Taylor’s experiment (1909)

slit

needle

diffraction pattern f(y)

film

Proceedings of the Cambridgephilosophical society. 15 114-115(1909)

Taylor’s experiment (1909)

slit

needle

diffraction pattern f(y)

Interpretation:

Classical: f(y) <E2(y)>

Early Quantum (J. J. Thompson): if photons are localized concentrations of E-M field, at low photon density there should be too few to interfere.

Modern Quantum:f(y) = <n(y)> = <a+(y)a(y)> <E-(y)E+(y)>E+(r) = a exp[i k.r – it]E-(r) = a+ exp[-i k.r + it]

f(y) same as in classical.

Dirac: “each photon interferes only with itself.”

film

Hanbury-Brown and Twiss (1956)

Nature, v.117 p.27Correlation g(2)

Tube position

Detectors view same point

Detectors view different points

I

t

I

t

Signal is:g(2) = <I1(t)I2(t)> / <I1(t)><I2(t)>

Hanbury-Brown and Twiss (1956)

Correlation g(2)

Tube position

Detectors view same point

Detectors view different points

I

t

I

t

Signal is:g(2) = <I1I2> / <I1><I2>= < (<I1>+I1>) (<I2>+I2>) > / <I1><I2>

Note: <I1> + I1≥<I2> + I2 ≥ <I1> = <I2> = 0

g(2) = (<I1><I2>+<I1><I2>+<I2><I1>+<I1I2>)/<I1><I2> = 1 + <I1I2>)/<I1><I2> = 1 for uncorrelated <I1I2> = 0 ≥ 1 for positive correlation <I1I2> = 0 e.g. I1I2

≤ 1 for anti-correlation <I1I2> < 0

Classical optics: viewing the same point, the intensities must be positively correlated.

I1= I0/2

I2= I0/2

I0

Kimble, Dagenais + Mandel 1977

PRL, v.39 p691

I1= I0/2

I2= I0/2

I0

n1=0 or 1

n2= 1 - n1

n0=1

Classical: correlated

Quantum: anti-correlated

Correlation g(2)

t1 - t2Correlation g(2)

t1 - t2

Kimble, Dagenais + Mandel 1977

PRL, v.39 p691

Kimble, Dagenais + Mandel 1977

PRL, v.39 p691

Interpretation:

g(2)() < a+(t)a+(t+)a(t+)a(t)> < E-(t) E-(t+) E+(t+)E+(t)>E+(t) = a exp[i k.r – it]E-(t) = a+ exp[-i k.r + it]

Pe

t time

Kuhn, Hennrich and Rempe 2002

Kuhn, Hennrich and Rempe 2002

Pelton, et al. 2002

Pelton, et al. 2002

fs pulserelax

emit

InAs QD

Pelton, et al. 2002

Goal: make the pure state|> = a+|0> = |1>Accomplished: make the mixed state 0.38 |1><1| + 0.62 |0><0|

Holt + Pipkin / Clauser + Freedman / Aspect, Grangier + Roger 1973-1982

J=0

J=0

J=1

Total angular momentum is zero.

For counter-propagating photonsimplies a singlet polarization state:|> =(|L>|R> - |R>|L>)/2

Holt + Pipkin / Clauser + Freedman / Aspect, Grangier + Roger 1973-1982

Total angular momentum is zero.

For counter-propagating photons,implies a singlet polarization state:|> =(|L>|R> - |R>|L>)/2

|> = 1/2(aL+aR

+ - aR+aL

+)|0> = 1/2(aH

+aV+ - aV

+aH+)|0>

= 1/2(aD+aA

+ - aA+aD

+)|0>

Detect photon 1 in any polarization basis (pA,pB), detect pA, photon 2 collapses to pB, or vice versa.

If you have classical correlations,you arrive at the Bell inequality-2 ≤ S ≤ 2.

Holt + Pipkin / Clauser + Freedman / Aspect, Grangier + Roger 1973-1982

a

a'b

b'

|SQM| ≤ 22 = 2.828...

22.5°