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European Quantum Electronics Conference (EQEC)

Measurement of the Wigner Function of a Matter Wave Packet

Christian Kurtsiefer, Tilman Pfau, J. Mlynek

Published Jan 1, 1996• 2 citations
Publisher
DOI
10.1109/eqec.1996.561743

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The Gouy phase is essential for accurately describing various wave phenomena, ranging from classical electromagnetic waves to matter waves and quantum optics. In this work, we employ phase-space methods based on the cross-Wigner transformation to analyze spatial and temporal interference in the evolution of matter waves characterized initially by a correlated Gaussian wave packet. First, we consider the cross-Wigner of the initial wave function with its free evolution, and second for the evolution through a double-slit arrangement. Different from the wave function which acquires a global Gouy phase, we find that the cross-Wigner acquires a Gouy phase difference due to different evolution times. The results suggest that temporal like-Gouy phase difference is important for an accurate description of temporal interference. Furthermore, we propose a technique based on the Wigner function to reconstruct the cross-Wigner from the spatial intensity interference term in a double-slit experiment with matter waves.
Spectral filtering of the time-separated neutrons passing through an interferometer reconstitutes the interference pattern through the formation of a macroscopic superposition out of the neutron beams and produces squeezed states. In this paper we use matter-waves squeezed states produced in this way to manipulate the rate of expansion of the neutron wave packet. We demonstrate that these quantum states also have nontrivial correlations 〈\ensuremath{\Delta}k\ensuremath{\Delta}x〉. The Heisenberg relation for the spread of the wave packet holds even in this case and the reversal of the wave packet spreading is impossible. However, one can manipulate the rate of the wave packet expansion by changing the phase shift in one of the arms of a neutron interferometer.
Abstract We investigate the scattering of a wave packet by the Pöschl-Teller potential in momentum representation. The scattering dynamics of the wave packet for a long-time evolution is feasible in this representation. With the wave function in momentum space, we can construct the time-dependent phase space Wigner function. The corresponding density function in coordinate space is then calculated through the Wigner function. The reflectionless wave packet for integer ν and partially reflected for non-integer ν are demonstrated by analyzing the Wigner function.