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Bell‘s theorem Photon Bell Test by Aspect Loopholes Photon Bell Test by Weihs Outlook
Photon Bell Tests
EPR-Paradoxon
Entanglement contradicts GR:
Measurement I is influenced by an event (measurement II) outside its backwards lightcone
Einstein also did not like the random character of QM• “Every complete theory must assign a value to
every element at every physical reality”
Bell‘s theorem Photon Bell Test by Aspect Loopholes Photon Bell Test by Weihs Outlook
Image source: http://rqgravity.net/images/paradox/Paradox-7N.gif (18.05.2013)
Emmission
Collapse Bob
+ +
Alice
Considerations:
• Quantum mechanics might be incomplete
• Unknown variables determine outcome of measurements prior to measurement- No randomness- Locality
For entangled photons:• Whether + or - is measured is determined before the
measurement
Bell‘s theorem Photon Bell Test by Aspect Loopholes Photon Bell Test by Weihs Outlook
Local hidden variable theory
Bell‘s theorem
“Quantum mechanics cannot arise from a theory of local pre-existing hidden variables”
Necessary conditions on theory for Bell’s theorem:
Locality Counterfactual definiteness
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
Bell‘s theorem Photon Bell Test by Aspect Loopholes Photon Bell Test by Weihs Outlook
Correlation
Hidden parameter Observed variables • Like polarization of photons
Expectation value: is probability measure
Correlation:
Bell‘s theorem Photon Bell Test by Aspect Loopholes Photon Bell Test by Weihs Outlook
Correlation
Correlation: measurement rate
Bell‘s theorem Photon Bell Test by Aspect Loopholes Photon Bell Test by Weihs Outlook
Image source: http://en.wikipedia.org/wiki/File:Bell%27s_theorem.svg (18.05.2013)
Parallel Pair 1 Pair 2 Pair 3 Pair 4 …
Alice + - + +
Bob + - + +
Correlation +1 +1 +1 +1 +1
Antiparallel Pair 1 Pair 2 Pair 3 Pair 4 …
Alice + - + +
Bob - + - -
Correlation -1 -1 -1 -1 -1
Correlation
Bell‘s theorem Photon Bell Test by Aspect Loopholes Photon Bell Test by Weihs Outlook
Image source: http://en.wikipedia.org/wiki/File:Bell%27s_theorem.svg (18.05.2013)
Orthogonal Pair 1
Pair 2 Pair 3 Pair 4 Pair 5 …
Alice + - - + +
Bob + + - + -
Correlation +1 -1 +1 +1 -1 0
measured with different detector settings
CHSH inequality
measured with different detector settings
Bell‘s theorem Photon Bell Test by Aspect Loopholes Photon Bell Test by Weihs Outlook
Image source: http://en.wikipedia.org/wiki/File:Bell%27s_theorem.svg (18.05.2013)
CHSH inequality
measured with different detector settings
Bell‘s theorem Photon Bell Test by Aspect Loopholes Photon Bell Test by Weihs Outlook
But…
For entangled photons:
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-Bohm Gedankenexperiment: A New Violation of Bell's Inequalities
A. Aspect, P. Grangier, G. Roger
Phys. Rev. Lett. 49, 2 (1982)
Bell‘s theorem Photon Bell Test by Aspect Loopholes Photon Bell Test by Weihs Outlook
Image source: http://phototheque.institutoptique.fr/picture.php?/7212 (18.05.2013)
Bell Test by Alain Aspect, 1981
Done in Paris
First experiment to measure the Bell inequality directly
Prior only single-channel-analyzer experiments
Bell‘s theorem Photon Bell Test by Aspect Loopholes Photon Bell Test by Weihs Outlook
Image source: http://phototheque.institutoptique.fr/picture.php?/7212 (18.05.2013)
Setup
Bell‘s theorem Photon Bell Test by Aspect Loopholes Photon Bell Test by Weihs Outlook
Image source: http://en.wikipedia.org/wiki/File:Bell-test-photon-analyer.png (18.05.2013)
WL-filter WL-filter
Single ratemonitor
Single rate monitor
Photon Source
Calcium-40 cascade is exited by two photon absorption
Pairs of photons are emitted
Wavelengths
Emission rate:
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 light reflected
Rotatable
Bell‘s theorem Photon Bell Test by Aspect Loopholes Photon Bell Test by Weihs Outlook
Image source: http://www.meadowlark.com/images/products_large/laserline_beamsplitting_polarizer_fig1_17_2_13895.gif (18.05.2013)
Polarizers
for
for
Bell‘s theorem Photon Bell Test by Aspect Loopholes Photon Bell Test by Weihs Outlook
Image source: http://www.meadowlark.com/images/products_large/laserline_beamsplitting_polarizer_fig1_17_2_13895.gif (18.05.2013)
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
Bell‘s theorem Photon Bell Test by Aspect Loopholes Photon Bell Test by Weihs Outlook
Image source: http://en.wikipedia.org/wiki/File:Single-channel_Bell_test.svg (18.05.2013)
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
Bell‘s theorem Photon Bell Test by Aspect Loopholes Photon Bell Test by Weihs Outlook
Setup
Bell‘s theorem Photon Bell Test by Aspect Loopholes Photon Bell Test by Weihs Outlook
Image source: http://en.wikipedia.org/wiki/File:Bell-test-photon-analyer.png (18.05.2013)
WL-filter WL-filter
Single monitor
Single monitor
Detection
Coincidence window
Lifetime of exited state All photon pairs included
From single-photon rate the accidental coincidences are estimated to be
Substracted from total coincidences
True coincidence rate
R++ R-+ R+- R--0
10203040506070
ρ(45°,22,5°)
CoincidenceAccidential Coincidence
Bell‘s theorem Photon Bell Test by Aspect Loopholes Photon Bell Test by Weihs Outlook
Result
Five runs at
Correction:
Bell‘s theorem Photon Bell Test by Aspect Loopholes Photon Bell Test by Weihs Outlook
Image source: [2]
Result
Overall corrections and errors:• Accidental coincidences• Poisson deviation
• Visibility (Not perfect transmission & reflection)• Asymetry of detectors
Bell‘s theorem Photon Bell Test by Aspect Loopholes Photon Bell Test by Weihs Outlook
Image source: [2]
Detection Loophole
Not every photon pair was measured• Emission rate: • Coincidence rate:
Corrected Bell ineq:
Possible violation in a test:
Bell‘s theorem Photon Bell Test by Aspect Loopholes Photon Bell Test by Weihs Outlook
Locality Loophole
No communication between measurements assumed
Even if separation spacelike:
Communication after changing the angle possible
Measurement basis (angle) has to be changed after photon emission
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)
Bell‘s theorem Photon Bell Test by Aspect Loopholes Photon Bell Test by Weihs Outlook
Image source: [3]
Bell Test by Gregor Weihs, 1998
Spacelike separation ofmeasurements
Random number generator todetermine measurement basis
Done during photon flight
First time Locality Loophole was closed
Bell‘s theorem Photon Bell Test by Aspect Loopholes Photon Bell Test by Weihs Outlook
Image source: [3]
Setup Aspect
WL-filter WL-filter
Bell‘s theorem Photon Bell Test by Aspect Loopholes Photon Bell Test by Weihs Outlook
Image source: http://en.wikipedia.org/wiki/File:Bell-test-photon-analyer.png (18.05.2013)
Setup Weihs
400 m
Random-number-generators
Laser
Modulator Modulator
Bell‘s theorem Photon Bell Test by Aspect Loopholes Photon Bell Test by Weihs Outlook
Image source: http://en.wikipedia.org/wiki/File:Bell-test-photon-analyer.png (18.05.2013)
Fibers
Single mode optical fibers
Depolarization
Each cable long ( coiled up)
Difference less than ()
Bell‘s theorem Photon Bell Test by Aspect Loopholes Photon Bell Test by Weihs Outlook
Image source: S. Johnson, Quantum Electronics FS2013 Summary of lecture notes, (30.07.2013)
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
Bell‘s theorem Photon Bell Test by Aspect Loopholes Photon Bell Test by Weihs Outlook
Image source: S. Johnson, Quantum Electronics FS2013 Summary of lecture notes, (30.07.2013)
Rotation Toggle frequency
Each setting is stored with time-tag
Atomic clock at each polarizer forsynchronization • Accuracy:
Bell‘s theorem Photon Bell Test by Aspect Loopholes Photon Bell Test by Weihs Outlook
Image source: S. Johnson, Quantum Electronics FS2013 Summary of lecture notes, (30.07.2013)
Locality of measurement
Measurement delays:• RNG + Amplifier • Electro-optic modulator• Photomultiplier• Sample storing• fiber length difference
Total
Separation of measurement stations:
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 between entanglement and measurement:
Bell‘s theorem Photon Bell Test by Aspect Loopholes Photon Bell Test by Weihs Outlook
Result
Visibility
Measured value:
Measurement 10 s long, 14700 coincidences collected
Efficiency Still detection loophole
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 maximally entangled photons
Superconducting TES-calorimeter • Arm efficiency:
Bell‘s theorem Photon Bell Test by Aspect Loopholes Photon Bell Test by Weihs Outlook
Image source: http://phonon.gsfc.nasa.gov/qcal/qcal_f4.html (18.05.2013)
Outlook
Bell‘s theorem Photon Bell Test by Aspect Loopholes Photon Bell Test by Weihs Outlook
1970 1975 1980 1985 1990 1995 2000 2005 2010 010
Matsukevich & Moehring
Bell test with two remote atomic qubits
Weihs‘ Bell test
Locality loophole closed
Freedman & Clauser
First Bell test
Aspect’s Bell Test Wineland et
al.
First time detection loophole closed with ions
Ansmann et. al.
Detection loophole closed with Josephson Qubits
Zeilinger’s test
Detection loophole closed for photons
Sources
[1] L. Maccone, A simple proof of Bell’s inequality, arXiv:1212.5214v2 (2013) [quant-ph]
[2] A. Aspect, P. Grangier, G. Roger, Experimental Realization of Einstein-Podolsky-Rosen-Bohm Gedankenexperiment: A New Violation of Bell's Inequalities, Phys. Rev. Lett. 49, 2 (1982)
[3] G. Weihs, T. Jennewein, C. Simon, H. Weinfurter, and A. Zeilinger, Violation of Bell’s Inequality under Strict Einstein Locality Conditions, Phys. Rev. Lett. 81, 23 (1998)
[4] D. N. Matsukevich, P. Maunz, D. L. Moehring, S. Olmschenk, C. Monroe, Bell Inequality Violation with Two Remote Atomic Qubits, Phys. Rev. Lett. 100, 150404
[5] M. Giustina, A. Mech, S. Ramelow, B. Wittmann, J. Kofler, J. Beyer, A. Lita, B. Calkins, T. Gerrits, S.W. Nam, R. Ursin. A. Zeilinger, Bell violation with entangled photons, free of fair-sampling assumption, arXiv:1212.0533 [quant-ph] (2013)
[6] Wikipedia Foundation, Bell’s theorem, http://en.wikipedia.org/wiki/Bell_inequalities (18.05.2013)
Source Argon ion laser
Parametric down conversionwith BBO-crystal
Entangled photon pairs
Bell‘s theorem Photon Bell Test by Aspect Loopholes Photon Bell Test by Weihs Outlook
Image source: http://en.wikipedia.org/wiki/File:Scheme_of_spontaneous_parametric_down-conversion.pdf (18.05.2013)
RNG 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
Bell‘s theorem Photon Bell Test by Aspect Loopholes Photon Bell Test by Weihs Outlook
Diode
PM
0
1BS
PM
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
Bell‘s theorem Photon Bell Test by Aspect Loopholes Photon Bell Test by Weihs Outlook