Wigner distribution for systems with cylindrical symmetry

B. Lesche

N. A. Denisova, V. L. Kon'kov

Alejandro Cámara, Tatiana Alieva, José A. Rodrigo +1 more

We propose a simple approach for the phase space tomography reconstruction of the Wigner distribution of paraxial optical beams separable in Cartesian coordinates. It is based on the measurements of the antisymmetric fractional Fourier transform power spectra, which can be taken using a flexible optical setup consisting of four cylindrical lenses. The numerical simulations and the experimental results clearly demonstrate the feasibility of the proposed scheme.

Lorenzo Galleani, Leon W. Cohen

Frank Kirtschig, Jorrit Rijnbeek, Jeroen van den Brink +1 more

Quantum processes can be described in terms of a quasiprobability distribution (the Wigner distribution) analogous to the phase-space probability distribution of the classical realm. In contrast to the incomplete glimpse of the wave function that is achievable in a single shot experiment, the Wigner distribution, accessible by quantum state tomography, reflects the full quantum state. We show that during the fundamental symmetry-breaking process of a generic quantum system, with a symmetry-breaking field driving the quantum system far from equilibrium, the Wigner distribution evolves continuously with the system undergoing a sequence of revivals into the symmetry-unbroken state, followed by collapses onto a quasiclassical state akin to the one realized in infinite-size systems. We show that generically this state is completely delocalized both in momentum and in real space.

Piotr Kazimierczyk, Arkadiusz Orłowski