Search for oscillations of fundamental constants using molecular spectroscopy

A possible implication of an ultralight dark matter (UDM) field interacting wibeginth the Standard Model (SM) degrees of freedom is oscillations of fundamental constants. Here, we establish direct experimental bounds on the coupling of an oscillating UDM field to the up, down, and strange quarks and to the gluons, for oscillation frequencies between 10 Hz and 10^8 Hz. We employ spectroscopic experiments that take advantage of the dependence of molecular transition frequencies on the nuclear masses. Our results apply to previously unexplored frequency bands, and improve on existing bounds at frequencies>5 MHz. We identify a sector of UDM - SM coupling space where the bounds from Equivalence Principle tests may be challenged by next-generation experiments of the present kind.


Introduction
There are strong theoretical reasons to assume that fundamental constants (FC) are, in fact, dynamical and can be effectively described as expectation values of scalar fields (see [1] for a review).Temporal evolution of these fields results in a time variation of the 'constants' that can be searched for at the precision frontier (see, for example, review [2]).If a scalar field constitutes ultralight dark matter (UDM) [3,4] with sub-eV mass, then its amplitude oscillates at its Compton frequency, f φ = m φ c 2 /h, where m φ is the scalar-particle mass, c is the speed of light in vacuum, and h is Planck's constant.
Constructing a natural theoretical model of an UDM is challenging.However, two concrete proposals relevant to this study have been put forward.In the first, the UDM mass is protected by an approximate scale-invariance symmetry [3].In the second, UDM is an axion-like particle, whose mass is protected by an approximate shift symmetry according to the Goldstone theorem [5] that is broken, together with the combined charge-parity (CP) invariance [6,7], by two independent sectors [8].This model is inspired by the relaxion paradigm [9].The two mod.els are qualitatively different, yet, in both frameworks, DM couples to the standard-model (SM) fields either due to the fact that the couplings break scale invariance [10] or via mixing with the Higgs [6], resulting in time-varying FC.An additional theoretical approach, that also leads to time-varying FC, is based on discrete symmetries [11,12].
As neither observations nor theoretical arguments can constrain the DM-particle mass [13], broadband searches, such as present here, are particularly motivated.Note that the preferred region of the model of Refs.[8,14] is m φ 10 −11 eV ∼ kHz , the frequency range studied here.
In the UDM-particle mass range above roughly 10 −18 eV, the most stringent constraints on time-varying UDM have been provided by equivalence-principle (EP) tests of gravity (see [15] and references therein).Here, we argue that there is a sense in which the bounds arising from direct DM searches are independent from any single EP test.Using this insight we shobeginw how the EP-bounds on UDM models can be challenged by atomic and molecular experiments in the near future.Prior to discussing direct searches for scalar UDM, we introduce the phenomenology of EP tests.
EP tests are conveniently expressed in terms of the Eötvös parameter, η Exp EP ≡ 2| a A − a B )/| a A + a B | , that is sensitive to the differential acceleration ( a) of two test bodies, A and B ( [16], for examaple).The parameter can be expressed in terms of the relevant DM couplings to the SM fields d i [see Eq. ( 1)].One defines the 'dilatonic charge' of a body, Q X i = ∂ ln m X /∂ ln g i , m X being the mass of the body X and g i a FC.Then, with the dilatonic charge difference (∆Q) In contrast to EP-violating acceleration searches, direct scalar-UDM experiments probe observables in either quantum or macroscopic systems arising due to the dependence of atomic transition energies, the length of solid objects, or the refractive indices of materials on the FCs.For a review, see, for example, [17], for proposals, see [18][19][20][21][22][23][24][25][26][27], and for experiments providing bounds on FC oscillations see [28][29][30][31][32][33][34][35][36][37].The sensitivities of different kinds of experiments are intrinsically different.Indeed, atomic experiments are sensitive to variation in the electron mass but are almost insensitive to changes in nuclear masses, molecular experiments probe for variation of both electron and nuclear masses, whereas EP tests probe nuclear masses and are largely insensitive to electron mass.Thus, EP tests and oscillating FC experiments are complementary to each other.We further quantify this statement below.
Moreover, the level of FC oscillations might be enhanced at ∼kHz frequencies and higher due to the presence of UDM halos around the Earth and the Sun [38].In such cases, the DM density and the coherence time are increased, leading to increased sensitivity of given experimental setups to FC oscillations.Such enhancement would not, however, apply to fifth-force experiments, as in these, the test masses exchange virtual DM particles, a process independent of the background DM density.In recent experiments searching for FC oscillations, the investigated parameter space was extended to frequencies higher than 1 Hz, to cover the audio and radiofrequency (RF) range [29,30,34,35].
While oscillations of the fine-structure constant α and m e have received substantial attention, here, we focus on 'nuclear' FCs: the quantum chromodynamics (QCD) energy scale Λ QCD 0.33 GeV, and the masses of the light quarks.These constants determine the nuclear mass.We show that molecular spectroscopy can be used to search for oscillations of these FCs with fractional 10 −14 − 10 −15 sensitivity over a seven-orders-wide frequency band, from 10 Hz to 100 Hz.

Theoretical model
To illustrate the interaction of a sub-eV scalar field φ with SM fields, we write the low-energy effective Lagrangian as where, X = e, u, d, s are the fermions with mass m X , F 2 = F µν F µν , G 2 = 1 2 Tr(G µν G µν ), F µν , G µν are the electromagnetic field and gluon field strength, respectively, d j are dimensionless coupling constants, and M Pl = c/(8πG N ) = 2.4 × 10 18 GeV is the Planck mass.The parameter g s is the strong-interaction coupling constant, α s ≡ g 2 s /4π.The function β(g s ) describes the evolution ("running") of the coupling constant with energy, via the renormalization-group equation (RGE) β(g s )/(2g s ) = −(11 − 2n f /3)α s /8π, with n f being the number of dynamical quarks.
As a consequence of the UDM-SM couplings in Eq. ( 1), the SM constants effectively acquire a dependence on the scalar field, The QCD scale Λ QCD depends on g s through the RGE and dimensional transmutation (see, for example, [39]).Thus, the variation of Λ QCD can be written in terms of the variation of α s as The mass of a nucleus m N is the sum of the nucleon masses, strong and electromagnetic binding energy.Neglecting the small electromagnetic binding energy proportional to α, the nucleon mass depends on the QCD scale Λ QCD and the light quark masses m u,d,s [16,40].The variation of m N can be related to variation of FCs as [41] δm where m ≡ (m u + m d )/2 is the mean mass of the up and down quarks and δm ≡ m u − m d is the mass difference.Note that, for the contribution of m s to the nucleon mass, we have used the lattice QCD result [41].Combining this result with Eqs. ( 2) and ( 5), we find with d ≡ (d α , d me , d gs , d m, d δm , d ms ) and QN ≈ 0, 0, 0.999, 0.092, 3 × 10 −4 , 0.047 defined to be a unit-length vector.
Assuming that φ is a viable UDM candidate, it can be treated as a classical oscillating field, with ρ ⊕ DM and β ⊕ being the UDM density and its typical velocity on the surface of the Earth, respectively.Gravitybased measurements yield a weak direct bound on ρ ⊕ DM (see, for instance, [38,42,43]).Below, we consider various scenarios for the properties of the DM around the Earth.In the standard scenario where UDM constitutes a galactic halo [44], with ρ ⊕ DM ≡ ρ G DM 0.3 GeV/cm 3 and β ⊕ c 220 km/s, it is reasonable to assume that during the UDM virialization process around the galaxy, different patches or quasiparticles obtain random phases.This results in the UDM field-amplitude admitting stochastic fluctuations around its commonly assumed value [45][46][47][48].In addition, we shall consider a scenario where the UDM forms a solar halo [43] with ρ ⊕ DM = 10 5 ρ G DM and β ⊕ c = 20 km/s and as long as m φ 10 −13 eV the number of patches in the halo is large and we still assume that the field amplitude is stochastic.Finally, we discuss an Earth halo phenomenological model, with ρ ⊕ DM , taking its maximally allowed value, that depends on the UDM-particle mass [38], and the UDM has a negligible velocity dispersion velocity (see Supplemental Material [Supp.Mat.]).
Experimental approach.

Experimental approach
Atomic clocks can be used to search for oscillations of the proton mass and the nuclear g-factor.However, the accessible frequency range is f φ 1 Hz due to the operation mode of the clocks.
A recently suggested alternative approach in this context is spectroscopy of molecules [49,50].Their transition frequencies contain contributions stemming from changes in rotational and vibrational energy.Here we focus on the latter.The vibrational energy ω vib of a diatomic molecule containing two nuclei N 1 , N 2 scales approximately as E Ryd m e /µ, where µ = m N1 m N2 /(m N1 + m N2 ) is the reduced nuclear mass.Thus, molecular transitions with a change of vibrational energy are sensitive to the nuclear mass.Furthermore, the electron-mass dependence is enhanced, beyond the scaling contained in E Ryd ∝ m e .
In a detection instrument based on spectroscopy, a reference quantum system having a resonance frequency ν (1)  is interrogated by the wave of frequency ν (2) emitted from an oscillator.ν (2) is tuned to the proximity of ν (1) .In practice, the oscillator is often stabilized to another reference (atomic ensemble or cavity).Both frequencies may depend on more than one FC.The fluctuation spectrum of the frequency deviation ∆ν(t)/ν = [ν (1) (t) − ν (2) (t)]/ν is measured.The dependence of a frequency ν (i) on a particular FC g may be characterized by the fractional derivative R (i) g = d ln ν (i) /d ln g.A hypothetical modulation δg/g of a constant g causes a modulation of the frequency deviation δν/ν = (R g )δg/g.One key parameter of a given experiment is, therefore, the differential sensitivity g , determined by the choice of reference and oscillator.

Apparatus and Operation
In our experiments, we use an electronic transition of molecular iodine (I 2 ) between the ground electronic state X and the excited electronic state B [51].The concepts of the experiments are shown in Fig. 1.Details are presented in the Supp.Mat.We have performed two experiments, A and B. In the apparatus A the reference is the well-known transition R(56)32-0 at 532 nm (υ = 0, υ = 32), with sensitivity R In both experiments, the interrogating oscillator is a laser (frequency ν (2) ).Apparatus A uses a monolithic Nd:YAG laser whose frequency is actively stabilized to a reference cavity.For this configuration, and the considered frequency range, R e = 1 (see Supp.Mat.).In apparatus B, the laser is a Ti:Sapphire laser and frequencies in the range 100 kHz-100 MHz are considered.As this range is above the acoustic cutoff frequency of the laser f (B) 2 50 kHz [30], the frequency ν (2,B) is essentially independent of the FCs [53].
Summarizing, experiments A and B provide sensitivity to α, m e , and m N .For experiment A, ∆R In both experiments, the instantaneous frequency deviation ∆ν is converted into a voltage signal V (k) (t) = D (k) ∆ν (k) (t), with the discriminators D (k) being system parameters, and k = A, B. This allows us to obtain the spectrum of the fractional frequency variation δν (k) /ν (k) .The time-varying FC (α, m e and m N ) contribute to the variation according to: The Eq. ( 8) is used to probe oscillations of the FC.The cavity vs. molecular transition comparison can be used to constrain a combination of several DM -SM coupling constants.

Search for oscillating fundamental constants
In the experiments, the lasers are tuned to the respective iodine transitions and the signals V (k) (t) are recorded.In experiment A, the voltage V (t) was recorded continuously with a 16-bit data acquisition (DAQ) system and a sampling rate of 250 kSa/s.Here, D 1 V/MHz.We analyzed a set of N = 2 34 samples spanning T 19 h.From the data was calculated.This is the same as the discretized power spectral density (PSD), multiplied by 1/T .Various peaks in the periodogram were investigated and identified as being of technical origin, in part by shifting the interrogation-laser frequency away from the resonance and repeating the measurement.This left no obvious candidate UDM signals in the spectrum.A number of frequency intervals exhibiting spectral peaks of technical origin are listed in the Supp.Mat.We do not give limits for these excluded intervals, that have widths of 5 Hz or smaller.From the periodogram, the upper limit of the coupling parameters d g was determined using the analysis of Ref. [54].The spectral amplitude of the recorded signal is shown in Fig. 2a.For interpretation see Supp.Mat.  ) .PSDF is the optimally filtered power spectral density (PSD), with a filter chosen appropriately for signals having the same linewidth f /Q0, Q0 1 × 10 6 , as standard galatic halo UDM.The width of the orange band corresponds to the mean of A ± σ(f ).(b): Experiment B. The bound (95% confidence level) on fluctuations of the signal ∆ν (B) (t) = V (B) (t)/D (B) .
In experiment B, the voltage V (t) was measured with the laser frequency tuned either on the slope of the I 2 resonance, or off-resonance, alternating between these UDM-sensitive and insensitive acquisition modes to account for spurious signals due to sources other than UDM.A 12-bit DAQ system sampled V (t) in successive T = 0.1 s-long intervals at a rate of 250 MSa/s and the corresponding periodograms were computed and continuously averaged.The periodogram difference between the on-and off-resonance acquisition modes was also computed and averaged over a 60-hr-long run.This spectrum will contain power in excess of statistical noise in the presence of FC oscillations, and it is subsequently investigated for UDM detection.A number of candidate peaks were identified with power in excess of a 95% detection threshold, which was computed with consideration of the 'look elsewhere' effect [55].All spurious signals were checked in auxiliary experiments and eventually attributed to technical noise.The post-inspected spectrum is used to obtain a constraint for δν (B) /ν (B) that is shown in Fig. 2 b.See Supp.Mat. for details.
We analyse the experimental data in the framework of three mentioned UDM models that differ in terms of the amplitude of the UDM field and its coherence time τ coh = 1/(ω φ (v vir /c) 2 ): In order to derive bounds to the UDM couplings, we assume that only one of the constants m e , α, or m N in Eq. (8) oscillates and analyze the three cases separately.See Supp.Mat. for details.In Fig. 3, we present our constraints together with existing EP constraints (turquoise line) on the combined quark and gluons couplings QN • d as a function of the UDM mass.
Constraints on the variation of α and m e and α are presented in Fig. 4a and Fig. 4b, respectively, alongside previous constraints.We show only the strongest existing constraints on the relevant parameter space.In principle, astrophysical bounds on our scenario could also apply, however, these are typically weaker than those discussed here and are less robust (see [56][57][58] for recent discussions).For the sake of clarity, these constraints are presented for the standard galactic UDM halo only.Our results cover the previously unexplored bands 10 − 50 Hz and 5 − 10 kHz, and improve on existing bounds in the range 5 − 100 MHz.
More generally, our experiments are sensitive to the following linear combinations of the full set of couplings, defined in Eq. ( 6), (8), that can be written as Q
We now discuss the complementarity between direct UDM searches and the bounds arising from EP tests.
Since UDM is allowed to couple to all fields, the relevant parameter space is of dimension five.One can find a direction Q⊥ Full (m φ ) in this space that is orthogonal to the best four EP-test bounds for a given mass.For example, in the mass range of 2 × 10 −12 m φ /eV 5 × 10 −9 , these are the Be-Al [59], Be-Ti [60], Cu-Pb [61] and Be-Cu [62] experiments.and we find Q⊥ Full (m φ ) 0.003 , −0.987 , 0.002 , −0.001 , −0.162 .For masses above 5 × 10 −9 eV, Q⊥ Full is perpendicular to the Be-Al [59], Be-Ti [60], Cu-Pb [61] and Cu-Pb-alloy [63] sensitivity vectors, with corresponding Q⊥ Full .Models of light scalar UDM with coupling direction defined according to Q⊥ Full (m φ ) • d would not be constrained by these four leading EP bounds.Note that throughout the whole the mass range Q⊥ Full (m φ ) has a substantial overlap with the d me direction (the second entry).Thus, experiments that are particularly sensitive to time-variation of m e , such as the ones being discussed here, test a sector of coupling space that the first four-best EP experiments are insensitive to.In Fig. 5, we present our bounds on Q⊥ Full • d, projected (for clarity) in the d me direction, as dotted red and blue lines.The fifth-best EP bound projected onto Q⊥ Full (m φ ) and further on d me , is shown by a brown dotted line.Note that we could only calculate the projection of Q⊥ Full into the remaining 5th-best EP bound to an accuracy of 1:10 3 due to the limited precision of the published test mass composition data.We find that in this sector of coupling space the bounds related to our direct UDM experiments are only two to three orders weaker than the bounds from the EP tests.Existing constraints: shaded regions in orange [34], yellow [35], pink [29], green [53], Magenta [37], and purple [67].Fifth-force/EP tests: turquoise [59,60,[64][65][66].
Be -C u, on ly dm e 6 = 0 Cu-Pb, only d me 6 = 0 < l a t e x i t s h a 1 _ b a s e 6 4 = " Cu-Pb alloy, only d me 6 = 0 < l a t e x i t s h a 1 _ b a s e 6 4 = " g L L Q I P y c 8 q S p X / t Z 2 U 9 e e a 7 8 q D 4 = " > A

Conclusion
Our molecular-spectroscopy experiments have resulted in the first bounds on the coupling of an oscillating UDM field to the gluon and quark fields, in a broad frequency range that spans seven decades (10 Hz-100 MHz).Within this range, improvements on previous limits for the coupling to the electromagnetic field and the electron field were also obtained within a small frequency window.Our experiments are not entirely free of technical noises.A new generation of similar experiments, with minimization of all noise sources, long acquisition times, high sampling rates, and, possibly, multiple setups enabling reduction of the noise level by statistical averaging, could further improve the present limits by several orders of magnitude.Furthermore, we have argued that there is a special class of dark matter couplings where the bounds from equivalence principle tests are significantly less stringent than expected.Consequently, in the near future experiments of the kind described here may be able to probe this class of UDM models with sensitivity competitive to EP tests.

I. EXPERIMENTS A. Introduction
A molecular transition frequency can be approximated as ν (1) = ν 0 + ν vib,B − ν vib,X , where hν 0 (hc)15769 cm −1 is the difference in the electronic binding energies of the two states and hν vib is the vibrational energy.Rotational energy contributions can be neglected, due to the large mass of iodine.We approximate the vibrational energies as hν vib,X = hω vib,X (υ + 1/2), hν vib,B = (υ + 1/2)hω vib,B , with the vibrational constants ω vib,X = c 214.5 cm −1 , ω vib,B = c 125.7 cm −1 .The vibrational quantum numbers in the states X and B are υ and υ , respectively.It is reasonable to assume that the electronic energy difference arises mostly from non-relativistic dynamics.Since both electronic and vibrational energies are proportional to the Rydberg energy, we have R 1 + (υ ω vib,B − υω vib,X )/2ν (1) and to the nuclear mass R (1) N −(υ ω vib,B − υω vib,X )/2ν (1) .Since the vibrational energy contribution is only a small fraction of the total transition energy, R N is small.In the future, the value can be increased by using pure vibrational transitions [1].Experiments A and B employ Dopplerfree and Doppler-broadened I 2 transitions, respectively.The observed Doppler-free transition in apparatus A has a width of a few MHz.This width determines the frequency range over which there is significant molecular response to FC oscillations.In apparatus B, the observed Doppler-broadened transition is of the order of 1 GHz.In addition to Doppler broadening, there is significant homogeneous broadening due to collisions (as discussed below), and the molecular response is essentially constant over the 100 MHz range probed for FC oscillations.Apparatus A, being equipped with a low-frequency-noise laser source, is better suited for probing low frequencies up to the molecular transition's observed linewidth (of order MHz).Experiment B offers a broad detection range set by the transition's pressure broadening (hundreds of MHz).Important features of the experimental setups are the power spectral noise densities of the fractional frequency fluctuations of the molecular reference, S y (f ).These contain contributions of technical or of fundamental origin.In order to obtain small values of S (1) y it is advantageous to employ references containing a large number of particles, here a substantial gas volume.

B. Experiment A
The oscillator interrogating the iodine gas is a Nd:YAG laser (laser 1).It is frequency-doubled to 532 nm by means of a fiber-coupled nonlinear conversion module.This wave has the frequency ν (2) .Laser 1 is phase-locked to a laser 2 that is frequency-stabilized to a 30 cm long ultrastable high-finesse ultra-low expansion glass (ULE) resonator.
The detected frequency range covers 10 Hz to 100 kHz.The lower end of this range covers frequencies smaller than the bandwidth of the frequency lock of the laser to the cavity, f 1 , the frequency ν (2,A) of the wave sent to the experiment is determined by the length of the ULE cavity.As widely discussed, for a cavity, R the laser resonator is the element determining the frequency fluctuations.Although the resonator is monolithic and the material has a refractive index larger than unity, to a good approximation, the same expressions for R α , R e hold.We neglect the effect of mechanical resonances [3].
Approximately 30 mW of laser radiation at 532 nm is sent to the spectroscopy setup.It is split into two beams (probe and saturation) using a 20%:80% beam splitter.These are sent from opposite directions into a 30 cm-long cell filled with iodine gas (I 2 ).The iodine saturation pressure in the cell is maintained at about 0.04 mbar by temperature stabilization of the cell's cold finger at about 0 o C using a Peltier element.The probe laser beam is frequency-shifted by 50 MHz using an AOM to prevent interference effects with the saturating beam.The counter-propagating probe and saturation beams are overlapped inside the cell allowing nonlinear saturation spectroscopy on the hyperfine structure (hfs) components of iodine rovibronic absorption lines.Saturation absorption resonances are detected in the power of the transmitted probe beam by means of a low-noise photodetector D2.
To reduce the effect of laser intensity noise we implemented balanced detection of the probe wave and a reference wave.The latter is obtained by splitting off part of the probe beam using a half-wave plate (HWP) and a polarizing beam splitter (PBS) in front of the cell.This reference beam is sent through the cell colinearly with the spectroscopy probe beam, however not interacting with the saturation beam.The reference beam is detected with a photodetector D3, similar to D2.
The outputs of both photodetectors are subtracted using a precision differential buffer, and the signal is then further amplified by a factor of approximately 10 4 using a low-noise preamplifier (Stanford Research Systems SRS 560).By adjusting the laser powers on the photodetectors by means of the HWP in front of the cell, the differential amplitude noise at the output of the amplifier can be reduced by about 40 dB over the bandwidth from DC to 1 MHz.The data were acquired using a 16-bit DAQ (digital acquisition) card (National Instruments USB-6343) referenced to a Maser.
In experiment A the spectroscopy was performed on the a1 hyperfine structure component of the R(56)32-0 electronic transition.total noise spectral density Ŝtot(f ) for the detection of the relative frequency fluctuations between interrogating oscillator and iodine reference.The peak at 120 kHz is due to relaxation oscillations of the laser.Magenta: Estimated frequency noise of the interrogation oscillator (laser 1), S y (f ).A contribution to the latter is the noise of laser 2 and an estimate for it is the green trace.It is the spectral density of the frequency fluctuations of a beat between two similar cavity-stabilized lasers, one of which is laser 2, normalized to their optical frequency (ν (2) /2 282 THz).Blue: total background noise of the detection process, S det (f ), obtained with the probe laser far detuned from the Doppler-free resonance.A contribution to the latter is the detector noise in absence of laser light, shown in cyan.

Characterization.
Figure 2a top shows one characteristic feature of the apparatus: the discriminator.It is recorded by slowly scanning the frequency of the laser ν (2) across the molecular resonance ν (1) and recording the signal (voltage) change.The full width of the saturated absorption resonance was 3.6 MHz (FWHM), caused by a relatively high iodine pressure and contamination in the iodine cell.The natural linewidth of the transition is approximately 300 kHz.For DM detection, the laser 1 frequency was tuned to the half-height of the resonance by tuning the local oscillator frequency of the phase lock.For the input signal to the DAQ system, the discriminator on the side of the molecular resonance is D 1 V/MHz.
The second characteristic is the noise level of the apparatus.It was determined by recording, for a comparatively short duration, the signal V (t) when ν (2) is kept at the operating point.(This recording was not part of the longduration data recording, so noise presented in the following is to be regarded as typical.)This noise [ Ŝtot (f )] 1/2 is f (Hz) FWHM (bin) Q-factor (10 Analysis of technical noise: heuristic approach.
Table I lists omitted frequency ranges that contain technical noise of substantial strength.In the following further analysis, these ranges as well as those around the 50 Hz-noise peak and its harmonics have been omitted.
A second step in the data analysis consists in checking weaker narrow-linewidth signals.We first mark any frequency bin having a signal strength above the detection limit.The latter is heuristically chosen as 3 standard deviations of the ROFP above its mean.Both standard deviation and mean are computed from the ROFP data in a small spectral window around the frequency of interest.Frequency bins that are above the threshold but within the expected lineshape of a previously marked bin will be rejected to avoid double counting.After the this procedure no candidate remained

Determination of detection limits: generalities
The value of the DM field φ in SI units, at the location of the experiment, can be expressed as [3][4][5] where f φ is the Compton frequency of the DM particle, φ 0 = 4πρ DM G N /c 2 is a normalized field amplitude, ρ DM is the local DM energy density, and G N is the gravitational constant.The dimensionless amplitudes α i (or order unity) and phases ϕ i are random numbers drawn from specific probability distributions [4].{ω i } are a set of regularly spaced angular frequencies starting at 2πf φ and extending over a narrow spectral window.Finally, F is a dimensionless weighting function that takes into account the velocity distribution of the DM particles and is specific to the assumed DM model.In particular, it is characterized by a fractional full-width at half maximum, Q −1 1 (see further below).The DM spectrum is proportional to F (ω) 2 .In the galactic halo DM model, ρ (G) DM
Determination of detection limits: approach of Derevianko (2018).For evaluation of experiment A, we apply Eq. ( 14) of Ref. [5].Our 95% bound is taken as 2σ For the Earth halo model with its infinite coherence time, there is but a single amplitude, α 1 = √ 2, and the bound has a particularly simple expression.
In the galactic and Sun halo models, the above bound holds for observations times significantly longer than the coherence time, say T ≥ 10 τ coh .For those low DM frequencies f φ for which the observation time is significantly shorter than the coherence time, T < 0.1 τ coh , we multiply the above expression by a factor 3, as discussed by Centers et al. [6].
In the intermediate range of observation times, 0.1 τ coh ≤ T ≤ 10 τ coh , the theory of the bound has not yet been worked out.We therefore conservatively apply the factor of 3 also in this range.
The following correction to the formulae in Ref. [5] is implemented [7]: in Sec.II A, the factors "2" appearing in the definitions of d e , d me are replaced by "4".For the galactic halo model, we use the velocity values given by Foster et al. [4], √ 2v vir = v 0 220 km/s, v g = v obs 232 km/s.

C. Experiment B
Apparatus.The apparatus of experiment B implements Doppler-broadened absorption spectroscopy in the R(122) 2-10 I 2 transition at 725 nm, and is shown in Fig. 1b.Iodine vapor is excited with ≈2 mW of light from a Ti:Sapphire laser (M squared SolsTiS) in a 10-cm long cell.The light beam is double-passed through the cell to increase the absorption signal.The cell body is maintained at ≈405 o C, sufficiently high to obtain adequate population in the electronic ground state's vibrational level with υ=10.The pressure in the I 2 cell is set to ≈30 mbar via heating of the cold finger of the cell, that is maintained to 87 • C to within ±1 • C. Balanced detection of the light transmitted through the cell is done with use of a secondary reference beam, to minimize the effects of laser amplitude noise.Small drifts in this balancing are corrected by monitoring the output of the balanced detector (Thorlabs PBD415A) and applying feedback to a stepper-motor mounted HWP (HWP 3 in Fig. 1b) to adjust the power of the beam headed to the I 2 cell.This results in suppression of laser amplitude noise by more than ×100 times.The output of the balanced photodetector is amplified ×100 times with a preamplifier (Femto HVA-200M-40-B) and is recorded with a 12-bit DAQ system (Picoscope 5244D) at a rate of 250 MSa/s.An electro-optic modulator (EOM) is used in auxiliary experiments to impose frequency modulation on the laser light, in order to measure the frequency response of the apparatus.This response may be characterized by an overall calibration function h(f ), which is primarily determined by the decaying response of molecules at frequencies larger than the transition's linewidth.This frequency modulation is checked with a Fabry-Perot (FP) cavity whose resonance has ≈ 150 MHz FWHM.The peak I 2 absorption corresponds to ≈ 1 absorption length for the Doppler-and pressure-broadened resonance The transition width of ≈ 970 MHz has contributions due to Doppler (≈ 485 MHz) and collisional broadening (≈ 240 MHz).The latter is estimated from comparison of the 970 MHz width with the value ≈ 730 MHz observed at much lower I 2 pressure (≈ 3 mbar).The molecular response is essentially constant over the 100 MHz range probed for FC oscillations (the function h(f ) was measured to be 1 for all frequencies probed).

Experimental protocol.
An experimental run proceeds as follows: First, the laser frequency is swept over the I 2 resonance and the reference beam power is set to obtain a zero-crossing of the photodetector output on the side of the resonance, at the half-height of absorption feature (see Fig. 2b).Then the laser frequency is tuned to the nominal zero crossing and stabilized to the reading of a He-Ne referenced wavemeter (drift ≈ 2 MHz/h), and subsequent slow drifts of the detector output are actively compensated, as mentioned above.A time series of the amplified detector signal is recorded in a 0.1 s window once every ≈1 s (i.e.10% measurement duty cycle), and corresponding FFT of these data are computed and the resulting periodograms, i.e. the squared magnitudes of the computed amplitudes, are continuously averaged.A flattop window is applied to the time-series data, to avoid parasitic effects in the periodograms due to the discrete nature of the computation.This windowing leads to an effective broadening of the single-bin width in the frequency domain to a resulting ≈ 37.7 Hz (It additionally reduces the integration time from 0.1 s to an effective 27 ms.).Thus, the resulting periodogram in the 100 kHz-100 MHz range consists of N ≈ 2.65 • 10 6 bins.After ≈ 200 s of data taken on the slope of the resonance, the laser frequency is detuned from resonance by 1.1 GHz, where the discriminator slope is ≈ 0, and the power of the beam headed to the I 2 cell is re-adjusted with feedback to maintain balanced detection, as mentioned above.Equal amount of data as before are taken in this FC-oscillation insensitive configuration.The corresponding periodogram is subtracted from that from data with sensitivity to FC oscillations, to minimize the impact of parasitic effects such as laser amplitude noise and instrumentation pickup.After cycling many times between the two configurations, a difference periodogram is obtained that is nearly free of parasitics and will contain power in excess of noise in the presence of FC oscillations.We henceforth refer to this as excess power spectrum (PS).We show this excess PS, produced using the data of our main 60-h-long DM run in Fig. 4. Note that this total measurement time exceeds the coherence times of the galactic halo and solar halo models for the considered range of f φ values, so that the Rayleigh probability distribution of the amplitudes α i is fully sampled.Check for DM candidate signals.
The excess PS of Fig. 4 is analyzed for possible FC oscillations.A DM signature would be excess power in the spectrum, above a detection threshold computed below and shown in Fig. 4. In addition to investigating such candidate signals, 'negative' peaks (i.e. with power significantly smaller than the mean background noise) are also investigated.It was established that all such peaks have technical origins and although their power in most cases is expected to cancel out in the excess PS, residual power for some of those remains.Checking the residual background power after they are accounted for, informs about potential FC oscillations in the respective frequency positions, as is the case of candidates with high excess power.
Auxiliary experiments were carried out to identify the origin of the candidate DM and spurious peaks and measure their respective powers.These experiments were done with use of a calibrated spectrum analyzer (Keysight N9320B) to acquire spectra over 5 kHz regions around the candidate peaks.This device is more time efficient in acquiring spectra than our primary acquisition system when recording spectra over narrow frequency windows.In one set of measurements, data were acquired to check for the high-frequency-range spurious signals (above 60 MHz), alternating between acquisition with laser frequency tuned on and off the I 2 resonance.The new excess PS was found to be consistent with background noise.All spurious signals above 60 MHz were found to be due to rf apparatus pickup, since the corresponding peaks were present in the absence of light arriving at the detector.In another experiment, an EOM (EOM 2 in Fig. 1b) was used to provide improved suppression of amplitude noise in the balanced photodetection employed in the setup.This resulted in the elimination of a peak at ≈ 181 kHz, which was identified to be due to laser amplitude noise, as it appeared in direct measurement of the laser output light.Finally, in another experiment, the power of a peak at ≈ 523 kHz, only present with the laser tuned on the slope of the I 2 resonance, was identified to be laser frequency noise with the FP (see Fig. 1b).Its power was measured on the slope of the FP resonance and subtracted from the excess PS.As a result of all checks following the main 60-hr long DM run, it was established that all peaks under investigation had a technical source, and after these were accounted for in the excess PS, the residual power in the respective frequencies was consistent with background noise and below the detection threshold.
Computation of DM constraints.Detection of FC oscillations in the excess PS of Fig. 4 is associated with power higher than noise.This noise is used to define a detection threshold P th at the 95% confidence level, so that if a spectral feature has excess power P ex > P th , there is probability p 0 = 5% that it is due to statistical fluctuations.Given a noise distribution function and associated cummulative disctribution function (CDF), one can express p 0 as: where CDF(P th ) represents the probability p(P ex < P th ) that the excess power is smaller than the threshold.The Eq. ( 2) may be be solved for the detection threshold P th .However this determination would only be valid for an experiment investigating a single frequency bin.In experiment B, where FC oscillations are looked for in N ≈ 2.65×10 6 bins (≈ 100 MHz search window consisting of 37.7 Hz bins), the threshold has to be raised to account for the fact that a fraction of bins (≈ 5%) are expected to have power in excess of P th [8].This requires raising the CDF in Eq. ( 2) in the N th power, so that: The noise distribution of the excess PS of Fig. 4 was checked in many frequency bins and it was found to be well described by a Gaussian.Given this, one can solve for the threshold power P th using the expression for the Gaussian CDF, and obtain: where µ and σ are the mean and standard deviation of the Gaussian noise.These parameters were determined throughout the spectrum of Fig. 4 by fitting the noise in consecutive 5-kHz-wide windows.
From the determined threshold P th , constraints are extracted on the frequency fluctuation δν .This fluctuation is given by δν = δV /D, where δV is the voltage fluctuation corresponding to the fluctuation δP in the excess PS spectrum of Fig. 4 (at the 95% confidence level: δP = P th − µ = 5.5σ).The discriminator slope D is discussed in the main text.The quantities δV and δP are related via δP = 2V av δV = 2 √ P av δV , where P av = V 2 av is the averaged PS recorded with sensitivity to FC oscillations (i.e. with laser tuned to the slope of the I 2 resonance).One obtains for δν: Effect of decoherence of DM field.
Before placing constraints on FC, one has to consider the effects of partial decoherence of the DM field, that if present, will result in reduced sensitivity to DM detection.In experiment B, decoherence needs to be accounted for within the galactic DM halo scenario: τ coh (6, 0.006) s at f φ = (10 5 , 10 8 ) Hz. Within the Solar and Earth halo scenarios, the Q-factor of the field is high enough so that there is negligible decoherence over the 27 ms acquisition time.In practice, a sensitivity penalty must be applied to the obtained δν/ν spectrum, to account for the decoherence during the effective 27-ms-long time interval of our data acquisition.This penalty becomes significant at a frequency f φ ≥ 1/27 ms ≈ 40 MHz.To compute this sensitivity loss, we considered the lineshape, f DM (f ), that arises in the lab as the laboratory moves through the virialized DM field with a velocity dispersion of v 0 ≈ 10 −3 c 0 (denoted above by √ 2v vir ), where v lab (denoted v g above) is the velocity of the laboratory in the galactic frame (232 km/s), and we have denoted for brevity.This lineshape is proportional to the power spectral density of the DM particle and has been derived previously in Refs.[4,5,9,10].(The relationship to F is f DM (f ) = F (ω) 2 T .) We had a constant frequency bin width equal to 37.7 Hz in experiment B due to the flat-top windowing in the time domain.At frequencies higher than ≈ 40 MHz the DM power spectral density will be broader than that of the bin-width, effectively leading to the power spreading over more than one point in our spectrum.We have calculated the loss due to this for different DM particle Compton frequencies, f φ , by integrating the lineshape in 37.7 Hz bins and steps of 10 Hz.The maximum of these bin-integrals is then compared to the total area of the lineshape.This procedure yields the fraction of the DM power that will be observed in our spectrum.For a sense of scale, at 10 MHz the sensitivity loss because of this is ≈ 1% and at 100 MHz it is ≈ 75%.

II. THEORY
Details of the Earth halo model.This model may alternatively be called the "gravitational hydrogen atom model".The DM field is monochromatic with infinite coherence time, following from the assumption that the earth halo is infinitely stable, i.e. the virial velocity is zero.The value of ρ ⊕ DM is a function of DM particle mass (see Fig. 2a in supplementary information of Ref. [11]), and is enhanced compared to ρ G DM by a factor increasing from 10 4 at f φ = 100 Hz to 10 19 at f φ = 3.4 MHz.However, beyond f φ 15 MHz the ratio ρ ⊕ DM /ρ DM drops below 1. Equivalence Principle (EP) tests.A scalar field φ with mass m φ would induce an Yukawa interaction between two bodies A and B in the range Λ = h/m φ c which is non-universal and thus violates the equivalence principle (EP).The total potential (gravitational and Yukawa) between these two bodies can be written as where, m A (m B ) is the mass of body A (B), G N is the Newtonian gravitational constant and r AB is the distance between A and B. α A,B are the strengths of the Yukawa interaction.They measure the susceptibility of the mass to φ, and thus can be written as, In the presence of a central body (the "source") S with mass m S at a distance r, the acceleration of a test body A can be written as The Eötvös parameter, η EP , which measures the differential acceleration between two test bodies A and B in the presence of a source S, follows as as [12,13] EP test experiments constrain η Exp EP as a function of Λ.This leads to bounds on α A,B,S as a function of m φ .Because α A,B,S depend on the fundamental constants (FCs) as shown in the following, a bound on η EP can be converted into a bound on the coupling coefficients d i .
FC dependence of atom mass.
To discuss how the mass of a body depends on FCs, let us start by noting that the mass of a generic atom a with atomic number A a and proton number Z a can be expressed as, where m a N is the mass of the nucleus of atom a and m e is the electron mass.The mass of the nucleus can be further decomposed as where, m p (m n ) is the proton (neutron) mass and E 3 (E 1 ) is the binding energy of the strong (electromagnetic) interaction.Note that E 1 is dominated by the electromagnetic effect within the nucleus [14] and thus we will ignore the electron effect on this.As m p , m n , E 3 and E 1 depend on the FCs, variation of the FCs would lead to a variation of nucleus and atom mass, and can be written as where g i is a generic FC, and we have also implied summation over repeated indices here and below.We have introduced the notation Q a i ≡ ∂ ln m a (φ)/∂ ln g i , the ith "dilatonic charge" of a body.The susceptibility of a FC to φ can be rewritten as ∂ ln g i /∂φ = d i /M Pl (See Eqs.(2)(3)(4)(5) in the main text).

Figure 1 .
Figure 1.The two molecular iodine experiments to search for FC oscillations.(a) Experiment A; (b) Experiment B.

Figure 2 .
Figure 2. (a): Experiment A. The spectral amplitude A = PSDF/T of the scaled discriminator signal ∆ν (A) (t) = t e x i t s h a 1 _ b a s e 6 4 = " x M 8 8 y q
t e x i t s h a 1 _ b a s e 6 4 = " x M 8 8 y q O 8 T u D C o d g = = < / l a t e x i t > M ic ro sc op e, on ly dme 6 = 0 t e x i t s h a 1 _ b a s e 6 4 = " 4 p 3 z H d 8 / D 8 5 3 6 r 4 O x V y W i 3 t H w w 7 m k F r a B 1 t I h / t o n 1 0 j E 5 Q H T F 0 h x 7 Q I 3 r y 7 r 1 n 7 8 V 7 / R o d 8 4 Y 7 q 2 g E 3 v s n j W 2 j n w = = < / l a t e x i t > E x p t B , o n ly dme 6 = 0 < l a t e x i t s h a 1 _ b a s e 6 4 = " 1 V v L I 7 h h z i z e E o / v x p h t H V p y 7 5 g = " > A A A C R X i c d V B N S x w x G M 6 o b e 3 2 a 2 u P v Y Q u h R 6 G J S N K 9 W Y r r R 4 V u i p s t k s m 8 6 4 b z G R C 8 o 6 4 D P O T / B 3 9 A T 0 V 2 r M n b + K 1 z a w j a G l f C D w 8 z / u R 5 0 m t V h 4 Z + x E t L C 4 9 e P h o + X H n y d N n z 1 9 0 X 6 4 c + K J 0 E g a y 0 I U 7 S o U H r Q wM U K G G I + t A 5 K m G w / R k u 9 E P T 8 F 5 V Z g v O L M w y s W x U R M l B Q Z q 3 N 3 h M i v Q 8 5 j H t O I u p 5 / O L P L 4 A 4 + V 4 X H N p w L p / l d u w d n x X P 9 c a l 3 f N m f K g W w W 1 e N u j / X X N z f W 2 C p l f T a v B i T J J k t o 0 j I 9 0 t b e u H v B s 0 K W O R i U W n g / T J j F U S U c K q m h 7 v D S g x X y R B z D M E A j c v Cj a m 6 4 p m 8 D k 9 F J 4 c I z S O f s 3 Y l K 5 N 7 P 8 j R 0 5 g K n / m + t I f + l D U u c b I w q Z W y J Y O T N o U m p K R a 0 S a 8 1 r G c B C O l U + C u V U + G E x J D x v S s + m J p C V n d C M r f 2 6 f / B w W o / W e + z / b X e 1 s c 2 o 2 X y m r w h 7 0 h C 3 p M t s k v 2 y I B I c k 6 + k 5 / k V / Q t u o y u o u u b 1 o W o n X l F 7 l X 0 + w + L i b I / < / l a t e x i t > • • • E xp t A in Q? Fu ll di re ct io n < l a t e x i t s h a 1 _ b a s e 6 4 = " E i B R A R W 1 U 6 x M M d Q 7 G B z 2 e U W i a y 4 = " > A A A C R H i c d V D P S x w x F M 5 o W 3 W 1 7 d Y e v Y Q u B Q / D M t O u P 4 5 i U X p U 6 K q w W Z d M 5 q 0 b z G R C 8 k a 6 D P M f + X f 4 B / Q m 9 e 6 l N / E q Z s c p 1 N I + C H z 5 v v f y 8 n 2 J U d J h F F 0 H c / M v X r 5 a W F x q L a + 8 f v O 2 / W 7 1 y O W F F d A X u c r t S c I d K K m h j x I V n B g L P E s U H C f n X 2 b 6 8 Q V Y J 3 P 9 D a c G h h k / 0 3 I s B U d P j d r 7 T K Q 5 O h a y s G Q 2 o 3 v f D b J w l 4 V S s 7 B i E 4 7 0 8 J Q Z s G Z U 6 / u F U h U L a X 1 J p Q U x e 6 c a t T t R N / r c i 3 o x 9 a A u D z a j e G s z p n H D d E h T B 6 P 2 L U t z U W S g U S j u 3 C C O D A 5 L b l E K B V W L F Q 4 M F + f 8 D A Y e a p 6 B G 5 a 1 3 4 p + 9 E x K x 7 n 1 R y O t 2 T 8 n S p 4 5 N 8 0 S 3 5 l x n L i / t R n 5 L 2 1 Q 4 H h 7 W E p t C g Q t n h a N C 0 U x p 7 P w G s N q 6 g E X V v q / U j H h l g v 0 E T / b 4 r y p C a R V y y f z 2 z 7 9 P z j 6 1 I 0 3 u t F h r 7 O z 2 2 S 0 S N b I B 7 J O Y r J F d s h X c k D 6 R J B L 8 o P 8 J D f B V f A r u A v u n 1 r n g m b m P X l W w c M j H d 6 y D w = = < / l a t e x i t > • • • E x p t B in Q? F u ll d ir e c ti o n < l a t e x i t s h a 1 _ b a s e 6 4 = " V t 5 b Z 8 w j I G O B s k S e l J x x w D a 2 j T e S j H d R A h + g I N R F D t + g e P a B H 7 8 5 7 8 p 6 9 l 8 / R M W + 0 s 4 p + w H v 7 A J B Y o 6 E = < / l a t e x i t > E x p t A , o n ly dme 6 = 0 < l a t e x i t s h a 1 _ b a s e 6 4 = " r u E J w d b T K T 8 8 5 o i 9 A T j q w 7 7 U z

< l a t e x i t s h a 1 _
b a s e 6 4 = " A a 0 8 z a m 8 f X Y D 3 7 / S K / 2 C t b 2 W G C U = " > A A A C S H i c d Z B B S 9 x A F M c n 2 9 r q q u 1 a j 1 4 G F 8 G D L L N G G y 8 F U Q / F k w V X h c 0 S J p M X M + z M J J 2 Z F E L I d + r n 6 A c o 9 K Q 3 r 7 2 V 3 p y s 2 1 K l P h j 4 8 3 v v 8 e b / j w v B j S X k h 9 d 5 8 X L h 1 e v F p e 7 y y u q bt 7 2 1 d x c m L z W D E c t F r q 9 i a k B w B S P L r Y C r Q g O V s Y D L e H r c 9 i + / g D Y 8 V + e 2 K m A i 6 b X i K W f U O h T 1 T k N J b c Y y q h N I Q 1 l l V Z G B + r C 5 e 9 K t Q y 3 x E f y F + J z v h D v N D O d K V E 7 j J K p l B E 2 o 4 D O J e n 0 y 8 P f 9 w A 8 w G Z B Z O e G / 9 0 k Q 4 O G c 9 N G 8 z q L e X Z j k r J S g L B P U m P G Q F H Z S U 2 0 5 E 9 B 0 w 9 J A Q d m U X s P Y S U U l m E k 9 8 9 z g L U c S n O b a P W X x j P 6 7 U V N p T C V j N 9 k 6 N E 9 7 L f x f b 1 z a 9 G B S c 1 W U F h R 7 O J S W A t s c t w H i h G t g V l R O U K a 5 + y t u 4 6 P M u p g f X T H O V A Z J 0 3 X J / L G P n x c X u 4 P h / o B 8 2 u s f H s 0 z W k Q b a B N t o y E K 0 C H 6 i M 7 Q C D H 0 F X 1 H N + j W + + b 9 9 H 5 5 v x 9 G O 9 5 8 Z x 0 9 q k 7 n H g M G s v U = < / l a t e x i t >Be -T i, on ly dm e 6 = 0 < l a t e x i t s h a 1 _ b a s e 6 4 = " a e E f Z 0A O p r E + A 4 L w w 8 R u j u 8 A Z p Y = " > A A A C S H i c d Z D N a t t A F I V H b t q m T n + U d p n N E B P o I h j 5 p 4 2 9 K K R J F i G r B O r Y Y B k x G l 1 Z Q 2 Z Gy s y o I I T e q c / R B y h 0 1 e 6 6 z S 5 k l 5 H j l L i k F w Y O 3 7 2 X O + e E G W f a e N 5 P p / F k 7 e m z 5 + s v m h s v X 7 1 + 4 2 6 + P d d p r / l a t e x i t > Be -A l, on ly dm e 6 = 0 < l a t e x i t s h a 1 _ b a s e 6 4 = " h m 7 3 d 5 d i j Z O U B Y I g J L R r p A s T K P s = " > A A A C S H i c d V B N a 9 w w F J Q 3 a Z N u P 7 J t j 7 2 I L I U e g p F 3 N 8 n m U A h N D y W n D X S T w H o x s v w c i 0 i y I 8 k F Y / y f 8 j v y A w I 9 t b d e e y u 5 R d 5 s S l P a A c E w 8 x 5 P M 3 E h u L G E f P U 6 K 6 u P H q + t P + k + f f b 8 x U b v 5 a t j k 5 e a w Z T l I t e n M T U g u I K p 5 V b A a a G B y l j A S X x + 0 P o n X 0 A b n q

Figure 5 .
Figure 5. Exclusion plot for dm e ; the solid lines assume a model where only dm e = 0.The dotted lines depict the bounds for a model defined by a vector of sensitivities, Q⊥ Full (m φ ), that is orthogonal to the sensitivities of four leading EP test experiments (see Supp.Mat. for details).The bounds from our experiments are shown in red and blue, whereas bounds from other published experiments, shown in Fig. 4, are not shown again here, for simplicity.The bound from the fifth-best EP test experiment in a given mass range, projected onto the Q⊥ Full (m φ ) direction, and further on the dm e direction, is shown as dotted brown line.

α = 2 .
The sensitivity to the electron mass is R(1) e

( 1 )
y (f ), and of the interrogating laser wave, S

Figure 2 .
Figure 2. Spectra of iodine transitions employed in experiments A and B. (a): Doppler-free, pressure-broadened iodine transition at 532 nm in experiment A. FWHM: 3.6 MHz.Data was recorded with 1 MHz detection bandwidth and 10 ms scan time.For DM detection, the laser frequency is tuned to the operating point indicated by the magenta circle.The discriminator slope D is found from the slope of the signal at this point and the electronics' amplification factor.(b): Doppler-and pressure-broadened I2 transition at 725 nm in experiment B. The magenta-color circles indicate the regions where the laser frequency is tuned to take data with, or without sensitivity to FC oscillations.The spectrum was recorded with 250 Hz bandwidth and 2 s scan time.
Figure 3.total noise spectral density Ŝtot(f ) for the detection of the relative frequency fluctuations between interrogating oscillator and iodine reference.The peak at 120 kHz is due to relaxation oscillations of the laser.Magenta: Estimated frequency noise of the interrogation oscillator (laser 1), S for the experiment-specific sensitivities.

Figure 4 .
Figure 4. Excess PS and detection threshold at the 95% CL.

Table I .
Some frequency windows containing technical noise.The quality factors Q are computed from the measured full half-widths at half maximum (FWHM).