Monte Carlo simulations towards the formation of a positronium coherent beam

Positronium (Ps) has emerged as a promising test particle within the QUantum interferometry with Positrons, positronium and LASers (QUPLAS) project, which aims to measure for the first time the gravitational effect on Ps, the entirely leptonic atom comprising an electron and a positron. In this work, we present a Monte Carlo simulation to generate a mono-energetic and highly coherent Ps beam by creating a negative Ps ion (Ps- consisting of two electrons and one positron) to be used in a Mach-Zehnder interferometer. We propose the equations to estimate the initial velocity distributions in the longitudinal and transversal directions of the Ps- emitted from the target converter (positron/Ps-) necessary for the Monte Carlo simulation. The resulting simulated device needs a very low divergence Ps beam at the interferometer entrance, for this reason an intensive positron beam is necessary, such as a high-flux electron LINAC. Subsequently, we utilize a Fabry- Perot IR laser cavity operating in CW at a wavelength of 1560 nm to selectively remove the extra electron. An alternative pulsed laser operating at a 3600 nm wavelength was studied to reduce broadening due to recoil and excitation. Here, we provide a Monte Carlo simulation to estimate the characteristics of the Ps beam, including its energy distribution and intensity profiles at two different temperatures (10 K and 300 K). Despite the limitations given by the assumptions mentioned in the text within the limit of our knowledge, these first simulation results obtained from our study will provide essential groundwork for future advancements in fundamental particles gravity measurements.