Historical research guide · 0601 · 2024
Thermal noise-limited beam balance as prototype of the Archimedes vacuum weight experiment and B-L dark photon search
Annalisa Allocca · Saverio Avino · Enrico Calloni · Sergio Caprara · Massimo Carpinelli · Andrea Contu · Luca D’Onofrio · Domenico D’Urso · Rosario De Rosa · L. Errico · Marina Esposito · Gianluca Gagliardi · Marco Grilli · Valentina Mangano · Maria Marsella · Luca Naticchioni · Antonio Pasqualetti · Gianpiero Pepe · Maurizio Perciballi · Paola Puppo · Piero Rapagnani · Fulvio Ricci · Luigi Rosa · Carlo Rovelli · Davide Rozza · Paolo Ruggi · Naurang L. Saini · Valeria Sequino · Valeria Sipala · Daniela Stornaiuolo · Francesco Tafuri · Lucia Trozzo
In one minute
Vacuum energy is the largest arithmetic mismatch in physics: quantum mechanics fills empty space with an enormous energy density, while the observed expansion of the universe says the part that gravitates is minute. The Archimedes collaboration, led from Naples by Enrico Calloni and including Carlo Rovelli, proposes to settle a piece of that by weighing it. The plan is to hang a high-temperature superconductor from a balance arm and cycle it through its transition temperature, because the electromagnetic vacuum energy inside the sample changes at the transition — so if that energy has weight, the balance tips, by a few times ten to the minus sixteen newtons. This paper reports the prototype: a half-metre aluminium arm, read by a Michelson interferometer, running closed-loop in the seismically quiet Sos Enattos mine in Sardinia. It reaches a torque noise of about seven times ten to the minus thirteen newton-metres per root hertz — its own suspension’s thermal limit, exactly the level the final cryogenic balance was designed around. The same dissimilar-metal balance also sets first limits on ultralight dark photons.
Connection
Chapter 2 says the vacuum is a real medium with a real energy density; chapter 3 says that energy is what gravity and inertia are made of. This is the experiment that puts a number on the join — a laboratory balance that asks whether a change in vacuum energy has weight — and chapter 1 cares that the prototype has already hit its designed noise floor, which turns the final measurement from a hope into a schedule.
From the source
The deepest open problem in the field is the cosmological one: the enormous vacuum energy density quantum mechanics attributes to empty space cannot be reconciled with the very much smaller cosmological constant the universe actually shows when that energy is inserted into Einstein’s equations. The Archimedes experiment attacks it experimentally rather than theoretically, by measuring how vacuum fluctuations interact with gravity.Sect. 1, Introduction, opening paragraph
The Archimedes method is to weigh the change in vacuum energy content at the superconducting transition of a high-temperature superconductor sample of about 0.2 kg. The final apparatus is a cryogenic balance working near 90 K, modulated around the transition temperature of GdBCO, and the weight variation expected is of the order of a few times 10⁻¹⁶ N at a modulation frequency of about 10 mHz.Sect. 1, Introduction, second paragraph
The room-temperature prototype reaches a torque noise of about 2 times 10⁻¹² Nm per root hertz at 10 mHz, falling to about 7 times 10⁻¹³ Nm per root hertz at around 60 mHz, corresponding to a force sensitivity of about 3 times 10⁻¹² N per root hertz. Between roughly 20 mHz and 100 mHz the measured spectrum is compatible with the thermal noise of the suspension itself, computed from the measured quality factor Q of 90 and the restoring constant of the 26 mHz resonance.Abstract; Sect. 3, Eq. (1) and Fig. 5
Reaching the thermal noise floor demonstrates that the optical and mechanical design is correct: the interferometric read-out, the nested closed loop with thermal actuators below the mHz and electrostatic actuators above it, and the choice of the extremely quiet Sos Enattos site all work as designed. The final balance needs a torque noise below 10⁻¹³ Nm per root hertz around 10 mHz on a 1.4 m arm, to be won from cryogenic operation at 77 K, a 5 mHz resonance, a moment of inertia of 0.3 kg m², and an improved suspension quality factor, with an integration time of order 10⁶ seconds — about two weeks.Sect. 1; Sect. 2; Sect. 3, Eq. (2) and Fig. 6
Because the balance carries a weight and a counterweight made of different materials — aluminium against lead — it is sensitive to an ultralight dark photon coupled to the B minus L current, which would drive an almost monochromatic force on the two masses in proportion to their differing neutron numbers. A first very short run of 21000 s already sets a limit on the B minus L coupling close to the standing limits from the EOT-WASH and MICROSCOPE free-fall experiments, in a frequency band from about 20 mHz to 200 mHz that direct searches have not yet covered.Sect. 4, Eqs. (4) and (7); Fig. 7
The named next measurements are the first scientific runs of the prototype, dedicated to a direct search for the B minus L dark photon in a mass band about a decade wide around 10⁻¹⁶ eV, taken during the mine’s holiday periods and with the remaining fan-cooled instruments removed; months of integration would be enough to overtake the current best limits. In parallel the collaboration is studying the suspension losses of the copper-beryllium joints, and other materials, for the cryogenic balance.Sect. 5, Discussion and future developments
The way in
https://doi.org/10.1140/epjp/s13360-024-04920-xHow to cite it
Annalisa Allocca, Saverio Avino, Enrico Calloni, Sergio Caprara, Massimo Carpinelli, Andrea Contu, Luca D’Onofrio, Domenico D’Urso, Rosario De Rosa, L. Errico, Marina Esposito, Gianluca Gagliardi, Marco Grilli, Valentina Mangano, Maria Marsella, Luca Naticchioni, Antonio Pasqualetti, Gianpiero Pepe, Maurizio Perciballi, Paola Puppo, Piero Rapagnani, Fulvio Ricci, Luigi Rosa, Carlo Rovelli, Davide Rozza, Paolo Ruggi, Naurang L. Saini, Valeria Sequino, Valeria Sipala, Daniela Stornaiuolo, Francesco Tafuri, Lucia Trozzo (2024) Thermal noise-limited beam balance as prototype of the Archimedes vacuum weight experiment and B-L dark photon search doi:10.1140/epjp/s13360-024-04920-x