Multiple-cavities interferometric analysis for dark matter axions directional-sensitive search based on signal cross-correlation processing

Abstract

Current axion detection limits neglect the relevance of the relative velocity between the axion field and the detectors. However, this aspect can lead to a daily modulation of the detected axion signal. In this work, we calculate the cross-correlation of various signals potentially originated in multiple-cavity setups, and we analyze how the signal-to-noise ratio and directional sensitivity depend on the signal cross-correlation among multiple cavities. The signal-to-noise ratio after cross-correlation exhibits a greater rate of increase over time compared to the power-summation technique, making it clear that this method could be potentially employed in a real setup for the reduction of the exposure time. For the study of the daily modulation, three interferometric experiments have been proposed in this manuscript: (i) three rectangular cavities in different Earth locations; (ii) three rectangular cavities located in the same Earth spot but oriented towards different perpendicular directions; (iii) six rectangular cavities in the same Earth location but oriented towards different directions. In each set-up, we have simulated three different cavity lengths. Similar results have been found for the cases (i) and (ii): when the highest length upon the three proposed is considered, a phase difference between the recorded voltages of more than $2^{\circ}$ has been obtained with our numerical calculations. We observe a daily modulation in the imaginary part of the signals cross-correlation for experiment (iii), that could be potentially used for the characterization of the axion velocity distribution. To the knowledge of the authors, this is the first time that the cross-correlation technique has been applied to the directional sensitivity analysis of an array of haloscopes.