Microwave cavity light shining through a wall optimization and experiment

It has been proposed that microwave cavities can be used in a photon regeneration experiment to search for hidden sector photons. Using two isolated cavities, the presence of hidden sector photons could be inferred from a “light shining through a wall” phenomenon. The sensitivity of the experiment has strong a dependence on the geometric construction and electromagnetic mode properties of the two cavities. In this paper we perform an in-depth investigation to determine the optimal setup for such an experiment. We also describe the results of our first microwave cavity experiment to search for hidden sector photons. The experiment consisted of two cylindrical copper cavities stacked axially inside a single vacuum chamber. At a hidden sector photon mass of $37.78\mu \mathrm{eV}$ we place an upper limit on the kinetic mixing parameter $\chi =2.9\times {10}^{-5}$. Whilst this result lies within already established limits our experiment validates the microwave cavity “light shining through a wall” concept. We also show that the experiment has great scope for improvement, potentially able to reduce the current upper limit on the mixing parameter $\chi$ by several orders of magnitude.

Figure 1

Diagram of cavity setup with radius $a$, length $L$ and separation distance $d$.

Figure 2

Curves for the ${\mathrm{TM}}_{01p}$ mode family labeled ($p$) where $p$ corresponds to the axial mode number. Each was calculated for a cavity aspect ratio of one and zero separation distance between the cavities.

Figure 3

Lines of ${\mathcal{F}}^2$ maximums for various families of modes against relevant mode numbers. All for a cavity aspect ratio of one and zero separation distance between the cavities.

Figure 4

Curves of ${\mathcal{F}}^2$ for the ${\mathrm{TM}}_{012}$ mode with aspect ratios (diameter divided by length) from $(1)1/3$ to (17)5, and zero separation distance between the cavities.

Figure 5

Trends of the full geometric function maximum against aspect ratio for various modes. In all cases the separation distance between the cavities is zero.

Figure 6

Plots of ${\mathcal{F}}^2$ for the ${\mathrm{TE}}_{012}$ mode in cavities of size $\mathrm{\text{length}}=\mathrm{\text{diameter}}=4\mathrm{cm}$ (aspect ratio 1) with a separation distance labeled ($d$) cm from 0 to 10.

Figure 7

Trend lines of maximal ${\mathcal{F}}^2$ against distance over length for the ${\mathrm{TE}}_{012}$ mode with aspect ratios as labeled.

Figure 8

Schematic of the experimental setup.

Figure 9

Diagram of the microwave circuit used in our cavity experiment.

Figure 10

Power spectral density showing the thermal noise of our detector cavity.

Figure 11

Limits from this experiment against current hidden sector photon bounds from Ref. 2.