Microwave cavity searches for low-frequency axion dark matter

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Microwave cavity searches for low-frequency axion dark matter

Robert Lasenby

Phys. Rev. D 102, 015008 – Published 14 July 2020

Abstract

For low-mass (frequency $≪ GHz$ ) axions, dark matter detection experiments searching for an axion-photon-photon coupling generally have suppressed sensitivity, if they use a static background magnetic field. This geometric suppression can be alleviated by using a high-frequency oscillating background field. Here, we present a high-level sketch of such an experiment, using superconducting cavities at $\sim GHz$ frequencies. We discuss the physical limits on signal power arising from cavity properties, and point out cavity geometries that could circumvent some of these limitations. We also consider how backgrounds, including vibrational noise and drive signal leakage, might impact sensitivity. While practical microwave field strengths are significantly below attainable static magnetic fields, the lack of geometric suppression, and higher quality factors, may allow superconducting cavity experiments to be competitive in some regimes.

Received 23 March 2020
Accepted 12 June 2020

DOI:https://doi.org/10.1103/PhysRevD.102.015008

Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI. Funded by SCOAP³.

Published by the American Physical Society

Physics Subject Headings (PhySH)

Axions Particle dark matter

Particles & FieldsGravitation, Cosmology & Astrophysics

Authors & Affiliations

Robert Lasenby ^*

Stanford Institute for Theoretical Physics, Stanford University, Stanford, California 94305, USA

^*rlasenby@stanford.edu

Article Text

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Issue

Vol. 102, Iss. 1 — 1 July 2020

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Images

Figure 1
Schematic illustration of an up-conversion experiment for axion DM detection. The left-most panel (“cavity modes”) illustrates a cavity in which we are interested in two modes, one with magnetic field profile $B_{0}$ , and another with electric field profile $E_{1}$ . The adjacent graph (“mode frequencies”) illustrates the frequencies of these modes as we vary the shape of the cavity (here, the length $d$ ), showing that they become degenerate at some $d$ . When the cavity length is tuned to be close to this point, the frequency splitting between the modes will be small. If the $ω_{0}$ mode is driven with high amplitude, then in the presence of an axion DM oscillation with $m_{a} ≃ | ω_{1} - ω_{0} |$ , power will be transferred to the $ω_{1}$ mode (illustrated in the “interaction” panel). This signal can be detected as excess power, above thermal (or quantum) fluctuations, in the $ω_{1}$ mode, as indicated in the “signal” panel. While some of the power in the $ω_{0}$ mode may leak into the detected signal (indicated as a dashed peak in the signal panel), the frequency difference between $ω_{0}$ and $ω_{1}$ helps to distinguish this from the axion signal (see Sec. 3c). The mode profiles shown here are schematic—Fig. 2 shows actual mode profiles for a particular cavity geometry.
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Figure 2
Illustration of the optimum drive and signal modes for a cylindrical cavity, as discussed in Sec. 2b. The $B_{0} \cdot E_{1}$ panel shows the dot product of the drive mode’s magnetic field with the signal mode’s electric field, with green indicating a positive value, and red a negative value—the integrated value over the volume gives $C_{01} ≃ 0.19$ , as defined in Sec. 2.
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Figure 3
Illustration of a toroidal corrugated waveguide, as discussed in Sec. 2b2. The radius of curvature $R$ is taken to be much larger than the waveguide radius $a$ .
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Figure 4
Sensitivity projection for an up-conversion experiment using a 60 litre (20 cm radius) cylindrical cavity, where the ${TE}_{012}$ mode is driven, and signals are picked up in the ${TM}_{013}$ mode. We assume that the maximum magnetic field for the drive mode at the cavity wall is $H_{s h} = 0.2 T$ , and an integration time of one year per e-fold in axion mass range. The sensitivity threshold is set at an expected SNR value of 3. The “thermal EM” line shows the sensitivity limit in the presence of thermal EM noise, at the assumed physical temperature of 1.4 K (see Sec. 3a). The “thermal vibrations” line is an estimate of the effect of thermal vibrations of the cavity walls, which up-convert power from the signal mode to the drive mode (Sec. 3b). The “acoustic vibrations” line also incorporates extra acoustic noise from external sources. The dashed line between them is an estimate of the effects of time-varying drive signal leakage (Sec. 3c). Taking all of these noise sources into account, the estimated sensitivity reach of the experiment is given by the blue shaded region. It should be noted that, while the “thermal EM” limit is set by basic physical parameters, the vibrational limits depend on guesses about the properties of the cavity system, and could be very different in a real experiment. Also, while we have extended the projected reach to axion frequencies $\sim 100 MHz$ , scanning an order one axion mass range at these frequencies would be difficult (see Sec. 2a). In Fig. 5, this reach is compared to other proposed experiments. The gray shaded regions correspond to the parameter space ruled out by observations of horizontal branch stars [43, 44, 45], SN1987A [46], existing cavity haloscope experiments [5, 47, 48, 49, 50, 51], and the ABRACADABRA-10 cm experiment [52]. The green diagonal band corresponds to the “natural” range of $g_{a γ γ}$ values at each QCD axion mass—if we write $g_{a γ γ} = \frac{α_{EM}}{2 π f_{a}} (\frac{E}{N} - 1.92)$ [2], then the upper edge of the band is at $E / N = 5$ [3], and the lower edge at $E / N = 2$ [2]. The gray diagonal lines indicate the Kim-Shifman-Vainshtein-Zakharov (KSVZ) (upper, $E / N = 0$ ) and Dine-Fischler-Srednicki-Zhitnitsky (DFSZ) (lower, $E / N = 8 / 3$ ) models.
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Figure 5
Comparison of sensitivity projections for different kinds of low-frequency axion DM detection experiments. The “60 L cylinder” region corresponds to the 20 cm cavity up-conversion experiment described in the text, with parameters given in Table 1 (we assume an integration time of 1 year per e-fold in axion mass range). At high frequencies ( $ν_{a} ≳ 200 kHz$ ), its sensitivity is limited by thermal EM noise from the cavity walls, while at lower frequencies it is limited by (a rough estimate of) up-converted acoustic noise from external sources (see Sec. 3b and Fig. 4). We also display the thermal-noise-limited sensitivities for the larger up-conversion experiments listed in Table 1. The “900 L cylinder” line corresponds to a scaled-up ${TE}_{012} \to {TM}_{013}$ experiment, with 50 cm radius. The “8 m toroid” line corresponds to a corrugated toroidal cavity, as described in Sec. 2b2; we assume an overall radius of 8 m, a waveguide radius of 13 cm, and a frequency of 2.8 GHz, resulting in the parameters listed in Table 1. We leave an analysis of the less fundamental noise sources for these larger up-conversion experiments to future work. The red lines are thermal noise limited sensitivity projections for representative static-magnetic-field experiments, modeled on the Dark Matter Radio proposal [13, 53]. The “0.5 T, 50 L” line corresponds to a 50 liter experiment, with a background magnetic field of $0.5 T$ , and a physical temperature of 10 mK—the resonator quality factor is taken to be $10^{6}$ , and the geometric overlap factor to be 0.2 [13] (in the sense that $P_{sig} ≃ {0.2}^{2} g^{2} B_{0}^{2} V Q \frac{ρ}{m} (m L)^{2}$ , where $L$ is the shielding length scale [9]). The “4 T, 1000 L” line corresponds to the same assumptions, but with a cubic metre volume, and a background magnetic field of 4 T. The quasistatic $\sim (m L)^{2}$ suppression used is only a dimensional estimate; the actual value would depend on the geometry of the experiment. We also show an example of a proposed optical-frequency up-conversion experiment, the “ADBC” proposal from [18]. This assumes a 2 meter Faby-Perot cavity, with a circulating optical power of 10 kW. The existing haloscope limits, QCD axion band, and astrophysical constraints are as per Fig. 4.
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Figure 6
Signal diagram of a cavity readout system using an amplifier isolated by a circulator, as discussed in Appendix pp2. The $T_{0}$ load represents the thermal noise from the environment (i.e., the cavity walls etc), while the $T_{c}$ load is a cold load that absorbs the amplifier’s back-action noise.
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