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

Abstract 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 <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mrow> <mml:mi>π</mml:mi> <mml:mrow> <mml:mo>/</mml:mo> </mml:mrow> <mml:mn>4</mml:mn> <mml:mstyle scriptlevel="0"/> <mml:mrow> <mml:mi>rad</mml:mi> </mml:mrow> </mml:mrow> </mml:math> , 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 <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mrow> <mml:mi>π</mml:mi> <mml:mrow> <mml:mo>/</mml:mo> </mml:mrow> <mml:mn>2</mml:mn> <mml:mstyle scriptlevel="0"/> <mml:mrow> <mml:mi>rad</mml:mi> </mml:mrow> </mml:mrow> </mml:math> 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.