The impact of raindrops on phase precision of Mach–Zehnder interferometer employing the coherent states and the squeezed vacuum states

The paper explores the influence of raindrops on the phase precision of Mach–Zehnder interferometer when the coherent states and the squeezed vacuum states are introduced into its input ports. The probability of photon loss η increases as the rain rate R or traveling distance L increases. In the presence of moderate or heavy rain, the loss probability η ranges from 0.2 to 0.48, or from 0.48 to 0.96 when the traveling distance L is close to 1 km. The threshold value R_th corresponds to the rain rate R at which the phase precision falls below the shot noise limit(SNL). At high squeezing level ( \(r = \arcsin h(\sqrt {N/2} )\) $r=arcsinh(\sqrt{N/2})$ , the light rain does not degrade the phase precision below SNL. We also calculate the threshold value of rain rate(R_th) at various low levels of squeezing and compare R_th for three low squeezing levels (15 dB,10 dB, and 6 dB) that can currently be achieved. The results show that, at the same traveling distance, R_th is larger for a 15 dB squeezing level compared to 10 dB and 6 dB squeezing levels. Even in the presence of moderate rain, the phase precision for 15 dB remains sub-SNL for long distances approaching 1 km. A feasible experimental proposal for investigating the influence of raindrops is put forward with the current technology.