The role of interaction in matter wave optics with motional states

TL;DR

This work examines how interparticle interactions push matter-wave optics into a nonlinear regime, altering diffraction, splitting, and interferometry in ultracold gases. Through representative experiments with strongly interacting Feshbach molecules and Bose–Einstein condensates on atom chips, it shows that interactions introduce density-dependent phase shifts and dephasing, but also enable squeezing and entanglement that surpass classical limits. The results encompass diffraction of interacting molecules with slowed dynamics, a double-well beam-splitter that generates number squeezing, and Ramsey and Michelson interferometers built from trapped molecules, collectively illustrating both the challenges and opportunities of nonlinear matter-wave devices. The findings lay the groundwork for a nonlinear matter-wave optics framework that could drive quantum-enhanced metrology, many-body physics investigations, and quantum simulation in strongly interacting regimes.

Abstract

Matter-wave optics is often viewed as a linear analogue of photonics, where noninteracting particles are coherently split, diffracted, and recombined, and interference arises from single-particle coherence. In ultracold quantum gases, however, interactions are intrinsic and can rival or exceed kinetic and optical energy scales. This drives matter-wave optics into a nonlinear regime: diffraction and momentum distributions become interaction-dependent, interference contrast degrades or collapses, and revival dynamics appear. In the mean time, interactions can generate squeezing and entanglement, enabling sensitivities beyond the standard quantum limit. We showcase representative examples - covering diffraction, splitting, and interferometry - that illustrate how interactions reshape the basic elements of matter-wave optics and open new opportunities for nonlinear quantum technologies.

Figures (8)

• Figure 1: (a) Schematic of the diffraction of strongly interacting mBECs from an optical lattice, with momentum space images taken before and after matter-wave focusing. Using a designed pulse sequence to return the diffracted molecules to the condensate (b) reveals the sources of scattering loss (c). Figure adapted from Liang2022.
• Figure 2: (a) Time carpets of momentum space distribution during the diffraction process for increasing interaction strengths (with scattering background removed for better visualization), showing a slowing-down of the evolution. (b) Zoomed view of the condensate recurrence peak. (c) The corresponding normalized populations of the 0 $\hbar k$ momentum mode (circle), and 1D GPE simulation results including a phenomenological scaling factor $\eta = 4.2$ (solid curve). (c) Slowing parameter $r$ for quantifying the slowing down from experimental data, and simulation results with and without scaling the interaction strength by the fudge factor $\eta$. Figure adapted from Liang2022.
• Figure 3: Splitting process, showing the ground state and first excited state energy levels. A BEC is prepared in a single well. The chemical potential energy and the temperature are lower than the harmonic oscillator energy such that the first exited state is empty and only features quantum fluctuations; it is the empty port of the beam splitter. For a fully split double well the first two eigenstates become degenerate and one finds a good description in a left/right basis (the two output ports of the beamsplitter).
• Figure 4: (a) Evolution of the interference pattern during ramp and hold times. Linear ramps (blue) induce strong excitations, whereas OC ramps (red) achieve splitting with negligible excitation. (b) Fast OC ramps to A = 0.5 trap with different ramp times (solid lines, upper panel), and the inferred number-squeezing factor (lower panel). Decreasing the ramp duration reduces the squeezing toward the standard quantum limit (SQL), as interaction does not result in significant effects in the short evolution time. Even for the fastest ramps, quantum properties are preserved, i.e., the relative phase is well-defined. Taken and adapted from Kuriatnikov_2025_fast_splitting.
• Figure 5: Mach-Zehnder interferometer. a) Schematic illustration of the Mach-Zehnder interferometer on an atomchip. The first beamsplitter is implemented via double-well splitting; tunneling dynamics during the recombineer phase maps the relative phase onto an atom number imbalance. b) Population imbalance at the interferometer output for different phase accumulation times. c) Mean phase accumulation versus hold time for different energy shifts. d) Phase spread due to atom number fluctuations; the dephasing can be reduced by introducing relative atom number squeezing (for detailed analysis see Zhang2024). Taken and adapted from Berrada2013.