Presentation on theme: "Interferometric Measurement of Spatial Wigner Functions of Light Bryan Killett Brian J. Smith M. G. Raymer Funded by the NSF through the REU and ITR programs."— Presentation transcript:
Interferometric Measurement of Spatial Wigner Functions of Light Bryan Killett Brian J. Smith M. G. Raymer Funded by the NSF through the REU and ITR programs.
What is a spatial Wigner function? BUT - can we define a joint probability density function? In other words, something like: Pr(x,k x ). Given a normalized wave function (x), we know how to construct single-variable probability densities:
What is a spatial Wigner function? A straightforward definition of Pr(x,k x ) would have to… 2. Allow for a physical interpretation at every point. Therefore, Pr(x,k x ) needs to be non-negative everywhere. 1.Integrate to unity and satisfy the following relations: UNCERTAINTY PRINCIPLE! The spatial Wigner function corresponding to (x) is simply a function that fulfills the above condition.
The spatial Wigner function: This function has some other interesting properties: A single integral along the x axis gives the probability density for k x and vice-versa for the other axis. A double integral over all x and all k x results in unity. - It is sometimes negative! Thus, we call it a quasiprobability distribution. - It is uniquely related to (x) so a measurement of W(x,k x ) can be transformed to reveal (x). (not merely (x) 2 !)
How do we measure W(x,k x )? Top Mirror Output Beam Input Beam
The Top Mirror rotates the field. Clockwise (CW) Beam Counter-Clockwise (CCW) Beam x y y x x yx y Top Mirror
Future work Examine single photon states like the Schrodinger Cat state. Analyze the effect of scattering and decoherence on the spatial Wigner function. Bell inequalities/entanglement measurements with two interferometers. See also a paper by our collaborators:Direct Measurement of the spatial Wigner function with area-integrated detection in Optics Letters Vol 28, #15, by E. Mukamel et. al.