Interferometric optical path measurement of a glass wedge with single photons and biphotons.

We have measured the phase structure of a glass wedge with single photons and biphotons in a Mach-Zehnder interferometer using parametric downconverted light from a Hong-Ou-Mandel particle interferometer as the source. By scanning the wedge through the focus of a microscope objective we find a doubling of the period of the interference pattern in the coincidence counts for biphotons compared to the single-photon experiment. We compare our measurement setup with classical ones and discuss some of the problems of superresolution in quantum lithography.

Nonlinearity of Pancharatnam's geometric phase in polarizing interferometers.

Earlier investigations show a time-variable nonlinear shift of the fringe pattern in a polarizing interferometer while rotating a polarizer at the exit. This effect was identified as Pancharatnam's geometrical phase and proposed for applications in interferometry and fast optical switching devices. A heterodyne analysis attributes moving fringes to a frequency difference between the interfering beams; thus changing fringe velocities point to a dynamic frequency development within the period of the uniformly rotating analyzer. This explanation offends the intuition and we undertake an experimental and theoretical investigation of the effect to solve the paradox. We determine, e.g., the complete frequency and mode spectrum of an arbitrary state of polarization P0 behind a rotating linear analyzer and behind a rotating arbitrary linear birefringent plate. We find that, in spite of a fast changing phase in the interferometer, no other (higher) frequency components appear in the spectral distribution of the intensity at the exit than the double of the rotary frequency of the analyzer: phase nonlinearities are compensated for by intensity changes. Only a phase-sensitive detector like an array of photodetectors is able to observe the nonlinearity of Pancharatnam's geometrical phase. A single detector only finds a sinusoidal intensity variation. Our insight into these relations leads us to two new applications of Pancharatnam's phase: supersensitivity of a polarizing double beam interferometer with a video camera acting as a phase detector and external tuning of a Fizeau interferometer.