Thermal noise-limited beam balance as prototype of the Archimedes vacuum weight experiment and B-L dark photon search

Abstract

AbstractWe describe the behavior of a beam balance used for the measurement of small forces, in macroscopic samples, in tens of mHz frequency band. The balance, which works at room temperature, is the prototype of the cryogenic balance of the Archimedes experiment, aimed at measuring the interaction between electromagnetic vacuum fluctuations and the gravitational field. The balance described has a 50-cm aluminum arm and suspends an aluminum sample of 0.2 Kg and a lead counterweight. The read-out is interferometric, and the balance works in closed loop. It is installed in the low seismic noise laboratory of SAR-GRAV (Sardinia—Italy). Thanks to the low sensing and actuation noise and finally thanks to the low environmental noise, the sensitivity in torque $$\tilde{\tau _n}$$ τ n ~ is about $$\tilde{\tau _n} \approx 2*10^{-12} \rm{Nm}/\sqrt {{\text{Hz}}}$$ τ n ~ ≈ 2 ∗ 10 - 12 Nm / Hz at 10 mHz and reaches a minimum of about $$\tilde{\tau _n} \approx 7*10^{-13} \rm{Nm}/\sqrt {{\text{Hz}}}$$ τ n ~ ≈ 7 ∗ 10 - 13 Nm / Hz at tens of mHz, corresponding to the force sensitivity $$\tilde{F_n}$$ F n ~ of $$\tilde{{F_{n} }} \approx 3*10^{{ - 12}} {\text{N/}}\sqrt {{\text{Hz}}}$$ F n ~ ≈ 3 ∗ 10 - 12 N/ Hz . The achievement of this sensitivity, which turns out to be compatible with thermal noise estimation, on the one hand, demonstrates the correctness of the optical and mechanical design and on the other paves the way to the completion of the final balance. Furthermore, since the balance is equipped with weight and counterweight made of different materials, it is sensitive to the interaction with dark B-L photons. A first very short run made to evaluate constraints on B-L dark photon coupling shows encouraging results that will be discussed in view of next future scientific runs.