Search for Dark Photon Dark Matter: Dark E-Field Radio Pilot Experiment
Benjamin Godfrey, J. Anthony Tyson, Seth Hillbrand, Jon Balajthy, Daniel Polin, S. Mani Tripathi, Shelby Klomp, Joseph Levine, Nate MacFadden, Brian H. Kolner, Molly R. Smith, Paul Stucky, Arran Phipps, Peter Graham, Kent Irwin
SSearch for Dark Photon Dark Matter:Dark E-Field Radio Pilot Experiment
Benjamin Godfrey, J. Anthony Tyson, ∗ Seth Hillbrand, Jon Balajthy, † DanielPolin, S. Mani Tripathi, Shelby Klomp, ‡ Joseph Levine, and Nate MacFadden § Physics Department, UC Davis, Davis, CA 95616
Brian H. Kolner and Molly R. Smith ¶ Electrical and Computer Engineering Department, UC Davis, Davis, CA 95616
Paul Stucky
Chemistry Department, UC Davis, Davis, CA 95616
Arran Phipps
Physics Department, CSU East Bay
Peter Graham and Kent Irwin
Physics Department, Stanford University (Dated: February 16, 2021)We are building an experiment to search for dark matter in the form of dark photons in thenano- to milli-eV mass range. This experiment is the electromagnetic dual of magnetic detectordark radio experiments. It is also a frequency-time dual experiment in two ways: We search for ahigh-Q signal in wide-band data rather than tuning a high- Q resonator, and we measure electricrather than magnetic fields. In this paper we describe a pilot experiment using room temperatureelectronics which demonstrates feasibility and sets useful limits to the kinetic coupling (cid:15) ∼ − over50–300 MHz. With a factor of 2000 increase in real-time spectral coverage, and lower system noisetemperature, it will soon be possible to search a wide range of masses at 100 times this sensitivity.We describe the planned experiment in two phases: Phase-I will implement a wide band, 5-millionchannel, real-time FFT processor over the 30–300 MHz range with a back-end time-domain optimalfilter to search for the predicted Q ∼ line using low-noise amplifiers. We have completed spotfrequency calibrations using a biconical dipole antenna in a shielded room that extrapolate to a5 σ limit of (cid:15) ∼ − for the coupling from the dark field, per month of integration. Phase-II willextend the search to 20 GHz using cryogenic preamplifiers and new antennas. I. INTRODUCTION
The physical nature of dark matter is unknown. Sen-sitive searches for weakly interacting massive particles(WIMPS) have found nothing [1]. In recent years theWIMP hypothesis has dominated searches for dark mat-ter since a generic weak-scale thermal relic could accountfor all of the observed dark matter in the universe [2].Experimenters continue to probe new WIMP parameterspace by developing larger and more sensitive detectors,however these tend to lose sensitivity when the mass ofthe dark matter particle is small, leaving a large range ofparameter space open for exploration [3].The 2014 P5 report [4] emphasizes the importance ofsearching for dark matter along every feasible avenue.To date, relatively little effort has been spent on detec-tion of ultra-low mass dark matter candidates where it is ∗ [email protected] † Now at Sandia National Laboratories. ‡ Now at Physics Department, Northwestern University. § Now at Physics Department, University of Waterloo. ¶ Now at Microsoft, Seattle, WA. best described as a wave rather than a particle [5]. Thisrequires development of new detectors.The dark photon is a hypothetical, low-mass vector bo-son which has been posed as a candidate for dark matter.Dark photons could account for much of the dark matter,and are theoretically motivated via fluctuations of a vec-tor field during the early inflation epoch of our universe.A relic abundance of such a particle could be producednon-relativistically in the early universe in a similar wayto axions, through either the misalignment mechanismor through quantum fluctuations of the field during in-flation [6, 7].In contrast to axions, a massive, inflation-producedvector boson like a dark photon would have a power spec-trum that is peaked at a length scale of roughly 10 km,and rapidly decreases in intensity at large length scales,consistent with CMB observations. Furthermore, a darkphoton would adopt the adiabatic fluctuations of the in-flaton making it a good dark matter candidate [7]. Thehigh phase space density required for dark photons toconstitute a significant portion of the local dark mat-ter density ( ∼ a r X i v : . [ phy s i c s . i n s - d e t ] F e b eral, for a theory with two U(1) symmetries, there wouldbe some weak coupling with a corresponding term in theLagrangian [8–10]. The Lagrangian then varies from thestandard model, L SM , as shown in Eq. 1. L = − F (cid:48) µν F (cid:48) µν + 12 m A (cid:48) µ A (cid:48) µ − (cid:15)F (cid:48) µν F µνEM + L SM (1)Here m is the mass of the dark photon, F µν and A µ arethe electromagnetic field strength and gauge potential, F (cid:48) µν and A (cid:48) µ are the dark photon field strength and gaugepotential, and (cid:15) is the dark photon-to-electromagneticcoupling factor which must be measured. The mixingterm between the two coupled fields is then (cid:15)F (cid:48) µν F µνEM .Through kinetic mixing, dark photons would be de-tectable in traditional electromagnetic searches, and (cid:15) can be measured. Previous experimental bounds on (cid:15) from direct detection are summarized in [11]. The otherunknown is the mass (frequency) of the dark photon.We are building an experiment to search for dark pho-tons in the nano- to milli-eV mass range. This experi-ment is the electromagnetic dual of magnetic dark pho-ton experiments performed by Parker, et al., [12] andChaudhuri, et al., [13]. We have completed a feasibil-ity test of our Dark E-field Radio experiment which hasshown that the full experiment can work. Here we reporton this pilot experiment. We plan to finish constructionof the experiment and carry out a comprehensive searchover a mass range spanning four orders of magnitude.For this, we are developing a novel time-spectrum detec-tor which optimally detects a monochromatic signal andrejects signals varying on timescales incompatible withthe model.The remainder of the paper is organized as follows.In Section II we review the detection technique, and theplans for an efficient wideband real-time FFT. In SectionIII we outline the current pilot experiment and plans forthe next phase. In Section IV we present a sensitivityanalysis describing how the limit on the kinetic couplingparameter (cid:15) depends on system parameters. In SectionV we discuss EM simulations of the response to a vol-ume electric field in the shielded room. In Section VIwe describe the details of this pilot experiment and itsS/N, while Section VII presents our data acquisition andanalysis methods. Signal injection tests of sensitivity aregiven in Section VIII. Section IX presents the search logicand preliminary results on (cid:15) in this pilot experiment, andin Section X we outline the eventual reach of the experi-ment in two future phases.
II. FEMTOVOLT TIME-SPECTRUMDETECTOR
Evidence for the existence of dark matter was discov-ered via its gravitational effects on large scale dynam-ics, and new astronomical probes promise to establishadditional constraints on its physical nature [14]. Astro-nomical observations [15, 16] jointly give the energy den-sity of dark matter, ρ DM , at our position in our Galaxy: 380 ±
180 TeV/m . For dark photons in free space, con-verting this energy density to its corresponding observedelectric field gives [13] (cid:12)(cid:12) (cid:126)E obs (cid:12)(cid:12) ≈ (cid:15) (cid:114) ε ρ DM (2)For our local dark matter energy density, this gives ∼ (cid:15) .Because the dark field will pass through any shield-ing, the entire experiment is placed inside an electro-magnetic shield to screen external, interfering electro-magnetic sources. This shielding, however, will affectthe sensitivity of the experiment. As a simple analyticexample, inside a cylindrical conducting shield whose ra-dius, R , is much smaller than the wavelength of the darkphoton oscillations ( λ = h/m γ (cid:48) c for dark photon mass m γ (cid:48) ), this observed field will be suppressed, giving [13] (cid:12)(cid:12) (cid:126)E obs (cid:12)(cid:12) ≈ ε (cid:114) ε ρ DM (cid:16) m γ (cid:48) c (cid:126) (cid:17) R (3)plus a term (that is negligible in our frequency range) ∝ m γ (cid:48) R v DM where v DM ∼ − c is the velocity of thedark matter. In the limit where λ (cid:28) R , the observedelectric field approaches its free space value. In the caseof more complex geometries such as a shielded room withfixtures, the general trend is the same, but a numericalsimulation must be performed.As in WIMP searches, there are two unknowns: thefrequency of the wave (a proxy for the mass) and itsweakly coupled amplitude. We measure the induced elec-tric field with a wideband antenna. The experiment isconducted inside a large ( ≈ ) electromagneticallyshielded room, searching for a weak narrowband signalbetween 30 MHz and 20 GHz from dark photons con-verting from within the shield. The antenna is polar-ization sensitive, enabling detection of the expected E -field in any direction whence aligned. The challenge isdetecting a 1 ppm spectrally pure signal, varying onlyon 12-hour timescales (Earth rotation), at femtovolt lev-els, in wideband noise. Since the frequency of the lineis unknown, the search must be over as wide a spectralrange as possible. For high spectral efficiency, we mustalso measure this small signal simultaneously at each can-didate frequency. Our experiment will use a 62-millionchannel real time fast Fourier transform (FFT) processorusing field-programmable gate arrays (FPGAs) similar toMacMahon et al.[17].In order to have high spectral efficiency plus highsensitivity, we leverage two new technologies: an ultra-low-noise radio receiving system inside a large shieldedroom, plus state-of-the-art wide-band spectrum monitor-ing. Together with time-domain filtering, the combina-tion will be a uniquely efficient real-time detector whichcan simultaneously search wide swaths of frequency forthe signal from dark photons converting to detectablephotons with fractional bandwidth (mass) of 1 ppm.To test this idea, we have built a pilot experiment in-side a shielded room using a wide-bandwidth biconicalantenna and room temperature preamps (Fig. 1). Todate, we have performed two proofs of concept: Firstly,we detect a 150 pV/m converted dark photon proxy sig-nal injected into the shielded room using an RF signalgenerator (outside the shielded room) connected to a low-gain dipole inside the room over the course of a 1-monthintegration.Secondly, we do a two-month long run between 50-300MHz with a Q of 10 looking for single bin anomalies ontop of the RF background. However, both runs sufferfrom ultra-low spectral efficiency because of the limitedfrequency span of the commercial real-time spectrum an-alyzer currently used in our pilot experiment. To cover awide spectral range we must integrate over each narrowspan and then step to the next span.For the next phase of the experiment, our plannedtime-spectrum detector with cryogenic preamps will solvethat problem by addressing the twin issues of simultane-ous wide spectrum sampling and time invariant signal fil-tering, enabling a sensitive search for dark photons overa large range of effective mass. III. THE EXPERIMENT
We propose to develop a novel 100% spectral efficiencydetector utilizing multiple special antennas, with cryo-genic preamps, and construct three efficient FFT spec-tral monitoring systems [18], along with the software fortime-signature filter and data analysis. A time-frequencysignal-matched filter significantly enhances the signal-to-background ratio by demanding that the signal occupyonly one spectral bin and be constant in time for hours.Because a monochromatic constant signal transmits noinformation, no intentional signal has this propertyInstrumenting two separated shielded rooms we plan torun simultaneous searches in multiple frequency bands,integrating for a month, covering a vast frequency range,ultimately THz. Spectral data will be stored frequentlyso that any candidate detection can be analyzed for timedependence because the power spectrum of a true darkmatter E -field signal will not vary on short timescales.Figure 1 shows the current 30–300 MHz setup in a3 . × . × .
67 m commercial shielded room with over100 dB isolation. For the pilot experiment all conductingfeatures in the room which could measurably affect oursimulations over a 50–300 MHz range have been includedin the solid model. We have done EM simulations versusfrequency of the induced currents in the walls due tothe weakly converting dark photon field and validatedthe predicted antenna voltage by injected signal tests.At frequencies above 200 MHz the room suppression ofthe signal is small, and the antenna transfer function(antenna factor) approaches that of free-space.Before describing the results of our pilot experiment, inthis section we describe plans for the next phases of theexperiment. In Phase-I (post-pilot), a wide band FFTover the 30–300 MHz region, with a back end optimal
FIG. 1. The Dark E-field Radio experiment inside a largeelectromagnetic shielded room, searching for a narrowbandsignal between 30 MHz and 20 GHz from dark photons con-verting inside the shield. The antenna is placed in the centerof the room. Features that affect the modes of the room areshown including light fixtures, electrical box, and door latch.All of these impact the antenna’s response to wall currents.The output from the antenna is fed into a low noise ampli-fier inside the shield, whose buffered output is connected to awideband real-time spectrum analyzer for data processing. filter, will be used for the initial search for the predicted Q ∼ line, using low-noise amplifiers. Phase-II willsearch up to 20 GHz and will use cryogenic preamps anda novel antenna design. We can ultimately cover a factorof 10,000 in mass range, at levels of sensitivity up to 10 times better than current astrophysical limits. IV. SENSITIVITY ANALYSIS
Of course the direction of a monochromatic E -fieldfrom dark photons is unknown. Although we do notrecord phase, the receiver is sensitive to E -field direc-tion due to the polarization sensitivity of the antenna.For example a dipole has peak sensitivity to an E -fieldaligned with its axis. We mount the antenna such thatit is most sensitive to the east-west component of an E -field, so that if a signal is detected, its amplitude will bemodulated on 12-hour periods by the Earth’s rotation.The sensitivity of the receiver in this pilot experimentis limited by the thermal noise of the low-noise pream-plifier, which dominates the thermal emission from thewall. The voltage presented at the input to the preampby thermal radio emission from the walls is reduced bytwo factors relative to the noise voltage generated in thepreamp: the emissivity of the wall, and the antenna fac-tor (see Section V).The measurable quantities are the total power, P T , andthe system noise power, P sys . The noise power can alsobe measured by averaging the measured power in nearbyfrequency bins. The signal power, P sig , adds linearly withthe noise power and thus can be found by subtracting thenoise power from the total power P sig = P T − P sys = V Re (cid:8) Z (cid:9) / | Z | (4)where V sig is the measured RMS voltage and Z is theimpedance of the antenna. We use a balun to matchthe impedance of the antenna to the transmission lineand therefore Re (cid:8) Z (cid:9) / | Z | ≈ / | Z | . The signal voltage isrelated to the electric field at the position of the antenna, (cid:126)E x by the antenna factor AF AF ≡ (cid:12)(cid:12)(cid:12)(cid:12) (cid:126)E x V sig (cid:12)(cid:12)(cid:12)(cid:12) (5)This response, AF , is defined as the electric field compo-nent coupling to the antenna divided by the correspond-ing voltage developed at the antenna terminals. AF hasunits of meters − .In free space, the dark matter energy density is relatedto the measured electric field via ρ DM = ε (cid:15) (cid:12)(cid:12)(cid:12) (cid:126)E (cid:48) (cid:12)(cid:12)(cid:12) (6)where (cid:15) is the small kinetic mixing parameter betweenthe dark photon and electromagnetism and ε is the per-mittivity of free space. From this, the signal power isrelated to the local dark matter energy density accord-ing to P sig = (cid:15)ε ( AF ) | Z | ρ DM (7)The uncertainty in a noise measurement on a narrowband signal, σ T , is given by the Dicke radiometer equa-tion [19] [20] σ T ≈ T sys (cid:112) ∆ ν RF τ (8)where T sys is the system noise temperature. The band-width, ∆ ν RF , times the integration time, τ , gives thenumber of trials in the integration. The random uncer-tainty in the measured power, σ P , is therefore given by σ P ≈ k B ∆ ν RF σ T (9)This uncertainty applies to both the measurement of to-tal power and to the measurement of the baseline power.The total power is measured for a single bin, whereasthe baseline power is measured using a large number ofbins, so the statistical uncertainty in the signal power isapproximately given by σ P ≈ k B σ T ≈ k B T sys (cid:112) ∆ ν RF τ (10) ( f - f o ) / f
20 15 10 5 0 5 10 15 N u m b e r o f S c a n s A m p li t ude ( n V )
70 80 90100110120130
FIG. 2. SNR dependence on number of scans averaged fora 10nV signal, relative to a 100 nV long-time averaged noisefloor, at a frequency of f . The red, blue, magenta, and greencurves represent the signal after 1, 10, 100, and 1,000 scans,respectively. The width of this signal is assumed to be ∆ f = f / . Note that even though the average noise level goesdown like the square root of time (Equation 11), the limit onthe scalar coupling constant, (cid:15) , goes as the quarter root oftime (Equation 12). Time M ea s u r ed S i gna l ( n V ) FIG. 3. Time dependence of a detection. The gray shadedregion shows the predicted ± σ band of the integrated voltagemeasurement from a 10 nV signal as a function of time. Thesolid blue line shows the 3 σ exclusion limit as a function oftime. The black dashed line and shaded region shows thepredicted time until a 3 σ detection. Figures 2 and 3 illustrate the predicted behavior of theaveraged spectral data and eventual measurement errorin the event of a detection of a 10 nV dark matter signal.Figure 2 shows the time-evolution of the baseline noisenear a detection. As the baseline averages down, the ex-clusion limit will decrease as (number of scans) / . As itapproaches the 10 nV signal, the additional power fromthe dark photon field will manifest as a worsened exclu-sion limit around the central frequency, f . Once the 5 σ threshold is crossed, the uncertainty on the measurementwill decrease as the inverse square root of time.Figure 3 depicts the integration time dependence ofthe 5 σ exclusion limit, and of the predicted integratedvoltage measurement from a 10 nV dark matter signal.The limit curve again decreases like the quarter root ofthe number of scans, and a discovery will occur whenthe measurement rises above this line. The exclusion lineenters the ± σ band of the voltage measurement at 1,428scans and exits at 3,272 scans. This means that althoughthe expected time until detection of such a signal is 2304scans, the actual time will vary by roughly 40%.The uncertainty in the coupling constant due to systemnoise, σ (cid:15) , can be found using standard error propagation σ (cid:15) = ∂∂P sig (cid:115) ( AF ) | Z | ε P sig ρ DM σ P σ (cid:15) = k B T sys (cid:115) ( AF ) | Z | ε ∆ ν RF ρ DM P sig τ (11)If a positive detection is defined as a signal equal to aconstant multiple of the system noise, ξ ∈ R + , the limitof detection for a given integration time is given by (cid:15)σ (cid:15) = 2 P sig k B T sys (cid:114) τ ∆ ν RF ≡ ξ(cid:15) (cid:12)(cid:12)(cid:12) SNR= ξ = (cid:18) ∆ ντ (cid:19) / (cid:115) ξk B T sys ( AF ) | Z | ε ρ DM (12)Equation 11 describes how the uncertainty of a givendark photon signal decreases with integration time, whileEqn. 12 (obtained by substituting Eqn. 7) describes howthe limit of detection is improved with integration time.The former scales like the inverse square root of time, andcan be thought of as an expression of the central limittheorem, while the latter scales as the inverse quarterroot of time. For example, in order to reduce the limitof detection measured using an hour of data by a factorof 10, the integration time would have to be increased toabout 1 year.From Eqn. 12, a factor of four decrease in system tem-perature is equivalent to a factor of 16 longer integrationper span. Clearly, cryogenic preamplifiers are necessary,and the limit on (cid:15) will improve until the preamplifiernoise temperature becomes small relative to the effectivetemperature of the thermal radiation from the walls. Asdiscussed in Section VI, there is a further trade-off be-tween integration time per FFT span and the number ofFFT spans. V. EM SIMULATION OF RESPONSE
The antenna and the shielded room are sufficientlycomplex that an analytic derivation the the effective an-tenna factor is impractical. As a cross validation, we cal-culated the antenna factor analytically for a thick dipolein a rectangular waveguide and in free space, and con-firmed the results using COMSOL electromagnetic sim-ulation software. Using both COMSOL and CST EMsoftware ([21] [22]) we carried out simulations of the re-sponse of our antenna to a converted volume E -field inthe shielded room. As mentioned above, this response isthe antenna factor ( AF ). For our antenna in a shieldedroom, the boundary conditions of the conducting wallsmean that the AF exceeds the free-space value (antennaresponse suppressed) at frequencies for which the wave-length is large compared to the size of the shielded room.At frequencies above this lower cutoff, the AF is quiteunlike the free space AF because of the strong couplingof the antenna to the modes of the shielded room. In fact,the antenna-room system becomes essentially a largerEM detector – providing gain (lower AF ) about a fac-tor of 10 in excess of the isolated dipole over wide fre-quency ranges [23]. The model for the shielded roomand antenna is taken from measurements with precisionof 0.2% of the shortest wavelength. An example of themode structure in the shielded room from a COMSOLsimulation is shown in Fig. 4. FIG. 4. COMSOL simulation of the TE520 room mode.The interior of the room with our biconical antenna isshown alongside a three dimensional heat-map of the E-fieldstrength. The cylinders in the sketch at the top of the roomare light fixtures. On the front-facing side, the electrical panelbox (left) and the door latch (right) are also shown
An EM simulation of the antenna factor for our bi-conical dipole antenna in the shielded room, using CST,is shown in Fig. 5. This simplified antenna plus roommodel “empty room” allows comparison to analyticallyderived modes. Even the presence of the antenna in theroom causes mode-mode coupling.
50 100 150 200 250 300
FREQUENCY (MHz) A N T E NN A F A C T O R ( d B m ) Simulated AF in shielded roomSimulated AF in free space
FIG. 5. CST simulation of the antenna factor of the biconicalantenna in the shielded room as a function of frequency witha broadband 50-180Ω balun matching network (red). Alsoshown is the simulation of the free-space AF (black) empha-sizing how the room and antenna become a strongly coupledsystem. VI. PILOT EXPERIMENT
The pilot study provides a proof of concept of experi-mental design. Data are collected from 50-300 MHz usingthe setup outlined in Fig. 1. For this feasibility study,a biconical antenna, low noise, room temperature am-plifiers, and a commercial real-time spectrum analyzer(RTSA: Rigol Model RSA5065-TG) are used.In the pilot experiment, memory limitations of the cur-rent RTSA require splitting up the entire spectral rangeinto a series of sequential spans, which reduces acquisi-tion efficiency. This span is, in part, defined for a givenwindow type, by a span per resolution ratio,
SRR . Givena required resolution, Q , (defined as frequency over res-olution bandwidth), a center frequency, CF , the span ofa scan can then be calculated fromSpan = CF (cid:20) QSRR + 12 (cid:21) − (13)As an example, for a fixed resolution of 10 and a 1024-point Kaiser window, this requires 454 separate scansto cover the entire range from 50-300 MHz. This lossin efficiency will be mitigated in the ultimate real-timedata acquisition system with 100% efficiency, allowingsimultaneous acquisition across the entire spectral range.In order to make external EM interference subdomi-nant to contributions from thermal and amplifier noise, the shielded room must have greater than 100 dB shield-ing across the entire spectral range surveyed. Experi-ments were done to verify that the shielded room metthese requirements by transmitting a signal of knownfrequency and constant power from the outer lab roomand observing the antenna response when the door tothe room was open versus closed. Care was taken notto overdrive amplifiers, and calibrated attenuators werenecessary. These data confirm that the dominant contri-bution to the noise floor is not from externally generatedEM sources. In addition, the outer lab itself is shielded.Nevertheless, a few high power known signals are de-tected inside the shielded room. Thus, monitoring of thespectrum outside the shielded room is a necessary featureof our experiment. Any signal detected in the shieldedroom must be at least 100 dB stronger outside if it is dueto external RF.The RF noise in the shielded room is non-zero and orig-inates from two sources. First, the 20% emissivity of the290 K walls creates a thermal background which tendsto pile up at the room resonances: k B T per degree offreedom. This is the strongest noise source in the caseof a low noise preamp. The second weaker contributioncomes from the noise coupling out of the input port ofthe preamp itself. Broadband noise from the input portof the preamp can couple to the antenna and radiate intothe shielded room exciting room modes. Both of theseroom noise signals are in addition to the wideband noiseof the preamp. This induced non-white room noise thencouples to the antenna into the preamp, creating a ∼ / added component (modulo the coupling of themode to the antenna polarization) on top of the 100 Knoise temperature preamp white noise spectrum of 530pV/Hz / . A noise spectrum covering the full range ofthe Phase-I bicon antenna is shown in Fig. 6. The mea-sured RMS noise-voltage spectral density vs. frequency isshown, referred to the output of the antenna. Also shownfor reference is the short-circuit noise spectral density ofthe preamp. VII. DATA ACQUISITION AND ANALYSIS
The goal of the experiment is to search for a Q ≈ ,time invariant signal on less than 12-hour time scales,that is completely submerged in noise. This is done us-ing the following process. For each span, small subsets ofdata are bin-averaged together. Any spans that have sig-nals 5 σ above the baseline are thrown out. This works asa data filter to remove high-amplitude transient signals,reducing unwanted noise.To search for a monochromatic signal (one spectralbin) in the presence of noise, the amplitude of each binmust be understood relative to the noise floor. This noisefloor is not flat, due to a combination of shielded roomand instrument effects. To resolve this, each bin-averagedspan is passed through an optimized high-pass filter toremove low frequency baseline shape.
50 100 150 200 250 300
FREQUENCY (MHz) N O I SE V O L T A G E ( n V / H z / ) SYSTEMSYSTEM + ANTENNA T E M PE R A T UR E ( K ) FIG. 6. Blue: The spectrum of noise in the shielded roomreferred to the input of the preamp, showing modes coupledto the polarization of the bicon antenna. This shielded roomthermal noise is on top of the wideband white noise of theroom temperature preamplifier. Red: System noise tempera-ture referenced to 50Ω (the input impedance of the preamp)for short-circuited pre-amp input. Future runs will use cooledpreamplifiers.
A post-FFT filter for the background noise floor is usedthat assigns weights to frequency bins near the trial fre-quency. This helps to determine whether a measuredsignal is significantly above the noise floor. The shape ofthis filter is optimized using signal injection tests by find-ing the window shape that maximizes the final measuredsignal-to-noise ratio for nearby background noise.Memory limitations in the RTSA used in this pilot ex-periment require dividing the 50-300 MHz range into aseries of smaller scans called spans, each of which hasthe required fractional spectral resolution. These nar-row spectral spans are further subdivided in time intosmaller, 10-second time intervals to maximize the abil-ity to veto spurious external noise while also being writ-ten sufficiently infrequently to avoid write-to-disk bottle-necks leading to losses in scanning efficiency. All datafiles are written out in a plain text format and saved todisk. Afterwards, they are converted to fixed-size, bi-nary format (HDF5) files for data processing. The re-sulting time-frequency database of time-tagged sequen-tial spectral spans enables a series of detection validationtests. Any detection of a monochromatic signal may beexamined for its time dependence and compared in am-plitude with the expected 100 dB stronger signal on aspectrum analyzer and broadband antenna outside theshielded room.
VIII. SIGNAL INJECTION TESTS
As a test of the sensitivity of the Phase-I system, weinject a small signal at one frequency and integrate theFFT over a narrow bandwidth. Figure 7 shows an exam-ple of the resulting spectrum. For this test, we inject asmall signal at 70.5 MHz into the shielded room using asmall bow-tie antenna. This signal is well below the noisefloor of the receiver. A narrow-band sweep from 70.48-70.51 MHz was then performed many times to extractthe signal from the noise. Since the span is narrow, wecan scan in real time, performing a nearly 100% efficientFFT over this frequency range. The result for 10 secintegration shows an amplitude of 42 pV (RMS) referredto the input of the preamplifier. Using the standard de-viation of the baseline in the narrow-band sweep, and theknown antenna factor, a 5 σ -limit on the kinetic mixingparameter, (cid:15) , of 6 . × − between 70.49 and 70.51 MHzcan be inferred. FREQUENCY (MHz) P O W E R SPE C T R A L D E N S I T Y ( W / H z ) FIG. 7. Power spectrum showing a 22 σ detection at 70.5 MHzafter 10 seconds integration (frequency span=10 kHz). Totalsignal power received by the antenna is 3.5 × − W, whichis a factor of 730 below our detection threshold without aver-aging. This signal injection test demonstrates the sensitivityof our pilot system.
We test the limiting detectable signal vs. integrationtime and find that the peak detectable power scales in-versely as the square root of integration time. As dis-cussed in Section IV, the limiting (cid:15) then scales as thefourth root of integration time. A study of the averageof many scans with a weak injected signal demonstratedthat the expected behavior from Eqn. 11 is observed.There is a trade off between channel width (needed toattain high Q ), number of spans, and integration time inthe search phase vs. followup phase for any detected sig-nal. In the search phase, detection of a monochromaticsignal buried in noise is the goal. This puts emphasis onintegration time per Hz. However, because the frequencyof the signal is unknown, the maximum range must becovered during the search phase. For example halving theFFT resolution doubles the spectral efficiency (half thenumber of required spans) for a given run time. Splittingthe spans during data acquisition into sequential timesamples enables additional filtering for the expected con-stant signal.Once candidate signals are detected above threshold,a run at high efficiency may be made with much higherspectral resolution in spans centered on the candidate fre-quencies. A surviving candidate may then be validatedby demanding a non-detection in the spectrum monitor-ing system with an antenna outside the shielded room. IX. SEARCH FOR A SIGNAL
In this section we outline the process of searching fora narrowband constant signal, and describe the resultsof our pilot Phase-I search. Due to the low efficiency ofsearching 50-300 MHz we consider two types of search:1. A 100% efficient search confined to several narrowspans at several spot frequencies2. A broadband search covering 50-300 MHz but at ∼ /
400 the efficiency of the spot limits.
FIG. 8. Flow chart describing the logic of the search process.Starting with the data from the measured spectrum, the fig-ure shows analysis of a detected signal, and the automatedmethodology for eliminating false positive signals.
After an initial run is performed, and our data are pro-cessed, we must determine where any potential high Q signals that match our criteria originate. The methodol-ogy for this process is outlined in Fig. 8.The RF spectrum outside the shielded room is domi-nated by electromagnetic signals which contain informa-tion. Thus, in general, they do not exhibit extremely high Q and constant amplitude. The nature of any sig-nal detected in the shielded room may be revealed bycomparing the signal measured inside the shielded roomto the signal outside the room. External electromagneticsignals in our frequency range should be attenuated in-side the shielded room by 100 dB or more.This search logic flowchart applies to our Phase-I andPhase-II experiments as well. Once a candidate high- Q apparently constant signal is detected there are area series of investigations that will occur. Using a higherresolution smaller span targeted run the shape of the linecould be investigated, and any time-variation detected.Based on those results, as well as non-detection outsidethe shielded room, the next step will be to confirm thesignal in an identical setup some distance away. We arepreparing that infrastructure. Finally, the next obviousstep will be to focus on that frequency with the vastly su-perior sensitivity of a superconducting quantum limiteddetector of the kind employed by the Stanford group [24].
50 100 150 200 250 300
FREQUENCY (MHz) l o g () FIG. 9. Reach of the pilot experiment after short test inte-grations. The blue curve is for only 3.8 hours of real-timedata collection. The orange dots show spot measurements at63.9,70.5, 152, and 247 MHz taken with at least 5 × secof real-time data extrapolated to 1 month of data acquisition(assuming the current noisy receiver), and are offset from theblue curve by the expected amount due to the different inte-gration times. Limits on (cid:15)
The first run of the pilot experiment was done overthe course of two months scanning between 50 and 300MHz. The goal was a proof of concept. Figure 9 showsthe results of approximately 3.8 hours of real-time datacollection from 50-300 MHz using the system show inFig. 1. This short effective integration resulted from thedead time of the RTSA inherent in the sequential fre-quency scans. The data taking procedure is outlined inSection VII. Conversion from voltage to electric field wasdone using the modeled antenna factor shown in Fig. 5.This was converted to an (cid:15) limit by looking at the stan-dard deviation of the electric field at each bin and calcu-lating the 5 σ limit.This search produced approximately 130 bins wherethere was a signal of interest (equal to 0.03 % of all binsin the search). Many of these signals are quickly ex-cluded via Step 2 in Fig. 8. Signals that remain afterthis process are generally excluded by Step 3. However,care must be taken because some of these candidates aretransient. Looking at the dependence of the voltage noiseabove baseline on the time of day the signal gives a fur-ther handle on whether to exclude these as possible can-didates. As described in Fig. 8, splitting up the data intoshort time bins, enables monitoring signals versus timein order to discriminate transient interference from can-didate dark photons. Figure 10 highlights the transientnature of one of these candidate peaks at 145.5 MHz,which is the location of a weekly ham radio net. :
00 02 :
00 04 :
00 06 :
00 08 :
00 10 :
00 12 :
00 14 :
00 16 :
00 18 :
00 20 :
00 22 : TIME A M P L I T UD E ( p V / H z . ) FIG. 10. Voltage above baseline of ∼
19 minutes of data overa 2-hour time window. At 145.5 MHz, a weekly ham radionet on the 100W K6JRB repeater at 12:30 p.m. is clearlydetected. This signal can be eliminated due to short termtime-variance. At 288.0 MHz, a possible candidate of un-known origin is shown. This is eliminated by checking thesignal outside the shielded room, finding it 110 dB stronger.
The other candidate detection at 288 MHz was elim-inated by comparing with the RF spectrum outside theshielded room. While there is variation in the SNR at288 MHz, the candidate is only conclusively excluded bydoing a narrow-band sweep around the candidate fre-quency outside the shielded room. The result of this isshown in Fig. 11. From this, it is clear that this signalhas terrestrial origins.
Limits on (cid:15) at four spot frequencies
Four narrow-span scans around 63.9, 70.5, 152, and247 MHz were chosen as a second calibration of sensitiv-ity as shown by the orange dots in Fig. 12. For each spot
FREQUENCY (MHz) A M P L I T UD E ( n V / H z / ) FIG. 11. A scan around a candidate signal at 288 MHz donewith a wide-bandwidth Vivaldi antenna outside the shieldedroom showing 1,000 seconds of real-time data. The signal is100 dB stronger than our shielded room detection. This ex-cludes this signal as a candidate. Other EM peaks, also fromthe same antenna, are evident but are below the sensitivityof the experiment when the shielded room door is closed. check, at least half a million seconds of data were ob-tained and used to compute a 5 σ limit on (cid:15) . This limit isextrapolated to a month using Eqn. 12. The locations ofspot frequencies were chosen to sample across the entire50-300 MHz span as well as to investigate the sensitivityof the experiment in regions with/without room modes.Span widths were selected to ensure a resolution of atleast one part in 10 and are the same as used in thepilot experiment (Fig. 9). X. REACH OF THE PROPOSED EXPERIMENT
Using data from our pilot experiment, we can esti-mate the constraining power vs. integration time in var-ious frequency (dark photon mass) bands. This is cross-checked with 100% efficiency narrow-span scans around63.9, 70.5, 152, and 247 MHz as a second calibration ofsensitivity. The limit plot in Fig. 12 shows measured andprojected limits between 50-300MHz. Figure 13 overlaysthese projections across a much wider parameter space.Recently, using a superconducting resonator and SQUIDdetector Phipps et al. [24] have obtained a limit point at0.49 MHz, shown by the red dot.Some discussion of the astrophysical limits and theirrobustness is in order. The γ – γ (cid:48) CMB bound (brown)comes from conversion of normal CMB photons to darkphotons and does not require that the dark photons bedark matter or even have a cosmic abundance. The γ (cid:48) – γ bound (dark photon to regular photon) is model depen-dent because it requires that the dark photon abundanceexist at the time of conversion [6]. Not only is it assumedthat the dark photon is dark matter today, it assumesthat it also existed back in the early universe, in mostcases before matter-radiation equality when we do notactually have any evidence that dark matter existed. Forthe dark photon to be dark matter today but not ex-0
250 500 750 1000 1250 m (neV) -9-10-11-12-13-14-15 l o g ()
50 100 150 200 250 300
Frequency (MHz)
SPOT CHECKPILOTPHASE-IPHASE-II
FIG. 12. Limit plot showing the reach of the experiment from50-300 MHz in several stages. Pilot (blue) shows 5 σ limitsafter 3.8 hours of data collection using the proof-of-conceptsetup. Phase-I (green) shows 5 σ extrapolated limits usingcurrent antenna with LNA noise temperature and RBW im-proved by a factor of 2 and 10, respectively, after 1-month ofreal-time data acquisition. Spot checks (orange) show mea-surements around 63.9, 70.5, 152, and 247 MHz taken with atleast 5 × sec of real-time data in the pilot experiment. Un-like Fig. 9, these values are not extrapolated to one-month. Asexpected, these limits lie between the measured and projectedlimits from the pilot and Phase-I runs, respectively. Phase-II(black) shows the projected 5 σ limits for a month-long datarun using a cryogenic amplifier. ist back then implies that it would have to be producedsometime between then and now (actually between thenand matter-radiation equality). Thus the γ (cid:48) – γ bound isweaker than other astrophysical bounds, and speculative.The IGM heat bound arises from dark photons convert-ing in the ionized intergalactic medium, below the plasmafrequency and heating it above observed IR bounds [28].This pilot experiment uses room temperature pream-plifiers and low efficiency spectrum acquisition. Since theerror on (cid:15) scales like the system temperature, as well asthe square root of the real-time spectral coverage, thenext obvious step is to transition to cooled preamplifiersand the GHz RTSA described above. Improvements inthe antennas are also planned. The dashed black linerepresents our forecast for the second phase of this ex-periment. It relies on a series of technical improvementsin the different frequency bands, ranging from cryogenicpreamplifiers at GHz frequencies to low temperaturebolometers at THz, and a range of frequency dependentantenna designs. Ultimately, this experiment will be lim-ited by the warm walls of the shielded room. As with anybroadband search, once a signal is detected and validatedwith multiple detectors, the next step would be to focuson that frequency with more sensitive quantum-limitedhigh- Q detectors.
12 9 6 3 log [m (eV)] -3-6-9-12-15 l o g () IGM heat P HA SE - I CMB ( ) stellar production CMB ( ) precision EM A D M X A x i on H a l o sc ope s X E N O N PHASE-II kHz MHz GHz THz
FIG. 13. Projected reach of the Dark E-Field Radio ex-periment in the next phase. The weak kinetic mixing fac-tor is plotted vs dark photon mass in eV. Regions excludedby astrophysics are shown. The light γ (cid:48) − γ CMB region isa model-dependent constraint above which hidden photonswould not account for the total dark matter density. For ref-erence, planned ADMX axion searches are shown in yellow,because those experiments may detect dark photons [6, 25].Recent results, [26, 27], may improve these limits. The orangepoints in Phase-I show calibrated exclusion regions at 4 spotfrequencies at 5 σ measured in the current noisy pilot experi-ment. The red dot shows the point exclusion limit measuredby Phipps et al. (2019). Our Phase-I and -II limits are basedon 1 month integration. Phase-I green region shows 5 σ ex-trapolated limits using current antenna with improved LNA.Phase-II are cryogenic experiments covering wider ranges. ACKNOWLEDGMENTS
We thank the Nokia and Xilinx for major donations.This project is supported by the Brinson Foundation andDOE grant DE-SC0009999. NSF grants PHY-1560482and PHY-1852581 supported three REU students (NM,SK, and JL). JB and BG were partially supported by theNuclear Science and Security Consortium, funded by theDOE under the grant DE-NA00003180. We acknowledgediscussions with Barbara Neuhauser and Werner Graf.JAT thanks Saptarshi Chaudhuri, Markus Luty, JeremyMardon, Surjeet Rajendran and Greg Wright for helpfuldiscussions. Some of this work was done at Aspen Cen-ter for Physics, which is supported by National ScienceFoundation grant PHY-1607611. We thank John Con-way and Eric Prebys for reviewing an early version ofthis paper.1 [1] Marc Schumann. Direct detection of wimp dark matter:concepts and status.
Journal of Physics G: Nuclear andParticle Physics , 46(10):103003, 2019.[2] Giorgio Arcadi, Ma´ıra Dutra, Pradipta Ghosh, et al. Thewaning of the wimp? a review of models, searches, andconstraints.
The European Physical Journal C , 78(3):1–57, 2018.[3] T. M. P. Tait. Dark matter candidates: status andperspectives. In , volume 34 of
International CosmicRay Conference , page 5, Jul 2015.[4] Steve Ritz et al. Building for Discovery: Strategic Planfor U.S. Particle Physics in the Global Context. 2014.[5] Marco Battaglieri et al. US Cosmic Visions: New Ideas inDark Matter 2017: Community Report. In
U.S. CosmicVisions: New Ideas in Dark Matter College Park, MD,USA, March 23-25, 2017 , 2017.[6] Paola Arias, Davide Cadamuro, Mark Goodsell, et al.WISPy cold dark matter.
Journal of Cosmology and As-troparticle Physics , 2012(06):013–013, jun 2012.[7] Peter W. Graham, Jeremy Mardon, and Surjeet Rajen-dran. Vector Dark Matter from Inflationary Fluctua-tions.
Phys. Rev. , D93(10):103520, 2016.[8] Bob Holdom. Two U(1)’s and ∈ charge shifts. PhysicsLetters B , 166(2):196–198, Jan 1986.[9] Robert Foot and Xiao-Gang He. Comment on Z-Z’mixing in extended gauge theories.
Physics Letters B ,267(4):509–512, Sep 1991.[10] Thomas G. Rizzo. Kinetic mixing and portal matter phe-nomenology.
Physical Review D , 99(11), Jun 2019.[11] M. Tanabashi et al. Review of particle physics.
Phys.Rev. D , 98:030001, Aug 2018.[12] Stephen R. Parker, John G. Hartnett, Rhys G. Povey,and Michael E. Tobar. Cryogenic resonant microwavecavity searches for hidden sector photons.
Phys. Rev. D ,88:112004, Dec 2013.[13] Saptarshi Chaudhuri, Peter W. Graham, Kent Irwin,et al. Radio for hidden-photon dark matter detection.
Phys. Rev. D , 92:075012, Oct 2015.[14] Alex Drlica-Wagner, Yao-Yuan Mao, Susmita Adhikari,et al. Probing the Fundamental Nature of Dark Mat-ter with the Large Synoptic Survey Telescope. arXive-prints , page arXiv:1902.01055, Feb 2019.[15] J. I. Read. The Local Dark Matter Density.
J. Phys. ,G41:063101, 2014. [16] Pablo F. de Salas. Dark matter local density determi-nation based on recent observations. arXiv e-prints , Oct2019.[17] David H. E. MacMahon, Danny C. Price, MatthewLebofsky, et al. The breakthrough listen search for in-telligent life: A wideband data recorder system for therobert c. byrd green bank telescope.
Publications of theAstronomical Society of the Pacific , 130(986):044502, feb2018.[18] Jack Hickish, Zuhra Abdurashidova, Zaki Ali, et al. ADecade of Developing Radio-Astronomy Instrumentationusing CASPER Open-Source Technology.
Journal of As-tronomical Instrumentation
Review of Scientific Instruments ,17:268, 1946.[21] COMSOL, Inc., One First Street, Suite 4 Los Altos, CA94022.
COMSOL Multiphysics , 5.4 edition. Available at .[22] Dassault Systemes, Inc., 625 Market St
CST Microwave Stu-dio 2019 , 2019 edition. Available at .[23] D. Hill.
Electromagnetic Fields in Cavities . Wiley, Hobo-ken, N.J., 2009.[24] A. Phipps, S. E. Kuenstner, S. Chaudhuri, et al.Exclusion Limits on Hidden-Photon Dark Matternear 2 neV from a Fixed-Frequency Superconduct-ing Lumped-Element Resonator. arXiv e-prints , pagearXiv:1906.08814, Jun 2019.[25] A Wagner, G Rybka, M Hotz, et al. Search for hiddensector photons with the admx detector.
Physical reviewletters , 105(17):171801, 2010.[26] N. Du, N. Force, R. Khatiwada, et al. Search for in-visible axion dark matter with the axion dark matterexperiment.
Phys. Rev. Lett. , 120:151301, Apr 2018.[27] T. Braine, R. Cervantes, N. Crisosto, et al. Extendedsearch for the invisible axion with the axion dark matterexperiment.
Phys. Rev. Lett. , 124:101303, Mar 2020.[28] Sergei Dubovsky and Guzm´an Hern´andez-Chifflet. Heat-ing up the Galaxy with hidden photons. jcapjcap