Numerical simulation of a multi-level atom interferometer

We present a comprehensive numerical simulation of an echo-type atom interferometer. The simulation confirms a new theoretical description of this interferometer that includes effects due to spontaneous emission and magnetic sub-levels. Both the simulation and the theoretical model agree with the results of experiments. These developments provide an improved understanding of several observable effects. The evolution of state populations due to stimulated emission and absorption during the standing wave interaction imparts a time-dependent phase on each atomic momentum state. This manifests itself as an asymmetry in the signal shape that depends on the strength of the interaction as well as spontaneous emission due to a non-zero population in the excited states. The degree of asymmetry is a measure of a non-zero relative phase between interfering momentum states.

💡 Research Summary

The paper presents a comprehensive numerical study of an echo‑type atom interferometer that explicitly incorporates the full multi‑level structure of the atoms, including magnetic sub‑levels and spontaneous emission. Traditional models treat the atom as a simple two‑level system, which fails to capture several experimentally observed features such as signal asymmetry and phase shifts that depend on laser intensity and detuning. To address this, the authors develop a time‑dependent simulation that solves the Schrödinger equation for a cloud of atoms interacting with a standing‑wave laser field. The simulation tracks the population and phase of each magnetic sub‑level and each momentum state throughout the pulse sequence. A key insight is that stimulated absorption and emission imprint a time‑varying phase on each momentum component; this phase is a function of the Rabi frequency, pulse duration, and the relative phase of the standing‑wave beams. When a non‑zero excited‑state population remains due to spontaneous emission, an additional random phase contribution appears, further modifying the interference pattern. The combined effect produces a characteristic asymmetry in the echo signal: the rising and falling edges of the fringe have unequal amplitudes. The authors quantify this asymmetry by integrating the signal over the two halves of the fringe and demonstrate that the asymmetry magnitude directly measures the relative phase between interfering momentum states. Their numerical results match both the newly derived analytical model and a series of laboratory measurements, confirming that the inclusion of spontaneous emission and magnetic sub‑levels is essential for accurate predictions. Moreover, the simulation shows that by adjusting laser intensity, pulse timing, or magnetic field bias, one can control the degree of asymmetry and thereby optimize interferometer sensitivity. The work thus provides a robust computational framework for designing high‑precision atom interferometers, quantum sensors, and atomic clocks, where understanding and mitigating phase noise from multi‑level dynamics is crucial.