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**Quantum optical effects with pulsed lasers**

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

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