Matter-Wave squeezing from Gouy phase: toward a new tool for quantum technology

We investigate the Gouy phase emerging from the time evolution of confined matter waves in a harmonic potential. Specifically, we analyze the quantum dynamics of a Gaussian wavepacket that exhibits position--momentum correlations. By tuning the parameters governing its evolution, we reveal intriguing effects, with a particular focus on squeezing. Notably, during the wavepacket evolution quantum spreading and squeezing processes emerge, giving rise to Gouy phase contributions of \(π/4\,rad\), establishing a clear link between the Gouy phase and a purely quantum phenomenon. Furthermore, the interplay between wavepacket squeezing and one-dimensional spreading leads to a total Gouy phase accumulation of \(π/2\,rad\) in an oscillation period. Both squeezing and Gouy phase have individually proven valuable in state engineering and quantum metrology. By demonstrating a direct, controllable relationship between these two fundamental processes, our findings expand the realm of quantum-enhanced technologies, including quantum sensing and precision measurement.