Taylor’s experiment (1909) slit needle diffraction pattern f(y) film Proceedings of the Cambridge philosophical society (1909)

Taylor’s experiment (1909) slit needle diffraction pattern f(y) Interpretation: Classical: f(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) = =  E + (r) =  a exp[i k.r – i  t] E - (r) =  a + exp[-i k.r + i  t] f(y) same as in classical. Dirac: “each photon interferes only with itself.” film

Hanbury-Brown and Twiss (1956) Nature, v.117 p.27 Correlation g (2) Tube position Detectors see same field Detectors see different fields I t I t Signal is: g (2) = /

Hanbury-Brown and Twiss (1956) Correlation g (2) Tube position I t I t Signal is: g (2) =  I 1 I 2  / = +  I 1 ) ( +  I 2 ) > / Note: +  I 1  ≥  +  I 2 ≥  = = 0 g (2) = ( )/ = 1 + )/ = 1 for uncorrelated = 0 > 1 for positive correlation  I 1  I 2  > 0 e.g.  I 1  I 2 < 1 for anti-correlation  I 1  I 2  < 0 Classical optics: viewing the same point, the intensities must be positively correlated. I 1 = I 0 /2 I 2 = I 0 /2 I0I0 Detectors see same field Detectors see different fields

Kimble, Dagenais + Mandel 1977 PRL, v.39 p691 I 1 = I 0 /2 I 2 = I 0 /2 I0I0 n 1 =0 or 1 n 2 = 1 - n 1 n 0 =1 Classical: correlated Quantum: can be anti-correlated Correlation g (2) t 1 - t 2 Correlation g (2) t 1 - t 2

Kimble, Dagenais + Mandel 1977 PRL, v.39 p691

Kimble, Dagenais + Mandel 1977 PRL, v.39 p691 Interpretation: g (2) (  )   H I (t)  -E  d  E + (t) |e> <e| H I (t) H I (t+  )  E - (t) E - (t+  ) |g> <e| + h.c. PePe t time

Kuhn, Hennrich and Rempe 2002

Pelton, et al. 2002

fs pulse relax emit InAs QD

Pelton, et al Goal: make the pure state |  > = a + |0> = |1> Accomplished: make the mixed state   0.38 |1> <0|

Holt + Pipkin / Clauser + Freedman / Aspect, Grangier + Roger J=0 J=1 Total angular momentum is zero. For counter-propagating photons implies a singlet polarization state: |  > =(|L>|R> - |R>|L>)/  2

Holt + Pipkin / Clauser + Freedman / Aspect, Grangier + Roger Total angular momentum is zero. For counter-propagating photons, implies a singlet polarization state: |  > =(|L>|R> - |R>|L>)/  2 |  > = 1/  2(a L + a R + - a R + a L + )|0> = 1/  2(a H + a V + - a V + a H + )|0> = 1/  2(a D + a A + - a A + a D + )|0> Detect photon 1 in any polarization basis (p A,p B ), detect p A, photon 2 collapses to p B, or vice versa. If you have classical correlations, you arrive at the Bell inequality -2 ≤ S ≤ 2.

Holt + Pipkin / Clauser + Freedman / Aspect, Grangier + Roger a a' b b' |S QM | ≤ 2  2 = °

Perkin-Elmer Avalanche Photodiode thin p region (electrode) absorption region intrinsic silicon multiplication region V positive V negative “Geiger mode”: operating point slightly above breakdown voltage e-e- h+h+

Avalanche Photodiode Mechanism Many valence electrons, each with a slightly different absorption frequency  i. Broadband detection.

“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 nm Lower 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 L MEASUREMENT OF TIME DELAYS IN THE PARAMETRIC PRODUCTION OF PHOTON PAIRS Phys. Rev. Lett. 54 (18): 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 downconverted photons (NIR). Process is “parametric” = no change in state of KDP. This requires energy and momentum conservation:  s +  i =  p k s + k i = k p 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 conservation k s + k i = k p collinear non-collinear or phase matching

Coincidence Detection with Parametric Downconversion FRIBERG S, HONG CK, MANDEL L MEASUREMENT OF TIME DELAYS IN THE PARAMETRIC PRODUCTION OF PHOTON PAIRS Phys. Rev. Lett. 54 (18): transit time through KDP ~400 ps  t < 100 ps TDC = time-to-digital converter. Measures delay from A detection to 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):

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): OCT 1987

Quadrature Detection Electronics P freq Spectrum analyzer environmental noise measurement frequency P time Slusher, et. al Wu, et. al. 1987

Quadrature Detection of Squeezed Vacuum LO phase input is vacuum input is squeezed vacuum  P   X2X2 X1X1 X2X2 X1X1 vacuum squeezed vacuum 63% V RMS (40% power)

Cauchy Schwarz Inequality Violation

9P 7S 7P nm nm 202 Hg e - impact

Cauchy Schwarz Inequality Violation

Two-photon diffraction D’Angelo, Chekhova and Shih, Phys. Rev. Lett (2001) Two IR photons (pairs) One IR photon Pump

Two-photon diffraction D’Angelo, Chekhova and Shih, Phys. Rev. Lett (2001) Two IR photons (pairs) One IR photon Two paths to coincidence detection: Pump

Not just for photons!

g (1) g (2)

Hong-Ou-Mandel effect Hong, Ou and Mandel, Phys. Rev. Lett (1987)

Hong-Ou-Mandel effect Hong, Ou and Mandel, Phys. Rev. Lett (1987)