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Quantum Non-Locality, Entanglement, Bell Testsand Foundations of Quantum Mechanics
Solvay Workshop on Bits, Quanta, and Complex Systems
Thomas Walther, TU Darmstadt
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5th Solvay Conference 1927
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Einstein-Podolsky-Rosen Paradox (1935)
Gedankenexperiment: Separated pairs of entangled state
Conclusions:
● Incompleteness of description
● Non-locality – Action-at-a-distance
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1964 - Bell's results
● Context of EPR Experiment
● Existence proof of Hidden-Variable Theories (LHVT)
● Local
● Completion of Quantum Mechanics
● Results:
● Statistical prediction of any LHVT fulfill an inequality● Statistical prediction of QM can violate the inequality
J.S. Bell, Physics 1, 195 (1964)
Experiment in principle feasible
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Principle of Experimental Tests
Preparation
CorrelationMagicBox
Manipulation
1
2
Separation
Alice
Bob
Measurement
Â
Â
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Requirements for Tests
● Measurement of Correlations
– Spatial Correlation
– Detection Efficiency
● Locality Condition
– Fast and random switching
● Various Forms of Bell Inequalities
– CHSH - Clauser Horne Shimony Holt
– BCH - Bell Clauser Horne
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Atomic Cascade
Cascade decay
● 1972 J.F. Clauser et al.
● 1976 E.S. Fry et al.
● 1982 A. Aspect et al.
Loopholes:
● Spatial Correlation
● Detection Efficiency
● Locality
Fry et al.
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The 80s – Switching
Analyser 1 Analyser 2
Polarizer #2b
AOM Polarizer #2a
Cascade decay
Source
A. Aspect et al, Phys. Rev. Lett. 49, 1804 (1982)
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P.G. Kwiat
SPDC: Source of Entangled Photons
UV Laser
Non-linearcrystal
Signal
Idler
χ (2)
Z.Y. Ou and L. Mandel, PRL 61 (1988) p. 50J. G. Rarity and P.R. Tapster, PRL 64 (1990) p. 2495 P.G. Kwiat, K. Mattle, H. Weinfurter, A. Zeilinger, A.V. Sergienko, and Y. Shih, PRL 75, (1995) 4337
Verticalpolarization
Horizontalpolarization
Entangled photons (polarization)
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SPDC experiments on EPR paradox
● 1986 Y. Shih and Alley● 1988 Z.Y. Ou and L. Mandel● 1995 P. Kwiat et al.● 1998 N. Gisin et al.● 1998 A. Zeilinger et al.
G. Weihs, T. Jennewein, C. Simon, H. Weinfurter, A. Zeilinger,Phys. Rev. Lett. 81, 5039 (1998)
Zeilinger et al.
Loophole : Detection Efficiency
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Locality Loophole
Randomnumber
generator
G. Weihs, T. Jennewein, C. Simon, H. Weinfurter, A. Zeilinger, PRL 81, 5039 (1998)
random switching by photons illuminating a beam splitter
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Random Number Generator
Th. Jennewein et al., Rev. Sci. Instr. 71 (2000)
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Decay of the Correlations?
coincidence
Laser diode
KNbO3
J.D. Franson, PRL 62, 2205, (1989)W. Tittel, J. Brendek, B. Gisin, T. Herzog, H. Zbinden and N. Gisin, PRL 81, 3563 (1998)
> 10 km
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Quantum correlations over long distance
W. Tittel, J. Brendek, B. Gisin, T. Herzog, H. Zbinden and N. Gisin, PRL 81, 3563 (1998)
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S = 2,7234±0,0032
EPR Experiment and Education
P.G. Kwiat et al. Phys. Rev. A 60, R773 (1999)D. Dehlinger, M.W. Mitchell, Am. J. of Phys. 70, 898 (2002), ibid. 903
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Detection Efficiency Loophole
● Be+-ions in a trap● Detection by resonance fluorescence● High efficiency● But: no enforcement of locality condition
M.A Rowe et al.; Nature, 409 (2001) p. 791
∣=12
{∣1 ∣2 ∣1 ∣ 2 }
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Entanglement of Be+ Ions
● 2001 D. Wineland et al.
M.A. Rowe, D. Kielpinski, V. Meyer, C.A. Sackett, W.M. Itano, C. Monroe, D.J. Wineland; Nature 409, 791 (2001)
Loopholes:
● Locality
● Alice-Bob Identity Crisis (Ian Percival)
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Heralded Entanglement of Yb+
D. N. Matsukevich, arXiv 0801-2184, (2008)
● Loopholes: Locality
● Fidelity?
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Previous Experiments on EPR Paradox
Cascade decay
● 1972 J.F. Clauser et al.
● 1976 E.S. Fry et al.
● 1980 A. Aspect et al.
● 1986 Y. Shih and Alley
● 1995 P. Kwiat et al.
● 1998 N. Gisin et al.
● 1998 A. Zeilinger et al.
● 2001 D. Wineland et al.
● 2008 C. Monroe et al.
Simulta
neous enforcement of a
ll loopholes m
issing
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Challenges
● Entanglement– Generation– Manipulation– Lifetime
● What is random?● How fast is Quantum Information?
– Spooky-Action-At-A-Distance– Non-Locality?
● When is a measurement a measurement?– APD vs. Many-World
● Simultaneous Closing of All Loopholes– Locality– Detection
● Test of Bell-Clauser Horne Inequality
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Entanglement
● Photon-Photon● Cascade: Clauser, Fry, Aspect● SPDC: Gisin, Kwiat, Mandel, Shih, Zeilinger, ...
● Atom-Atom● Micromaser: E. Hagley et al., Phys. Rev. Lett. 79, 1 (1997)
● Ion-Ion● M.A. Rowe et al., Nature 409, 791 (2001)● C.F. Roos et al., Phys. Rev. Lett. 92, 220402 (2004)● D. N. Matsukevich, arXiv 0801-2184, (2008)
● Ion-Photon● B.B. Blinov et al., Nature 428, 153 (2004)
● Single-Atom Single Photon● T. Wilk et al., Science 317, 488 (2007).
● Polarization Entanglement Transfer● Atomic Ensemble Entanglement
● J. Laurat et al., Phys. Rev. Lett. 99, 180504 (2007)
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Talk by Nicolas Gisin
How fast is Quantum Information? When is a measurement a measurement?
D. Salart et al., arXiv/0803.2425
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Bell-Clauser-Horne Inequality (BCH)
S 1 ,2 ,1' ,2
'=R 1 ,2−R 1 ,2
'R 1
' ,2R 1' ,2
'
R1 1R22'
≤1
● Ratio of coincidence rates to singles rates!
● No further restrictions
● Not yet tested
● Experimental requirements extremely challenging
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Quantum mechanical expectation value
S 1 ,2 ,1' ,2
'=R 1 ,2−R 1 ,2
'R 1
' ,2R 1' ,2
'
R1 1R22'
≤1
Bell-Clauser-Horne Inequality:
SQM 135o ,0o ,225o ,90o=
12 g [12F −
2
]1.207 Detection efficiency
Spatial correlation
Measure of discrimination
Measure of purity
Quantum Mechanical Expectation Value:
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Entanglement by Photodissociation
Measurement of correlationsbetween components of
nuclear spin
199Hg2
E.S. Fry, ThW, S. Li; Phys. Rev. A 52 (1995) p. 4381E.S. Fry, ThW; Adv. At. Mol. Opt. Phys. 42 (2000) p. 1
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Photodissociation of 199Hg2
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Entangled States
∣S =12
∣ 1∣ 2−∣ 1∣ 2Singlet:
Triplet:∣T =
12
∣ 1∣2∣ 1∣ 2
∣T =12
∣ 1∣ 2±∣ 1∣ 2
Molecule ∣=∣e∣v∣ r∣N
Pauli-principle: Anti-symmetric wave function with respect to exchange of particles
1 g
Ground state even
Vibration of a diatomic molecule: even
J=0,2,4,6,... evenJ=1,3,5,7,... odd
Singlet: oddPhoto dissociation of rotational level with J=0,2,4,...
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Dimer dissociatingLaser beam: 355 nm
Dimer excitationLaser beam: 266 nm
Hg2 (Dimer)
Z
X
Y
Experimental Setup – Step I
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Ionizing laserbeam: 197.3 nm
Ionizing laserbeam: 197.3 nm
Analyzing laserbeam: 253.7 nm
Analyzing laserbeam: 253.7 nm
Detection Planes
Z
X
Y
2
1
HgAtom
HgAtom
2
1
Experimental Setup
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Spin analysis
Ionization limit
Level 2
Level 1
Level 3 F=1/2
F=3/2
F=1/2
F=1/2
(6p2) 3P0
(6s6p) 63P1
o
(6s2) 61S0
-3/2 -1/2 1/2 3/2
22 GHz
Ionization laser (197.3 nm)
Analysis laser (253.7 nm) -
Selection rule: -- polarized light : △m = -1
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Spatial correlation (Monte-Carlo Simulations)
E.S. Fry, ThW, S. Li; Phys. Rev. A 52, 4381 (1995)E.S. Fry, ThW; in 'Quantum (Un)speakables', Bertlmann, Zeilinger (eds.); (Springer 2002)
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Trapping of Neutral Mercury
3 D3
125 ns3P1
6.67 s3P
2
5.56 s3P
0
1S0
3S1
Tdoppler
= 30K
253.7 nm
365.0 nm546.0 nm
435.8 nm
404.0 nm
● Results:
● Densities >1011 cm-3
● Trap center of r = 300 m
● > 106 atoms
● Assumptions
● Basis molecular gas flow dynamics codeG.A. Bird, Molecular Gas Dynamics and the Direct Simulation of Gas Flows, (Oxford Science Publications, Oxford, 1998)
● Magnetic fields gradients 6-10 G/cm
● 6 lasers @ 253.7 nm, 0=5mm, I
0 = 2 I
sat
Monte-Carlo Simulations
ThW, J. of Mod. Opt. 54, 2523 (2007).
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Mercury Isotopes
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Source for 253.7 nm radiation
• FHG of 1014.8-nm Yb Disc-Laser
• > 100 mW of 253.7 nm-light
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Vibrational Cooling
ThW, in ''Interactions in Ultracold Gases: From Atoms to Molecules'', Weidemüller, Zimmermann (eds.), Wiley-VCH, 2003ThW, J. of Mod. Opt. 54, 2523-2532 (2007).
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Summary I: Quantum Mechanics
● Wave-Particle Duality– Hanbury-Brown Twiss Experiment– Interference– Welcher-Weg detection
● Schrödinger's Cat● Entanglement and Einstein-Podolsky-Rosen Paradox
– Detection loophole– Locality loophole– ...
● Applications based on specific quantum mechanical laws– Quantum Information
● Quantum Computing● Quantum Cryptography● Quantum Teleportation
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Summary II
● Entanglement by photodissociation– Spectroscopic selection of singlet state
● Einstein-Podolsky-Rosen Experiment– Test with massive fermionic particles– Selective detection via photo ionization– Potentially Loophole free
● Mercury as a trapping species– Time standard
● (similar work at Syrte and by Katori et al.)– Photo association of dimers– Basis for loophole-free experimental test of EPR paradox
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