Theoretical Description of Beamsplitters and Mirrors in Potentials via Oscillator Equations

Atom interferometry has shown to be very successful in a myriad of applications including its use for sensing gravity [1], magnetic fields and its gradients [2], and has shown potential to detect dark matter [3, 4]. Recently the focus has shifted towards improving the sensitivity to reach an accuracy beyond the standard quantum limit [5]. In order to keep the Bose-Einstein-Condensate (BEC) entangled over the interferometer sequence, experiments have shown that beam splitters and mirrors need to reach a high level of efficiency [6]. Therefore an in-depth study of the underlying diffraction process in beam splitters and mirrors is crucial for performing interferometry where the BEC’s external degrees of freedom are entangled.

Here, we provide an approach for the theoretical modeling of the diffraction process by considering operator-valued oscillation equations for arbitrary trapping potentials. We provide explicit, non-trivial examples that can be solved in a straight-forward manner with our method.

[1] Phys. Rev. A 88, 043610 (2013).

[2] Phys. Rev. A 84, 063623 (2011).

[3] AVS Quantum Sci. 6, 10.1116/5.0175683 (2024).

[4] Rep. Prog. Phys. 81, 066201 (2018).

[5] Rev. Mod. Phys. 90, 035005 (2018).

[6] Phys. Rev. Lett. 127, 140402 (2021).