Axion dark matter search using arm cavity transmitted beams of gravitational wave detectors

Axion is a promising candidate for ultralight dark matter which may cause a polarization rotation of laser light. Recently, a new idea of probing the axion dark matter by optical linear cavities used in the arms of gravitational wave detectors has been proposed [Phys. Rev. Lett. 123, 111301 (2019). In this article, a realistic scheme of the axion dark matter search with the arm cavity transmission ports is revisited. Since photons detected by the transmission ports travel in the cavity for odd-number of times, the effect of axion dark matter on their phases is not canceled out and the sensitivity at low-mass range is significantly improved compared to the search using reflection ports. We also take into account the stochastic nature of the axion field and the availability of the two detection ports in the gravitational wave detectors. The sensitivity to the axion-photon coupling, $g_{a\gamma }$, of the ground-based gravitational wave detector, such as Advanced LIGO, with 1-year observation is estimated to be $g_{a\gamma }\sim 3\times {10}^{-12}{\mathrm{GeV}}^{-1}$ below the axion mass of ${10}^{-15}\mathrm{eV}$, which improves upon the limit achieved by the CERN Axion Solar Telescope.

Figure 1

The probabilistic amplitude of axion field $A_N^{\mathrm{low}}(p)$ given in Eq. (12). We expect the actual axion RMS amplitude $A_N$ is larger than or equal to $A_N^{\mathrm{low}}(p)$ by probabilities of $p=68\%$ (Cyan) and 95% (Red). The horizontal axis denotes the experiment time divided by the coherent time, $T_{\mathrm{obs}}/\tau$, which corresponds to the number of time domain $N$ for $T_{\mathrm{obs}}/\tau >1$, while $N$ remains unity for $T_{\mathrm{obs}}/\tau <1$.

Figure 2

Schematic of experimental setup for axion search with (a) a linear optical cavity and (b) a gravitational wave detector. FI, Faraday isolator; HWP, half wave plate; PBS, polarizing beam splitter; PD, photodetector; BD, beam dump; BS, beam splitter. In the detection port at the cavity transmission, polarization analysis is performed with the HWP, PBS, and PD, and the axion signal can be detected. Components for phase measurement are not shown. Two PBSs in FI are placed rotated by 45 degrees along the optical path.

Figure 3

Response functions for the transmission port $H^{\text{Trans}}$ (blue) of DECIGO. $H^{\text{Trans}}$ has two contributions, $H_a(m)$ (red dashed) and $H_a^{\prime }$ (yellow dashed) given in Eqs. (20) and (30), respectively.

Figure 4

Sensitivity comparison of the several parameter sets shown in table 1. The dotted lines represent the sensitivity without modification of the stochastic effect. Although the higher mass range seems to be filled, they have sensitivity peaks at mass of $m=\pi (2N-1)/L_{\mathrm{cav}}(N\in \mathbb{N})$. The gray and green band express the current limits provided by CAST [7] and the astrophysical observations (SN1987A [16], M87 [18], and NGC 1275 [19]). The dashed lines are sensitivities using reflection port shown in [37] with modification of the stochastic effect.