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سمينار دانشجويي

ldquoDelay choice Experiment

ارائه دهنده رضا امین زاده نیک91آذر ماه

What We Hear in This Lecture

Wave-Particle DualityDouble-slit experimentDelayed Choice ExperimentQuantum Eraser

Wave-Particle Duality

Antiquity (Egypt Greece)

particles towards orfrom the eye (Epicure

Aristotle Euclid)

XVIIth centWaves (as

ldquoriddles onwater(rdquo

Huyghens

Newton)Opticks

1702(particles

)of variouscolours(

XIXth cent The triumph of waves

Young Fresnel (1822)interference diffractionpolarisationlight is a transverse wave

Maxwell)1870 (light

is anelectromagneticwave

Early XXth Photons(particles come back)

bullEinstein (1905) Light made of quanta elementarygrains of energy and momentum

)named ldquophotonsrdquo in 1926 only(1048766Quantitative predictions for the photoelectric effectE = hν p = hν cHow to reconcile the particle description with typical wave phenomenonof diffraction interference polarisation Particle or wave

1048766Ideas not accepted until Millikanrsquosexperiments on photoelectric effect (1915)

1048766Nobel award to Einstein (1922) for thephotoelectric effect1048766Comptonrsquos experiments (1923) momentumof photon in the X ray domain

Wave particle duality

Light is both waves (capable to interfere) and an

ensemble of particles with defined energy and

momentumhellip

Similarly particles such as electrons behave like a

wave (diffraction interference)

Einstein 1909

Louis de Broglie 1923

Double-slit experiment

Delayed Choice Experiment

Proposed by John Archibald Wheeler in 1978

The method of detection in this experiment can be changed after the

photon passes the double slit so it is possible to delay the choice of whether to detect the path of the particle or detect its interference with itself

Father of black hole

2M1M

1P

2P

A

B

Source

r r

t t

This experiment is done with a single photon

Time interval between of two successive emission is long enough

In this case each photon is detected with one of these detectorsSo photon behaves like a particle

Semi -transparent mirror

rt tr

rt rt

The arrangement is set in such a way that this part is destructive

The arrangement is set in such a way that this part is constructive

Now photon behaves like a wave

It seems that causality is reversed

Maalool taghaddom bar ellat darad

An implementation of the experiment in 2007 showed that the act of observation ultimately decides whether the photon will behave as a particle or wave

Cho Adrian After a Short Delay Quantum Mechanics Becomes Even Weirder ScienceNOW Daily News 16 February 2007

Quantum Eraser Experiment

The Which-way information that once established can be erased

The idea was first proposed by Marlan O Scully and K Druhl(1982)M O Scully and K Druhl Phys Rev A 252208 (1982)

Marlan O Scully 1963 Graduates from Yale University with MS in Physics 1966 Graduates from Yale University with PhD in Physics

1969 Professor of Physics and Optical Sciences University of Arizona through 1980

1980 Distinguished Professor of Physics University of New Mexico through 1992

1992 Professor of Physics Texas AampM University through 1996

2004 Professor of Chemical Engineering Texas AampM University through present

2005 Professor of Mechanical and Aerospace Engineering and Materials Science Princeton University through present

1i1s2i

2s

VVi

Vi

Vi sieseieC Lsi

2211

These photons are correlated in that they are created simultaneously and they both have the same polarization (Here vertical to the plane of

the experiment)

iD

sD

iD

sD

2i1i

1s2s

VVi

Vi

Vi sieseieC Lsi

2211

VVii sieeC Lsi )(

VVi

Vi

Vi sieseieC Lsi

2211

Assume that the photons have the same frequency and they are indistinguishable so

Intensities at the two detectors are identical and are proportional to

))cos(1(2)(

Lsiii Lsi ee

The which-way effect can be seen when the upper mirror is removed In that case there is no reflected s photon associated with the reflected i photon which allows us to distinguish between the two i photons

Analogous to knowing which of the two slits

a photon passes through (good start)

iD

sD

2i

1i

1s

2s

Plate that rotates the polarization from V to H

VVi

Vi

Vi sieseieC Lsi

2211

VV

iH

i

VVi

VHi

sieieC

siesieC

Lsi

Lsi

21)(

2211)(

No interference

Because we have a which-way situation

Distinguishing the reflected i photon then distinguishes the reflected s photon since these are all produced in pairs

VVi

Hi sieieC Lsi

21)(

By expressing the photon state in terms of states rotated through plusmn45 degree

)(2

1)(

2

1 VH

We have

Vii siieiieC Lsi )()()(

iD

sD

Vi2

Hi1

Vs

Vs


By putting a 45 degree filter in front of the upper detector

We have

)()()()(V

iV

ii sieCsieieC Lsi

So the which-way information is erased

amp

We have fringes

Thanks for listening


Slide 2




Early XXth Photons (particles come back)




Slide 10

Slide 11


Marlan O Scully

Slide 14

Slide 15

Slide 16

Slide 17

Slide 18

Slide 19

Slide 20

Slide 21

Slide 22


Wave-Particle DualityDouble-slit experimentDelayed Choice ExperimentQuantum Eraser




Aristotle Euclid)



Huyghens

Newton)Opticks

1702(particles

)of variouscolours(



Maxwell)1870 (light










momentumhellip



Einstein 1909








2M1M

1P

2P

A

B

Source

r r

t t





rt tr

rt rt

















1i1s2i

2s

VVi

Vi

Vi sieseieC Lsi

2211


the experiment)

iD

sD

iD

sD

2i1i

1s2s

VVi

Vi

Vi sieseieC Lsi

2211

VVii sieeC Lsi )(

VVi

Vi

Vi sieseieC Lsi

2211



))cos(1(2)(

Lsiii Lsi ee




iD

sD

2i

1i

1s

2s


VVi

Vi

Vi sieseieC Lsi

2211

VV

iH

i

VVi

VHi

sieieC

siesieC

Lsi

Lsi

21)(

2211)(

No interference



VVi

Hi sieieC Lsi

21)(


)(2

1)(

2

1 VH

We have


iD

sD

Vi2

Hi1

Vs

Vs



We have

)()()()(V

iV

ii sieCsieieC Lsi


amp

We have fringes



Slide 2








Slide 10

Slide 11


Marlan O Scully

Slide 14

Slide 15

Slide 16

Slide 17

Slide 18

Slide 19

Slide 20

Slide 21

Slide 22




Aristotle Euclid)



Huyghens

Newton)Opticks

1702(particles

)of variouscolours(



Maxwell)1870 (light










momentumhellip



Einstein 1909








2M1M

1P

2P

A

B

Source

r r

t t





rt tr

rt rt

















1i1s2i

2s

VVi

Vi

Vi sieseieC Lsi

2211


the experiment)

iD

sD

iD

sD

2i1i

1s2s

VVi

Vi

Vi sieseieC Lsi

2211

VVii sieeC Lsi )(

VVi

Vi

Vi sieseieC Lsi

2211



))cos(1(2)(

Lsiii Lsi ee




iD

sD

2i

1i

1s

2s


VVi

Vi

Vi sieseieC Lsi

2211

VV

iH

i

VVi

VHi

sieieC

siesieC

Lsi

Lsi

21)(

2211)(

No interference



VVi

Hi sieieC Lsi

21)(


)(2

1)(

2

1 VH

We have


iD

sD

Vi2

Hi1

Vs

Vs



We have

)()()()(V

iV

ii sieCsieieC Lsi


amp

We have fringes



Slide 2








Slide 10

Slide 11


Marlan O Scully

Slide 14

Slide 15

Slide 16

Slide 17

Slide 18

Slide 19

Slide 20

Slide 21

Slide 22



Maxwell)1870 (light










momentumhellip



Einstein 1909








2M1M

1P

2P

A

B

Source

r r

t t





rt tr

rt rt

















1i1s2i

2s

VVi

Vi

Vi sieseieC Lsi

2211


the experiment)

iD

sD

iD

sD

2i1i

1s2s

VVi

Vi

Vi sieseieC Lsi

2211

VVii sieeC Lsi )(

VVi

Vi

Vi sieseieC Lsi

2211



))cos(1(2)(

Lsiii Lsi ee




iD

sD

2i

1i

1s

2s


VVi

Vi

Vi sieseieC Lsi

2211

VV

iH

i

VVi

VHi

sieieC

siesieC

Lsi

Lsi

21)(

2211)(

No interference



VVi

Hi sieieC Lsi

21)(


)(2

1)(

2

1 VH

We have


iD

sD

Vi2

Hi1

Vs

Vs



We have

)()()()(V

iV

ii sieCsieieC Lsi


amp

We have fringes



Slide 2








Slide 10

Slide 11


Marlan O Scully

Slide 14

Slide 15

Slide 16

Slide 17

Slide 18

Slide 19

Slide 20

Slide 21

Slide 22









momentumhellip



Einstein 1909








2M1M

1P

2P

A

B

Source

r r

t t





rt tr

rt rt

















1i1s2i

2s

VVi

Vi

Vi sieseieC Lsi

2211


the experiment)

iD

sD

iD

sD

2i1i

1s2s

VVi

Vi

Vi sieseieC Lsi

2211

VVii sieeC Lsi )(

VVi

Vi

Vi sieseieC Lsi

2211



))cos(1(2)(

Lsiii Lsi ee




iD

sD

2i

1i

1s

2s


VVi

Vi

Vi sieseieC Lsi

2211

VV

iH

i

VVi

VHi

sieieC

siesieC

Lsi

Lsi

21)(

2211)(

No interference



VVi

Hi sieieC Lsi

21)(


)(2

1)(

2

1 VH

We have


iD

sD

Vi2

Hi1

Vs

Vs



We have

)()()()(V

iV

ii sieCsieieC Lsi


amp

We have fringes



Slide 2








Slide 10

Slide 11


Marlan O Scully

Slide 14

Slide 15

Slide 16

Slide 17

Slide 18

Slide 19

Slide 20

Slide 21

Slide 22







2M1M

1P

2P

A

B

Source

r r

t t





rt tr

rt rt

















1i1s2i

2s

VVi

Vi

Vi sieseieC Lsi

2211


the experiment)

iD

sD

iD

sD

2i1i

1s2s

VVi

Vi

Vi sieseieC Lsi

2211

VVii sieeC Lsi )(

VVi

Vi

Vi sieseieC Lsi

2211



))cos(1(2)(

Lsiii Lsi ee




iD

sD

2i

1i

1s

2s


VVi

Vi

Vi sieseieC Lsi

2211

VV

iH

i

VVi

VHi

sieieC

siesieC

Lsi

Lsi

21)(

2211)(

No interference



VVi

Hi sieieC Lsi

21)(


)(2

1)(

2

1 VH

We have


iD

sD

Vi2

Hi1

Vs

Vs



We have

)()()()(V

iV

ii sieCsieieC Lsi


amp

We have fringes



Slide 2








Slide 10

Slide 11


Marlan O Scully

Slide 14

Slide 15

Slide 16

Slide 17

Slide 18

Slide 19

Slide 20

Slide 21

Slide 22












1i1s2i

2s

VVi

Vi

Vi sieseieC Lsi

2211


the experiment)

iD

sD

iD

sD

2i1i

1s2s

VVi

Vi

Vi sieseieC Lsi

2211

VVii sieeC Lsi )(

VVi

Vi

Vi sieseieC Lsi

2211



))cos(1(2)(

Lsiii Lsi ee




iD

sD

2i

1i

1s

2s


VVi

Vi

Vi sieseieC Lsi

2211

VV

iH

i

VVi

VHi

sieieC

siesieC

Lsi

Lsi

21)(

2211)(

No interference



VVi

Hi sieieC Lsi

21)(


)(2

1)(

2

1 VH

We have


iD

sD

Vi2

Hi1

Vs

Vs



We have

)()()()(V

iV

ii sieCsieieC Lsi


amp

We have fringes



Slide 2








Slide 10

Slide 11


Marlan O Scully

Slide 14

Slide 15

Slide 16

Slide 17

Slide 18

Slide 19

Slide 20

Slide 21

Slide 22

iD

sD

2i1i

1s2s

VVi

Vi

Vi sieseieC Lsi

2211

VVii sieeC Lsi )(

VVi

Vi

Vi sieseieC Lsi

2211



))cos(1(2)(

Lsiii Lsi ee




iD

sD

2i

1i

1s

2s


VVi

Vi

Vi sieseieC Lsi

2211

VV

iH

i

VVi

VHi

sieieC

siesieC

Lsi

Lsi

21)(

2211)(

No interference



VVi

Hi sieieC Lsi

21)(


)(2

1)(

2

1 VH

We have


iD

sD

Vi2

Hi1

Vs

Vs



We have

)()()()(V

iV

ii sieCsieieC Lsi


amp

We have fringes



Slide 2








Slide 10

Slide 11


Marlan O Scully

Slide 14

Slide 15

Slide 16

Slide 17

Slide 18

Slide 19

Slide 20

Slide 21

Slide 22

VVii sieeC Lsi )(

VVi

Vi

Vi sieseieC Lsi

2211



))cos(1(2)(

Lsiii Lsi ee




iD

sD

2i

1i

1s

2s


VVi

Vi

Vi sieseieC Lsi

2211

VV

iH

i

VVi

VHi

sieieC

siesieC

Lsi

Lsi

21)(

2211)(

No interference



VVi

Hi sieieC Lsi

21)(


)(2

1)(

2

1 VH

We have


iD

sD

Vi2

Hi1

Vs

Vs



We have

)()()()(V

iV

ii sieCsieieC Lsi


amp

We have fringes



Slide 2








Slide 10

Slide 11


Marlan O Scully

Slide 14

Slide 15

Slide 16

Slide 17

Slide 18

Slide 19

Slide 20

Slide 21

Slide 22




iD

sD

2i

1i

1s

2s


VVi

Vi

Vi sieseieC Lsi

2211

VV

iH

i

VVi

VHi

sieieC

siesieC

Lsi

Lsi

21)(

2211)(

No interference



VVi

Hi sieieC Lsi

21)(


)(2

1)(

2

1 VH

We have


iD

sD

Vi2

Hi1

Vs

Vs



We have

)()()()(V

iV

ii sieCsieieC Lsi


amp

We have fringes



Slide 2








Slide 10

Slide 11


Marlan O Scully

Slide 14

Slide 15

Slide 16

Slide 17

Slide 18

Slide 19

Slide 20

Slide 21

Slide 22

VVi

Hi sieieC Lsi

21)(


)(2

1)(

2

1 VH

We have


iD

sD

Vi2

Hi1

Vs

Vs



We have

)()()()(V

iV

ii sieCsieieC Lsi


amp

We have fringes



Slide 2








Slide 10

Slide 11


Marlan O Scully

Slide 14

Slide 15

Slide 16

Slide 17

Slide 18

Slide 19

Slide 20

Slide 21

Slide 22

iD

sD

Vi2

Hi1

Vs

Vs



We have

)()()()(V

iV

ii sieCsieieC Lsi


amp

We have fringes



Slide 2








Slide 10

Slide 11


Marlan O Scully

Slide 14

Slide 15

Slide 16

Slide 17

Slide 18

Slide 19

Slide 20

Slide 21

Slide 22



Slide 2








Slide 10

Slide 11


Marlan O Scully

Slide 14

Slide 15

Slide 16

Slide 17

Slide 18

Slide 19

Slide 20

Slide 21

Slide 22

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