Gouy phase in matter waves: an experimental proposal

The propagation of gaussian packets of free particles presents a phase term that we identify analogous to the well-known Gouy phase observed in the paraxial propagation of light. This phase undergoes shift in the focus proximities equal to an integer multiple of pi/2. Such phase shift is an intrinsically wavelike phenomenon. The current state-of-art in atom optics allows for the control, focusing and the realization of interference experiments involving atom/particles beams. In this work, we propose an experiment to measure the Gouy effect in the propagation of matter waves. We analyze the feasibility of the experiment in terms of the limitations of the devices (lenses, interferometers) and of the different species of particles that form the beam. Gouy Phase The Gouy phase shift is the well-known npi/2 axial phase shift that a converging light wave experiences as it passes through its focus in propagating from − ∞ to +∞. Here the dimension n equals 1 for a line focus (cylindrical wave) and equals 2 for a point focus (spherical wave)[1,2,3]. The experimental setup to measure the Gouy phase shift in a Gaussian light beam is shown in the figure below: Figure 1: Experimental setup to measure the Gouy phase shift in gaussian light beam. Figure 2: Gouy phase in function of z with origin of the axis centered on focus. The intensity I of the combined beam depends on the phase difference between the beams following different paths [4], i.e Iα[1 + cos(kl + ξ1(z) − ξ2(z))]. (1) The phase difference ξ1(z) − ξ2(z) change the interference patterns. The time evolution of a gaussian state is given by the general form ψ(x, t) = ( u pi)1/4 exp(−i x̄p