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Marco Bellini, Silvia Viciani, Alessandro Zavatta Istituto Nazionale di Ottica Applicata (Firenze) Francesco Marin,F. Tito Arecchi Francesco Marin, F. Tito Arecchi Università di Firenze - Dipartimento di Fisica Marco Bellini, Silvia Viciani, Alessandro Zavatta Istituto Nazionale di Ottica Applicata (Firenze) Francesco Marin,F. Tito Arecchi Francesco Marin, F. Tito Arecchi Università di Firenze - Dipartimento di Fisica No filter Filter on Detection of photon 1 after the monochromator collapses the SPDC wavefunction on a spectrally filtered state (with a longer coherence time The correlation time τ c is limited by the pump coherence. Pump coherence time Visibilities of fourth-order interference fringes vs. width of the spectral filter Detection of an idler photon after the Michelson collapses the SPDC wavefunction onto a coherent superposition of pulses displaced by T. The Michelson interferometer is kept unbalanced, a click is observed by D i if: Measurement of the signal spectrum conditioned on photodetection in D i Measurement of the signal spectrum conditioned on photodetection in D i M. Bellini et al., Physical Review Letters 90, 043602 (2003) Non-local pulse shaping with entangled photon pairs Quantum Homodyne Tomography Photocurrent difference P θ (x θ ) xθxθ x Time Θ is the relative phase between signal and local oscillator Strong coherent field unknown state | > Marginal distribution 82 MHz pulse train The measured field is an attenuated version of the laser output (coherent state) Control of LO phase Vacuum field ~ 1 Reconstruction of weak coherent states Reconstruction of weak coherent states Evaluation of density-matrix elements Evaluation of density-matrix elements (Poissonian photon-number distributions) A. Zavatta et al., Journal of the Optical Society of America B 19, 1189 (2002) Single-photon state Preliminary results... vacuumvacuum Overall Efficiency 16% Single-photon Wigner function Marginal distributions for different values of the detection efficiency Wigner function sections Negative values ! More than 50% of detection efficiency needed to observe negative valued Wigner functions Complete set of marginal distributions Radon transform of the Wigner function Wigner function Density matrix elements Density matrix elements Inverse Radon transform Quantum sampling method G.M. DAriano in Quantum Optics and the Spectroscopy of Solids 175-202 (T. Hakioglu et al. eds., Kluwer, 1997). Quantum optical effects with pulsed lasers p = i + s k p =k i +k s p = i + s k p =k i +k s Parametric down- conversion (SPDC) in non-linear crystals Parametric down- conversion (SPDC) in non-linear crystals Energy and momentum conservation SPDC Entangled state: or The properties of a single photon are not defined individually but are completely correlated to those of the other Generation of two-photon entangled states The monochromator filter can be replacend by etalons: SPDC emission probability... also the UV pump can be filtered by an etalon! convolution of the SPDC emission probability with the transmission function of the filters and the spectral response of the Michelson interferometer. Idler-filter transmission function: Monochromator or etalon. S. Viciani et al., in press (2004) Ghost interference …ghost spectral interference fringes appear! Measurement of the coherence time (1/ ) Measurement of the coherence time (1/ ) 1 2 Università degli Studi di Firenze Dipartimento di Fisica Quantum Computation The coincidence count rate is given by Classical-Bit Quantum-Bitqubit 0 or 1 Well defined by a single measurement. State of a quantum system (atomic energy levels, nuclear spin, polarization of photons, etc…) and more generally Superposition state: | | 2 and | | 2 are the probabilities to find the qubit in the 0 and 1 state respectively after a single measurement. 2-qubit state: Entangled state: DiDi The Wigner function is reconstructed from marginal distributions via quantum tomography Istituto Nazionale di Ottica Applicata entangled pair of qubits.

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