Measuring Entanglement by Attempting to Undo it with Ultra-Broadband Bi-Photons

1. Measuring Entanglement by Attempting to Undo it with Ultra-Broadband Bi-Photons  Yaakov Shaked, Roey Pomeranz and Avi Pe’er Department of Physics and BINA Center for Nano-technology, Bar-Ilan University, Ramat-Gan 52900, Israel avi.peer@biu.ac.il Abstract: We demonstrate a unique source of ultra broadband bi-photons with a correlation time of 10-14sec, emitting an ultra-high flux of >1012time-energy entangled photon-pairs per second. Using a pairwise “Mach-Zehnder” interferometer we fully characterize the quantum state of the bi-photons (amplitude and phase), and show that the interference visibility is a direct measure for the bi-photons purity. We support our results with a theoretical model, which fully reconstructs the observed square root dependence of the fringe visibility on internal loss. Interpretation Conceptually, the second nonlinear medium serves as a physical detector of entanglement, where the existence of an entangled pair is detected by attempting to annihilate it. Since this operation affects bi-photons, only, the fringe contrast is a direct measure of the bi-photon purity, thereby providing a method to measure entanglement by attempting to undo it. By attenuating the bi-photon (and pump) field between the two crystals we reduce the single photon flux linearly, but the ”surviving” bi-photon flux quadratically, thereby reducing the quantum bi-photon state purity and reducing the pairwise interference visibility. We compare this scenario with attenuation of the two fields before the first crystal reducing the bi-photon flux but not the quantum bi-photon state purity, and indeed the interference visibility remains constant. Experimental layout Concept Bi-photons are generated in the 1st crystal (12mm long PPKTP), pumped by a single-frequency diode laser at 880 nm with up to 1 W power. Reflection of the bi-photons from mirrors M2 and M3 is accompanied by a spectral phase shift. Both bi-photons and pump enter the 2nd identical crystal. The resulting bi-photons spectrum is measured by a home-built spectrometer composed of a prism (SF11) and a CCD IR camera. The last mirror (M4) separates the pump from DC light, allowing a pump power measurement. Attenuation is achieved either before the 1st crystal by a half-wave plate and polarizer beam splitter, or between the two crystals with a polarizer P1, and a polarizer P2 in front of the camera. The inset shows a measured intensity spectrum of the ultra-broadband bi-photons after the first crystal. (a) Bi-photons produced in a first non-linear (NL) crystal via spontaneous parametric down conversion (SPDC) enter an identical second NL crystal together with the original pump, and are either enhanced by further down conversion (DC), or up-converted back to the pump, depending on the relative phase between the pump and the bi-photons. Since the two possibilities for bi-photon generation, in the first or second NL crystal, are indistinguishable, their probability amplitudes interfere quantum mechanically. Thus, the setup is analogous to a Mach-Zehnder interferometer (b) for bi-photons, where the crystals represent two-photon beam splitters that couple the pump and DC fields. Results Two calibrated fringe spectra with a pphase shift between them (blue and dotted green lines), and the corresponding calculated spectral phase j(w)/2of the bi-photons (red line). Interference visibility Vs. loss Measured interference visibility as a function of attenuation with corresponding theoretical fits before the first crystal (squares + dotted fit) and between crystals (circles + solid fit). Pairwise interference of bi-photons (CCD image) ArXiv:1209.4194 [physics.optics]