Systematic effects in two-dimensional trapped matter-wave interferometers

Trapped matter-wave interferometers (TMIs) present a platform for precision sensing within a compact apparatus, extending coherence time by repeated traversal of a confining potential. However, imperfections in this potential can introduce unwanted systematic effects, particularly when combined with errors in the associated beam-splitter operations. This can affect both the interferometer phase and visibility, and can make the performance more sensitive to other experimental imperfections. I examine the character and degree of these systematic effects, in particular within the context of two-dimensional TMIs applicable for rotation sensing. I show that current experimental control can enable these interferometers to operate in a regime robust against experimental imperfections.

Figure 1

Schematic of 2D interferometer sequence. The left column shows the case with no imperfections present. Top: A wave packet initially at rest a distance $d$ from the center is split in the orthogonal direction by imparting momenta $\pm p$. The wave packets recombine at the position that they were split (yellow circle). Bottom: The ideal case assumes a purely harmonic potential. The right column shows the various imperfections that may enter the system. Top: Misalignment of the initial displacement or momenta and an initial velocity common to both wave packets. Bottom: Anharmonic imperfections to the trapping potential.

Figure 2

Summary of the various systematic effects considered. The trajectories in real space are shown to aid intuition. Green arrows represent the directions of the imparted momenta. Yellow circles indicate points of recombination. All effects are exaggerated for clarity. The affected interferometer properties (see Sec. 2b for description) are listed. (a) Ideal case; no imperfections. (b) Common misalignment of imparted momenta. (c) Relative misalignment of imparted momenta. (d) Misalignment of initial displacement. (e) Common velocity of both wave packets. (f) Mismatch in trap frequencies. (g) Anharmonicity. (h) Coupling of principal axes.