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## Experiments With Entangled Photons

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**Experiments With Entangled Photons**Paulo Henrique Souto Ribeiro Instituto de Física - UFRJ Summer School of Optics Concépcion January/2010**Group members**Experiments: Prof. Paulo Henrique Souto Ribeiro Prof. Stephen Patrick Walborn Theory: Prof. Luiz Davidovich Prof. Nicim Zagury Prof. Ruynet Matos Filho Prof. Fabricio Toscano Msc and PhD students: Adriana Auyuanet Larrieu, Adriano H. de Oliveira Aragão, Bruno de Moura Escher , Bruno Taketani, Daniel Schneider Tasca, Gabriel Horacio Aguilar, Osvaldo Jimenez farias, Gabriela Barreto Lemos, Rafael Chaves.**UFAL**UFMG UFF UFRJ USP-SÃO PAULO**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-conversion**Espontaneous emission Twin Photons Stimulated emission**Parametric down-conversion: quantum state**Time evolution Time evolution operator Time integral**Simultaneity in parametric down-conversion**Quantum state for weak interaction**Simultaneity in parametric down-conversion**Quantum state including some approximations**Simultaneity in parametric down-conversion**Calculation of expectation values Electric field operator Intensity Coincidence**Simultaneity in parametric down-conversion:**very simple view**Simultaneity in parametric down-conversion:**very simple view Quantum state: simple version Electric field operator: plane wave, almost monochromatic Coincidence**Simultaneity in parametric down-conversion:**very simple view Plane wave pumping field**Measurement of time delays**s=168ps s=185ps**Simultaneity in parametric down-conversion:**very simple view + detection filters Plane wave pumping field**Simultaneity in parametric down-conversion:**very simple view + detection filters Interference filter: typical Dl = 10nm, Dw = 3.8 x 1013 Hz, Dt = 82 fs << 100ps**Simultaneity in parametric down-conversion:**very simple view + timing resolution**Hong, Ou and Mandel Interferometer:**single mode approach Beam splitter Input-output relations**Hong, Ou and Mandel Interferometer:**single mode approach Two-photon input state Beam splitter Coincidence probability**Part II**- Polarization entanglement - Bell’s inequalities - Entanglement measurement**Polarization entanglement:**generation Kwiat et al. PRL 75, 4337 (1995)**Polarization entanglement:**generation 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)**Mixed states and entangled states**Mixed state Pure entangled state**Bell inequality and Bell states**Bell-CHSH inequality**Bell inequality and Bell states**Bell states for the photon polarization Coincidence rate for f+:**Bell inequality and Bell states**Bell states for the photon polarization Coincidence rate for f+:**Bell inequality and Bell states**Maximal violation**Bell inequality and Bell states**Maximal violation**Bell inequality and Bell states**Maximal violation**Bell inequality and entanglement**• 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**Quantum state tomography**Take a set of measurements : Reconstruction of the density matrix**Quantum state tomography**With r12 one can compute all quantities related to the system**Direct measurement of entanglement**Concurrency: