Presentation on theme: "Quantum optical effects with pulsed lasers"— Presentation transcript:
1 Quantum optical effects with pulsed lasers Marco Bellini, Silvia Viciani, Alessandro ZavattaIstituto Nazionale di Ottica Applicata (Firenze)Francesco Marin, F. Tito ArecchiUniversità di Firenze - Dipartimento di FisicaIstituto Nazionale di Ottica ApplicataUniversità degli Studi di FirenzeDipartimento di FisicaGeneration of two-photon entangled statesQuantum ComputationClassical-BitParametric down-conversion (SPDC) in non-linear crystals0 or 1Well defined by a single measurement.Quantum-BitqubitState of a quantum system (atomic energy levels, nuclear spin, polarization of photons, etc…)orand more generallywp=wi+wskp=ki+ksSuperposition 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 otherEnergy and momentum conservation2-qubit state:SPDC Entangled state:Entangled state:entangled pair of qubits.Non-local pulse shaping with entangled photon pairsMeasurement 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 filter1The monochromator filter can be replacend by etalons:No filterPump coherence time2DiDetection of photon 1 after the monochromator collapses the SPDC wavefunction on a spectrally filtered state (with a longer coherence timeFilter onThe correlation time τc is limited by the pump coherence.Measurement of the signal spectrum conditioned on photodetection in Di“Ghost” interferenceThe Michelson interferometer is kept unbalanced, a “click” is observed by Di if:S. Viciani et al., in press (2004)SPDC emission probabilityThe coincidence count rate is given byconvolution 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 TomographyvacuumPreliminary results...Θ is the relative phase between signal and local oscillatorunknown state |y>Single-photon stateControl of LO phase82 MHz pulse trainqMarginal distributionThe Wigner function is reconstructed from marginal distributions via quantum tomographyThe 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 efficiencyxθxReconstruction of weak coherent statesSingle-photon Wigner functionStrong coherent fieldTimePhotocurrent differenceQuantum sampling methodNegative values !Complete set of marginal distributionsDensity matrix elements<n> ~ 1G.M. D’Ariano in Quantum Optics and the Spectroscopy of Solids (T. Hakioglu et al. eds., Kluwer, 1997).Vacuum fieldWigner function sections≡Inverse Radon transformRadon transform of the Wigner functionEvaluation of density-matrix elements (Poissonian photon-number distributions)Wigner functionMore than 50% of detection efficiency needed to observe negative valued Wigner functionsA. Zavatta et al., Journal of the Optical Society of America B 19, 1189 (2002)
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