Measuring arbitrary-order coherences: Tomography of single-mode multiphoton polarization-entangled states

A scheme is discussed for measuring $N$th-order coherences of two orthogonally polarized light fields in a single spatial mode at very limited experimental cost. To implement the scheme, the only measurements needed are the $N$th-order intensity moments after the light beam has passed through two quarter-wave plates, one half-wave plate, and a polarizing beam splitter for specific settings of the wave plates. It is shown that this method can be applied for arbitrarily large $N$. A set of explicit values is given for the settings of the wave plates, constituting an optimal measurement of the $N$th-order coherences for any $N$. For Fock states the method introduced here corresponds to a full state tomography. Applications of the scheme to systems other than polarization optics are discussed.

Figure 1

A sketch of the setup with two quarter-wave plates (QP${}_1$ and QP${}_2$), one half-wave plate (HP), and a polarizing beam splitter (PBS). At the detector (D), the $N$th-order intensity moment is measured.