An atomic Fabry-Perot interferometer using a pulsed interacting Bose-Einstein condensate

We numerically demonstrate atomic Fabry-Perot resonances for a pulsed interacting Bose-Einstein condensate (BEC) source transmitting through double Gaussian barriers. These resonances are observable for an experimentally-feasible parameter choice, which we determined using a previously-developed analytical model for a plane matter-wave incident on a double rectangular barrier system. By simulating an effective one-dimensional Gross-Pitaevskii equation, we investigate the effect of atom number, scattering length, and BEC momentum width on the resonant transmission peaks. For ${}^{85}$Rb atomic sources with the current experimentally-achievable momentum width of $0.02\mathrm{\hslash }{k}_0$ [$k_0=2\pi \mathrm{/}(780\text{ nm})$], we show that reasonably high contrast Fabry-Perot resonant transmission peaks can be observed using a) non-interacting BECs of ${10}^5$ atoms, b) interacting BECs of ${10}^5$ atoms with $s$-wave scattering lengths $a_s=\pm 0.1a_0$ [$a_0$ is the Bohr radius], and c) interacting BECs of ${10}^3$ atoms with $a_s=\pm 1.0a_0$. Our theoretical investigation impacts any future experimental realisation of an atomic Fabry-Perot interferometer with an ultracold atomic source.