quantum non-locality: all the experiments done till now -

Quantum Non-Locality, Entanglement, Bell Testsand Foundations of Quantum Mechanics

Solvay Workshop on Bits, Quanta, and Complex Systems

Thomas Walther, TU Darmstadt

5th Solvay Conference 1927

30. April 2008 | Thomas Walther | TU Darmstadt | 3

Einstein-Podolsky-Rosen Paradox (1935)

Gedankenexperiment: Separated pairs of entangled state

Conclusions:

● Incompleteness of description

● Non-locality – Action-at-a-distance


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


Principle of Experimental Tests

Preparation

CorrelationMagicBox

Manipulation

1

2

Separation

Alice

Bob

Measurement

Â

Â


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


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.


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)


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)


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


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


Random Number Generator

Th. Jennewein et al., Rev. Sci. Instr. 71 (2000)


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


Quantum correlations over long distance

W. Tittel, J. Brendek, B. Gisin, T. Herzog, H. Zbinden and N. Gisin, PRL 81, 3563 (1998)


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


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 }


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)


Heralded Entanglement of Yb+

D. N. Matsukevich, arXiv 0801-2184, (2008)

● Loopholes: Locality

● Fidelity?


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


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


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)


Talk by Nicolas Gisin

How fast is Quantum Information? When is a measurement a measurement?

D. Salart et al., arXiv/0803.2425


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


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:


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


Photodissociation of 199Hg2


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,...


Dimer dissociatingLaser beam: 355 nm

Dimer excitationLaser beam: 266 nm

Hg2 (Dimer)

Z

X

Y

Experimental Setup – Step I


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


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


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)


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).


Mercury Isotopes


Source for 253.7 nm radiation

• FHG of 1014.8-nm Yb Disc-Laser

• > 100 mW of 253.7 nm-light


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).


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


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

quantum non-locality: all the experiments done till now -

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