interaction Singlet and Strong CP Invariance

Can Confinement Ensure Natural CP Invariance of Strong Interactions?

The QCD axion, precisely

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Ultra-High Field Solenoids and Axion Detection

An antenna for directional detection of WISPy dark matter

Directional Resolution of Dish Antenna Experiments to Search for WISPy Dark Matter

Dish Antenna Searches for WISPy Dark Matter: Directional Resolution Small Mass Limitations

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Single-photon imager based on a superconducting nanowire delay line

Directional axion detection

Dark photon limits: A handbook

Superconducting Nanowire Single-Photon Detectors

Bolometers for infrared and millimeter waves

Advances in bolometer technology for fundamental physics

Bolometer operating at the threshold for circuit quantum electrodynamics

QCDet representing quantum capacitance detector avoids ambiguity with QCD denoting quantum chromodynamics

Infrared Laboratories, Bolometers

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Large array of low-frequency readout quantum capacitance detectors

Detecting Sub-GeV Dark Matter with Superconducting Nanowires

Single-photon detection in the midinfrared up to 10 micron wavelength using tungsten silicide superconducting nanowire detectors

An application of electrothermal feedback for high resolution cryogenic particle detection

Transition-edge sensors

Superconducting transition edge sensors for quantum optics

Ultra-low-noise MoCu transition edge sensors for space applications

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Photon shot noise limited detection of terahertz radiation using a quantum capacitance detector

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Demonstration of a low-noise near-infrared photon counter with multiphoton discrimination

Counting near-infrared single-photons with 95% efficiency

Energy-resolved detection of single infrared photons with λ = 8 µm using a superconducting microbolometer

Solar constraints on hidden photons re-visited

New axion and hidden photon constraints from a solar data global fit

Cosmological evolution of light dark photon dark matter

Dark Photon Oscillations in Our Inhomogeneous Universe

First results of the CERN Resonant Weakly Interacting sub-eV Particle Search (CROWS)

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Direct Searches for Hidden-Photon Dark Matter with the SHUKET Experiment

Searching for Dark Matter with a Superconducting Qubit

First results from the WISPDMX radio frequency cavity searches for hidden photon dark matter

Search for Solar Axions by the CERN Axion Solar Telescope with 3 He Buffer Gas: Closing the Hot Dark Matter Gap

New CAST Limit on the Axion-Photon Interaction

A Telescope Search for Decaying Relic Axions

Searching for light in the darkness: Bounds on ALP dark matter with the optical MUSE-faint survey

Green Bank and Effelsberg Radio Telescope Searches for Axion Dark Matter Conversion in Neutron Star Magnetospheres

New Limits on Axionic Dark Matter from the Magnetar PSR J1745-2900

Towards robust constraints on axion dark matter using PSR J1745-2900

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