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Experiments With Entangled Photons. Paulo Henrique Souto Ribeiro Instituto de Física - UFRJ. Summer School of Optics Concépcion January/2010. Quantum Optics Group at IF/UFRJ. Group members. Experiments: Prof. Paulo Henrique Souto Ribeiro Prof. Stephen Patrick Walborn Theory: - PowerPoint PPT Presentation

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  • Experiments With Entangled PhotonsPaulo Henrique Souto RibeiroInstituto de Fsica - UFRJSummer School of OpticsConcpcion January/2010

  • Quantum Optics Group at IF/UFRJ

  • Group membersExperiments:Prof. Paulo Henrique Souto Ribeiro Prof. Stephen Patrick Walborn

    Theory:Prof. Luiz Davidovich Prof. Nicim ZaguryProf. Ruynet Matos FilhoProf. Fabricio Toscano

    Msc and PhD students: Adriana Auyuanet Larrieu, Adriano H. de Oliveira Arago, Bruno de Moura Escher , Bruno Taketani, Daniel Schneider Tasca, Gabriel Horacio Aguilar, Osvaldo Jimenez farias, Gabriela Barreto Lemos, Rafael Chaves.

  • UFRJUFMGUSP-SO PAULOUFALUFF

  • Outline:

    Part I-Simultaneity in parametric down-conversion-Violation of a classical inequality-Consequences of simultaneity: i)localized one-photon state; ii)the Hong-Ou-Mandel interferometer iii) measurement of the tunneling timePart II-Polarization entanglement-Bells inequalities -Entanglement measurement

    Part III-Entanglement dynamics-Kraus operators-Entanglement sudden death-Process tomography-Evolution of entanglementPart VI-Spatial correlations-The transfer of the angular spectrum-Continuous variables etanglement- EPR paradox-Non-gaussian entanglement-Non-local optical vortex

  • Part I

    - Simultaneity in parametric down-conversion

    - Violation of a classical inequality

    - Consequences of simultaneity:

    i) localized one-photon state;

    ii) the Hong-Ou-Mandel interferometer

    iii) measurement of the tunneling time

  • Parametric Down-conversionEspontaneous emissionStimulated emissionTwinPhotons

  • Parametric Down-conversion

  • Observation of simultaneity

  • Observation of simultaneity

  • Parametric down-conversion: quantum stateTime evolutionTime evolution operatorTime integral

  • Simultaneity in parametric down-conversionQuantum state for weak interaction

  • Simultaneity in parametric down-conversionQuantum state including some approximations

  • Simultaneity in parametric down-conversionCalculation of expectation valuesElectric field operatorIntensityCoincidence

  • Simultaneity in parametric down-conversion:very simple view

  • Simultaneity in parametric down-conversion:very simple viewQuantum state: simple versionElectric field operator: plane wave, almost monochromaticCoincidence

  • Simultaneity in parametric down-conversion:very simple viewPlane wave pumping field

  • Coincidence detection

  • Coincidence detection

  • Measurement of time delayss=168pss=185ps

  • Simultaneity in parametric down-conversion:very simple view + detection filtersPlane wave pumping field

  • Simultaneity in parametric down-conversion:very simple view + detection filtersInterference filter: typical Dl = 10nm, Dw = 3.8 x 1013 Hz, Dt = 82 fs

  • Simultaneity in parametric down-conversion:very simple view + timing resolution

  • Localized one photon state

  • Localized one photon state

  • Violation of a classical inequality

  • Violation of a classical inequality

  • Hong, Ou and Mandel Interferometer

  • Hong, Ou and Mandel Interferometer:single mode approachBeam splitterInput-output relations

  • Hong, Ou and Mandel Interferometer:single mode approachBeam splitterTwo-photon input stateCoincidence probability

  • Hong, Ou and Mandel Interferometer

  • Single-photon tunneling time

  • Part II

    - Polarization entanglement

    - Bells inequalities

    - Entanglement measurement

  • Polarization entanglement:generationKwiat et al. PRL 75, 4337 (1995)

  • Kwiat et al. PRA 60, R773 (1999)White et al. PRL 83, 3103 (1999)Polarization entanglement:generation

  • Kwiat et al. PRA 60, R773 (1999)White et al. PRL 83, 3103 (1999)Polarization entanglement:generation

  • Mixed statePure entangled stateMixed states and entangled states

  • Detection of entanglement: violation of the Bell inequality

  • Bell-CHSH inequalityBell inequality and Bell states

  • Bell states for the photon polarizationCoincidence rate for f+:Bell inequality and Bell states

  • Bell states for the photon polarizationBell inequality and Bell statesCoincidence rate for f+:

  • Maximal violation Bell inequality and Bell states

  • Maximal violation Bell inequality and Bell states

  • Maximal violation Bell inequality and Bell states

  • Violation of a Bell inequality

    Detects but does not quantify the entanglement properly - Some entangled states do not violate the Bell inequality Valid for dichotomic or dichotomized systems

    Bell inequality and entanglement

  • Take a set of measurements :Reconstruction of the density matrixQuantum state tomography

  • Quantum state tomography

  • Quantum state tomography

  • Quantum state tomographyWith r12 one can compute all quantities related to the system

  • Concurrency:Direct measurement of entanglement

  • Mintert, Kus, and Buchleitner, Phys. Rev. Lett. 95 260502 (2005).

    Direct measurement of entanglement using copies of states

  • Direct measurement of entanglement: pure statesPure stateTwo copiesMaximally entangled stateTwo copies

  • Experiment with entangled photons

  • Two copies of a state in a single photonPolarization state

  • Linear momentum stateTwo copies of a state in a single photon

  • Simultaneous entanglement in polarization and linear momentumTwo copies of a state in a single photon

  • Bell state projectionBell states combining momentum and polarization

  • C-NOT with a SAGNAC interferometer

  • Spatial rotations with cilyndrical lenses

  • Spatial rotations with cilyndrical lenses

  • Direct measurement of entangled with two copies

  • S. P. Walborn, P. H. Souto Ribeiro, L. Davidovich, F. Mintert, A. Buchleitner, Nature 440 1022 (2006)Direct measurement of entangled with two copies

  • S. P. Walborn, P. H. Souto Ribeiro, L. Davidovich, F. Mintert, A. Buchleitner, Nature 440 1022 (2006)Direct measurement of entangled with two copies

  • Part III

    -Entanglement dynamics

    -Kraus operators

    -Entanglement sudden death

    -Process tomography

    -Evolution of entanglement

  • Entanglement dynamicsT. Yu, J. H. Eberly, Phys. Rev. Lett. 93, 140404 (2004). T. Yu, J. H. Eberly, Phys. Rev. Lett. 97, 140403 (2006).

  • Amplitude decay channel Quantum channel and Kraus map

  • Operadores de Kraus para o canal de amplitudeQuantum channel and Kraus operators

  • Amplitude decay channel for one photon polarization

  • Amplitude decay channel for one photon polarization

  • Amplitude decay channel for one photon polarization

  • Amplitude decay channel for one photon polarization

  • Amplitude decay channel for one photon polarization

  • Amplitude decay channel for one photon polarization

  • Amplitude decay channel for one photon polarization

  • Amplitude decay channel for one photon polarization

  • Amplitude decay channel for one photon polarization

  • Amplitude decay channel for one photon polarization

  • Amplitude decay channel for one photon polarization

  • Amplitude decay channel for one photon polarization

  • Amplitude decay channel for one photon polarization

  • Amplitude decay channel for one photon polarization

  • Amplitude decay channel for one photon polarization

  • Amplitude decay channel for one photon polarization

  • Amplitude decay channel for one photon polarization

  • Amplitude decay channel for one photon polarization

  • Amplitude decay channel for one photon polarization

  • Amplitude decay channel for one photon polarization

  • Kwiat et al. PRA 60, R773 (1999)White et al. PRL 83, 3103 (1999)Polarization entangled state

  • M. P. Almeida et al., Science 316, 579 (2007)Experimental observation of theentanglement sudden death

  • M. P. Almeida et al., Science 316, 579 (2007)Experimental observation of theentanglement sudden death

  • Process tomography

  • Reconstruction of the Kraus operators

  • T. Konrad et al., Nature Physics 4, 99 (2008).A dynamical law for the entanglement

  • A dynamical law for the entanglement

  • A dynamical law for the entanglement

  • A dynamical law for the entanglement

  • A dynamical law for the entanglement

  • O. Farias et al., Science 324, 1414 (2009)A dynamical law for the entanglement

  • O. Farias et al., Science 324, 1414 (2009)A dynamical law for the entanglement:experimental test

  • A dynamical law for the entanglement:generalization for mixed statesT. Konrad et al., Nature Physics 4, 99 (2008).

  • A dynamical law for the entanglement:generalization for mixed states

  • A dynamical law for the entanglement:generalization for mixed states

  • A. Jamiokowski, Rep. Math. Phys. 3, 275 (1972)

    How to find $'A dynamical law for the entanglement:generalization for mixed states

  • O. Farias et al., Science 324, 1414 (2009)A dynamical law for the entanglement:generalization for mixed statesexperimental test

  • Part VI

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