Comparing Instrument Spectral Sensitivity of Dissimilar Electromagnetic Haloscopes to Axion Dark Matter and High Frequency Gravitational Waves

Abstract

It is known that haloscopes that search for dark matter axions via the axion-photon anomaly are also sensitive to gravitational radiation through the inverse Gertsenshtein effect. Recently this way of searching for high frequency gravitational waves has gained momentum as it has been shown that the strain sensitivity of such detectors, are of the same order of sensitivity to the axion-photon theta angle. Thus, after calculating the sensitivity of a haloscope to an axion signal, we also have calculated the order of magnitude sensitivity to a gravitational wave signal of the same spectral and temporal form. However, it is unlikely that a gravitational wave and an axion signal will be of the same form, since physically the way the signals are generated are completely different. For gravitational wave detection, the spectral strain sensitivity is in units strain per square root Hz, is the natural way to compare the sensitivity of gravitational wave detectors due to its independence on the gravitational wave signal. In this work, we introduce a systematic way to calculate the spectral sensitivity of an axion haloscope, so instrument comparison may be achieved independent of signal assumptions and only depends on the axion to signal transduction sensitivity and noise in the instrument. Thus, the calculation of the spectral sensitivity not only allows the comparison of dissimilar axion detectors independent of signal, but also allows us to compare the order of magnitude gravitational wave sensitivity in terms of spectral strain sensitivity, allowing comparisons to standard gravitational wave detectors based on optical interferometers and resonant-mass technology.

Sensitivity of Resonant Axion Haloscopes to Quantum Electromagnetodynamics

“…so the single mode may act as its own background field. [68,69] This technique has been detailed in ref. [68] and included the QEMD terms to show that this technique was sensitive to the sum of g a𝛾𝛾 and g aBB , where the helicity is equivalent to the overlap functions defined for the two-mode upconversion detectors.…”

“…Another upconversion technique worth mentioning is the use of the anyon cavity resonator, which uniquely allows the detection of ultra‐light axion dark matter due to the non‐zero normalized helicity of the cavity mode, given by $$$$\begin{equation} \begin{aligned} \mathcal {H}_1=\frac{2 \operatorname{Im}[\int \mathbf {B}_1(\vec{r})\cdot \mathbf {E}^*_1(\vec{r})\nobreakspace dV]}{\sqrt {\int \mathbf {E}_1(\vec{r})\cdot \mathbf {E}_1^*(\vec{r})\nobreakspace dV\int \mathbf {B}_1(\vec{r})\cdot \mathbf {B}_1^*(\vec{r})\nobreakspace dV}} \end{aligned} \end{equation}$$$$so the single mode may act as its own background field. [ 68,69 ] This technique has been detailed in ref. [68] and included the QEMD terms to show that this technique was sensitive to the sum of $$g_{a\gamma \gamma }$$ and $$g_{aBB}$$, where the helicity is equivalent to the overlap functions defined for the two‐mode upconversion detectors.…”

Searching for Low-Mass Axions using Resonant Upconversion

“…Furthermore, we have generalized these calculations to include the monopole coupling terms [26,27], whereby we find upconversion experiments to be additionally sensitive to the axion-photon coupling term, g aBB , defined in [26], so in our case limits set on g aγγ are equivalent to limits on g aBB . Finally, it is worth mentioning that this type of axion haloscope may also be sensitive to high frequency gravitational waves [51,52].…”

“…It was shown recently that when one compares dissimilar axion haloscopes the use of spectral density of photonaxion theta angle noise is a practical comparison parameter to use [52], and is given by (here subscript 0 represents the background mode and 1 the readout mode),…”

“…Eqn. 9 leads to the signal to noise ratio for a signal of virialized galactic halo dark matter axions to be given by [52],…”