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 see same field

Detectors see different fields

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°

Perkin-Elmer Avalanche Photodiode

thin p region (electrode)

absorption region intrinsic silicon

multiplication regionV positive

V negative

“Geiger mode”: operating pointslightly above breakdown voltage

e- h+

Avalanche Photodiode Mechanism

Many valence electrons, each with a slightly differentabsorption frequency i.Broadband detection.

k

E

valence band(filled)

conduction band (empty)

possible transitions

= E/hbar Di

“Classic” Photomultiplier Tube

Many valence electrons, each can be driven into the continuum i.Broadband detection.

E

Photocathode Response

Broad wavelength range: 120 nm – 900 nmLower efficiency: QE < 30%

Microchannel Plate Photomultiplier Tube

For light, use same photocathode materials, same Q. Eff. and same wavelength ranges. Much faster response: down to 25 ps jitter (TTS = Transit time spread)

Coincidence Detection with Parametric Downconversion

FRIBERG S, HONG CK, MANDEL LMEASUREMENT OF TIME DELAYS IN THE PARAMETRIC PRODUCTION OF PHOTON PAIRS Phys. Rev. Lett. 54 (18): 2011-2013 1985

Using MCP PMTs for best time-resolution.CF Disc. = Constant-fraction discriminator: identifies “true” detection pulses, rejects background, maintains timing.TDC = “Time to digital converter”:Measures delay from A detection to B detection.PDP11: Very old (1979) computer from DEC.

Physical Picture of Parametric Downconversion

valence

conduction

Material (KDP) is transparent to both pump (UV) and downconvertedphotons (NIR). Process is “parametric” = no change in state of KDP.This requires energy and momentum conservation: s + i = p ks + ki = kp Even so, can be large uncertainty in s i

Intermediate states (virtual states) don’t even approximately conserve energy.Thus must be very short-lived. Result: signal and idler produced at same time.

k-vector conservationks + ki = kp

collinear

non-collinearor

phase matching

Coincidence Detection with Parametric Downconversion

FRIBERG S, HONG CK, MANDEL LMEASUREMENT OF TIME DELAYS IN THE PARAMETRIC PRODUCTION OF PHOTON PAIRS Phys. Rev. Lett. 54 (18): 2011-2013 1985

transit time through KDP~400 ps

Dt < 100 ps

TDC = time-to-digitalconverter. Measuresdelay from A detectionto B detection.

Quadrature Detection of Squeezed Light (Slusher, et. al. 1985)

SLUSHER RE, HOLLBERG LW, YURKE B, et al.

OBSERVATION OF SQUEEZED STATES GENERATED BY 4-WAVE MIXING IN AN OPTICAL CAVITY

Phys. Rev. Lett. 55 (22): 2409-2412 1985

Quadrature Detection (Wu, Xiao, Kimble 1985)

WU L-A., Xiao M., KIMBLE H.J.SQUEEZED STATES OF LIGHT FROM AN OPTICAL PARAMETRIC OSCILLATOR JOSA B 4 (10): 1465-1475 OCT 1987

Quadrature Detection Electronics

P

freq

Spectrumanalyzer

environmental noise

measurementfrequency P

time

Slusher, et. al. 1985 Wu, et. al. 1987

Quadrature Detection of Squeezed Vacuum

LO phase

input isvacuum

input issqueezedvacuum

P

D1

D2

LO

in

Di(t)

X2

X1

X2

X1

vacuum squeezedvacuum

63% VRMS

(40% power)