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Bell tests with Photons

Bell tests with Photons. Henry Clausen. Photon Bell Tests. Bell‘s theorem Photon Bell Test by Aspect Loopholes Photon Bell Test by Weihs Outlook. EPR-Paradoxon. Bob. Alice. Collapse.

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Bell tests with Photons

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  1. Belltestswith Photons Henry Clausen

  2. Photon Bell Tests

  3. Bell‘s theorem • Photon Bell Test by Aspect • Loopholes • Photon Bell Test by Weihs • Outlook EPR-Paradoxon Bob Alice Collapse • Entanglement contradicts GR:Measurement I is influenced by an event (measurement II) outsideitsbackwardslightcone • Einstein also did not like the random character of QM • “Every complete theory must assign a value to every element at every physical reality” + + Emmission Image source: http://rqgravity.net/images/paradox/Paradox-7N.gif (18.05.2013)

  4. Bell‘s theorem • Photon Bell Test by Aspect • Loopholes • Photon Bell Test by Weihs • Outlook Local hidden variable theory • Considerations: • Quantum mechanicsmightbeincomplete • Unknown variables determineoutcomeofmeasurementspriortomeasurement • Norandomness • Locality • Forentangledphotons: • Whether+or - ismeasuredisdeterminedbeforethemeasurement

  5. Bell‘s theorem • Photon Bell Test by Aspect • Loopholes • Photon Bell Test by Weihs • Outlook Bell‘stheorem • “Quantum mechanics cannot arise from a theory of local pre-existing hidden variables” Necessary conditions on theory for Bell’s theorem: • Locality • Counterfactual definiteness

  6. Bell‘s theorem • Photon Bell Test by Aspect • Loopholes • Photon Bell Test by Weihs • Outlook Locality • No influence of events outside the backwards light cone Counterfactual definiteness • A property is assigned to a system at all times independently of whether the measurement is carried out

  7. Bell‘s theorem • Photon Bell Test by Aspect • Loopholes • Photon Bell Test by Weihs • Outlook Correlation • Hidden parameter Observed variables • Like polarizationofphotons Expectationvalue: isprobabilitymeasureCorrelation:

  8. Bell‘s theorem • Photon Bell Test by Aspect • Loopholes • Photon Bell Test by Weihs • Outlook Correlation • Correlation: measurement rate Image source: http://en.wikipedia.org/wiki/File:Bell%27s_theorem.svg (18.05.2013)

  9. Bell‘s theorem • Photon Bell Test by Aspect • Loopholes • Photon Bell Test by Weihs • Outlook Correlation • measured with different detector settings  Image source: http://en.wikipedia.org/wiki/File:Bell%27s_theorem.svg (18.05.2013)

  10. Bell‘s theorem • Photon Bell Test by Aspect • Loopholes • Photon Bell Test by Weihs • Outlook CHSH inequality • measured with different detector settings Image source: http://en.wikipedia.org/wiki/File:Bell%27s_theorem.svg (18.05.2013)

  11. Bell‘s theorem • Photon Bell Test by Aspect • Loopholes • Photon Bell Test by Weihs • Outlook CHSH inequality • measured with different detector settings

  12. Bell‘s theorem • Photon Bell Test by Aspect • Loopholes • Photon Bell Test by Weihs • Outlook But… • For entangled photons:

  13. Bell‘s theorem • Photon Bell Test by Aspect • Loopholes • Photon Bell Test by Weihs • Outlook Bell Test by Alain Aspect, 1981 • Paper:Experimental Realization of Einstein-Podolsky-Rosen-BohmGedankenexperiment: A New Violation of Bell's Inequalities • A. Aspect, P. Grangier, G. Roger • Phys. Rev. Lett. 49, 2 (1982) Image source: http://phototheque.institutoptique.fr/picture.php?/7212 (18.05.2013)

  14. Bell‘s theorem • Photon Bell Test by Aspect • Loopholes • Photon Bell Test by Weihs • Outlook Bell Test by Alain Aspect, 1981 • Donein Paris • First experimenttomeasurethe Bell inequalitydirectly • Prior only single-channel-analyzerexperiments Image source: http://phototheque.institutoptique.fr/picture.php?/7212 (18.05.2013)

  15. Bell‘s theorem • Photon Bell Test by Aspect • Loopholes • Photon Bell Test by Weihs • Outlook Setup WL-filter WL-filter Single rate monitor Single ratemonitor Image source: http://en.wikipedia.org/wiki/File:Bell-test-photon-analyer.png (18.05.2013)

  16. Bell‘s theorem • Photon Bell Test by Aspect • Loopholes • Photon Bell Test by Weihs • Outlook Photon Source • Calcium-40 cascade is exited by two photon absorption  Pairs of photons are emitted • Wavelengths • Emission rate:

  17. Bell‘s theorem • Photon Bell Test by Aspect • Loopholes • Photon Bell Test by Weihs • Outlook Polarizers • Two prisms separated by thinfilm • Parallel polarized light transmitted • Orthogonal polarized lightreflected • Rotatable Image source: http://www.meadowlark.com/images/products_large/laserline_beamsplitting_polarizer_fig1_17_2_13895.gif (18.05.2013)

  18. Bell‘s theorem • Photon Bell Test by Aspect • Loopholes • Photon Bell Test by Weihs • Outlook Polarizers for for Image source: http://www.meadowlark.com/images/products_large/laserline_beamsplitting_polarizer_fig1_17_2_13895.gif (18.05.2013)

  19. Bell‘s theorem • Photon Bell Test by Aspect • Loopholes • Photon Bell Test by Weihs • Outlook Advantage of two-channel polarizers • A one-channel polarizer always blocks one polarization (-) • Coincidence rates and cannot be measured directly • Measurement of not direct  No sufficient violation Image source: http://en.wikipedia.org/wiki/File:Single-channel_Bell_test.svg (18.05.2013)

  20. Bell‘s theorem • Photon Bell Test by Aspect • Loopholes • Photon Bell Test by Weihs • Outlook Detection • One Photomultiplier for each channel (4 in total) • Photon-coincidence and single-photon-detection are both measured and stored • Single-photon detection rate • Dark rate

  21. Bell‘s theorem • Photon Bell Test by Aspect • Loopholes • Photon Bell Test by Weihs • Outlook Setup WL-filter WL-filter Single monitor Single monitor Image source: http://en.wikipedia.org/wiki/File:Bell-test-photon-analyer.png (18.05.2013)

  22. Bell‘s theorem • Photon Bell Test by Aspect • Loopholes • Photon Bell Test by Weihs • Outlook Detection • Coincidence window • Lifetimeofexitedstate All photonpairsincluded • Fromsingle-photon rate theaccidentalcoincidencesareestimated to be  Substractedfrom total coincidences • True coincidence rate

  23. Bell‘s theorem • Photon Bell Test by Aspect • Loopholes • Photon Bell Test by Weihs • Outlook Result • Five runs at • Correction: Image source: [2]

  24. Bell‘s theorem • Photon Bell Test by Aspect • Loopholes • Photon Bell Test by Weihs • Outlook Result • Overall correctionsanderrors: • Accidentalcoincidences • Poissondeviation • Visibility (Not perfecttransmission & reflection) • Asymetryofdetectors Image source: [2]

  25. Bell‘s theorem • Photon Bell Test by Aspect • Loopholes • Photon Bell Test by Weihs • Outlook DetectionLoophole • Not everyphoton pair was measured • Emission rate: • Coincidence rate: • Corrected Bell ineq: • Possibleviolation in a test:

  26. Bell‘s theorem • Photon Bell Test by Aspect • Loopholes • Photon Bell Test by Weihs • Outlook LocalityLoophole • Nocommunicationbetweenmeasurementsassumed • Even ifseparationspacelike: Communication after changingthe angle possible • Measurement basis (angle) hastobechanged after photonemission

  27. Bell‘s theorem • Photon Bell Test by Aspect • Loopholes • Photon Bell Test by Weihs • Outlook Bell Test by Gregor Weihs, 1998 • Paper:Violation of Bell’s Inequality under Strict Einstein Locality Conditions • G. Weihs, T. Jennewein, C. Simon, H. Weinfurter, and A. Zeilinger • Phys. Rev. Lett. 81, 23 (1998) Image source: [3]

  28. Bell‘s theorem • Photon Bell Test by Aspect • Loopholes • Photon Bell Test by Weihs • Outlook Bell Test by Gregor Weihs, 1998 • Spacelikeseparationofmeasurements • Random numbergeneratortodeterminemeasurementbasis • Doneduringphotonflight • First time LocalityLoophole was closed Image source: [3]

  29. Bell‘s theorem • Photon Bell Test by Aspect • Loopholes • Photon Bell Test by Weihs • Outlook Setup Aspect WL-filter WL-filter Image source: http://en.wikipedia.org/wiki/File:Bell-test-photon-analyer.png (18.05.2013)

  30. Bell‘s theorem • Photon Bell Test by Aspect • Loopholes • Photon Bell Test by Weihs • Outlook Setup Weihs Laser Modulator Modulator 400 m Random-number-generators Image source: http://en.wikipedia.org/wiki/File:Bell-test-photon-analyer.png (18.05.2013)

  31. Bell‘s theorem • Photon Bell Test by Aspect • Loopholes • Photon Bell Test by Weihs • Outlook Fibers • Single modeopticalfibers • Depolarization • Eachcablelong (coiledup) • Differencelessthan () Image source: S. Johnson, Quantum Electronics FS2013 Summary of lecture notes, (30.07.2013)

  32. Bell‘s theorem • Photon Bell Test by Aspect • Loopholes • Photon Bell Test by Weihs • Outlook Rotation • Rotation of the polarized light, not the polarizers • Done by electro-optic modulator Voltage controlled optic axis • If voltage applied, polarization rotates by • Voltage controlled by RNG Image source: S. Johnson, Quantum Electronics FS2013 Summary of lecture notes, (30.07.2013)

  33. Bell‘s theorem • Photon Bell Test by Aspect • Loopholes • Photon Bell Test by Weihs • Outlook Rotation • Toggle frequency • Eachsettingisstoredwith time-tag • Atomicclock at eachpolarizerforsynchronization • Accuracy: Image source: S. Johnson, Quantum Electronics FS2013 Summary of lecture notes, (30.07.2013)

  34. Bell‘s theorem • Photon Bell Test by Aspect • Loopholes • Photon Bell Test by Weihs • Outlook Locality of measurement • Measurement delays: • RNG + Amplifier • Electro-optic modulator • Photomultiplier • Sample storing • fiber length difference • Total • Separation of measurement stations:

  35. Bell‘s theorem • Photon Bell Test by Aspect • Loopholes • Photon Bell Test by Weihs • Outlook Locality of measurement • Measurement delays: • RNG + Amplifier • Electro-optic modulator • Photomultiplier • Sample storing • fiber length difference • Total • Time betweenentanglementandmeasurement:

  36. Bell‘s theorem • Photon Bell Test by Aspect • Loopholes • Photon Bell Test by Weihs • Outlook Result • Visibility • Measuredvalue: • Measurement 10 s long, 14700 coincidencescollected • Efficiency  Still detection loophole

  37. Bell‘s theorem • Photon Bell Test by Aspect • Loopholes • Photon Bell Test by Weihs • Outlook Outlook • Detection loophole for photons closed 2013 by Zeilinger group • Used Eberhard inequality, not CHSH • Only required • Not maximallyentangledphotons • Superconducting TES-calorimeter • Arm efficiency: Image source: http://phonon.gsfc.nasa.gov/qcal/qcal_f4.html (18.05.2013)

  38. Bell‘s theorem • Photon Bell Test by Aspect • Loopholes • Photon Bell Test by Weihs • Outlook Outlook

  39. Sources

  40. Bell‘s theorem • Photon Bell Test by Aspect • Loopholes • Photon Bell Test by Weihs • Outlook Source • Argon ionlaser • Parametric down conversionwith BBO-crystal • Entangled photon pairs Image source: http://en.wikipedia.org/wiki/File:Scheme_of_spontaneous_parametric_down-conversion.pdf (18.05.2013)

  41. Bell‘s theorem • Photon Bell Test by Aspect • Loopholes • Photon Bell Test by Weihs • Outlook RNG Diode • Diode emits light onto beam splitter • One photomultiplier correspondsto “0”, one to “1” • Toggle frequency () • “0” and “1” not necessarily equally often • Stored in coincidence monitor 1 BS PM PM 0

  42. Bell‘s theorem • Photon Bell Test by Aspect • Loopholes • Photon Bell Test by Weihs • Outlook Detection • Rotation switched many time between two coincidences Very high resolved time tags () and synchronization required • Atomic clock at each stationSynchronized before measurement  Coincidences + polarization setting can be identified without confusion

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