Measurement of the Wigner distribution function of non-separable laser beams employing a toroidal mirror

Abstract

We present a new experimental approach to determine the Wigner distribution function of non-separable laser beams. A rotatable toroidal mirror is employed to focus an IR laser beam at a wavelength of 1064 nm. For different rotation angles of the mirror, intensity profiles of the reflected beam are captured. The resulting data suffices to fully reconstruct the four-dimensional Wigner distribution from which the global degree of coherence is derived. A comparison to theoretical expectations reveals validity of the applied formalism. Since the setup dispenses with any transmissive optics it can be applied to a broad spectral range, especially to extreme UV and soft x-ray radiation.

Quantum phase diagrams of matter-field Hamiltonians II: Wigner function analysis

“…Experimentally, the Wigner function for quantum optical systems can be reconstructed using homodyne tomography [16], field ionisation detectors [17,18], photon-counting [19], two-window heterodyne measurements [20], etc. For non-separable laser beams through a toroidal mirror see [21]. For other classes of systems it can also be determined: one can mention two Bell states and the five-qubit Greenberger-Horne-Zeilinger (GHZ) spin Schrödinger cat state [22]; a single harmonically trapped atom [23]; an ensemble of helium atoms formed by partially coherent illumination of a double slit [24], etc.…”