Bell tests with Photons Henry Clausen. Outline: Bell‘s theorem Photon Bell Test by Aspect Loopholes Photon Bell Test by Weihs Outlook Photon

Bell tests with Photons

Henry Clausen

Outline:

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”


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


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


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


Correlation

Hidden parameter Observed variables • Like polarization of photons

Expectation value: is probability measure

Correlation:


Correlation

Correlation: measurement rate


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



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




CHSH inequality



But…

For entangled photons:


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)


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


Image source: http://phototheque.institutoptique.fr/picture.php?/7212 (18.05.2013)

Setup


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:


Polarizers

Two prisms separated by thinfilm

• Parallel polarized light transmitted

• Orthogonal polarized light reflected

Rotatable


Image source: http://www.meadowlark.com/images/products_large/laserline_beamsplitting_polarizer_fig1_17_2_13895.gif (18.05.2013)

Polarizers

for

for


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


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


Setup



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


Result

Five runs at

Correction:


Image source: [2]

Result

Overall corrections and errors:• Accidental coincidences• Poisson deviation

• Visibility (Not perfect transmission & reflection)• Asymetry of detectors


Image source: [2]

Detection Loophole

Not every photon pair was measured• Emission rate: • Coincidence rate:

Corrected Bell ineq:

Possible violation in a test:


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 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]

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


Image source: [3]

Setup Aspect

WL-filter WL-filter



Setup Weihs

400 m

Random-number-generators

Laser

Modulator Modulator



Fibers

Single mode optical fibers

Depolarization

Each cable long ( coiled up)

Difference less than ()


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



Rotation Toggle frequency

Each setting is stored with time-tag

Atomic clock at each polarizer forsynchronization • Accuracy:



Locality of measurement

Measurement delays:• RNG + Amplifier • Electro-optic modulator• Photomultiplier• Sample storing• fiber length difference

Total

Separation of measurement stations:


Locality of measurement

Measurement delays:• RNG + Amplifier • Electro-optic modulator• Photomultiplier• Sample storing• fiber length difference

Total

Time between entanglement and measurement:


Result

Visibility

Measured value:

Measurement 10 s long, 14700 coincidences collected

Efficiency Still detection loophole


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:


Image source: http://phonon.gsfc.nasa.gov/qcal/qcal_f4.html (18.05.2013)

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


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


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


Documents

Bell tests with Photons Henry Clausen. Outline: Bell‘s theorem Photon Bell Test by Aspect Loopholes Photon Bell Test by Weihs Outlook Photon