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Taylor’s experiment (1909)

Taylor’s experiment (1909). film. slit. needle. diffraction pattern f(y). Proceedings of the Cambridge philosophical society. 15 114-115 (1909). Taylor’s experiment (1909). Interpretation: Classical: f(y)  <E 2 (y)>

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Taylor’s experiment (1909)

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  1. Taylor’s experiment (1909) film slit needle diffraction pattern f(y) Proceedings of the Cambridge philosophical society. 15 114-115 (1909)

  2. Taylor’s experiment (1909) 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 – iwt] E-(r) =  a+ exp[-i k.r + iwt] f(y) same as in classical. Dirac: “each photon interferes only with itself.” film slit needle diffraction pattern f(y)

  3. Hanbury-Brown and Twiss (1956) Nature, v.117 p.27 Correlation g(2) Tube position I Detectors see same field t I Detectors see different fields Signal is: g(2) = <I1(t)I2(t)> / <I1(t)><I2(t)> t

  4. Signal is: g(2) = <I1I2> / <I1><I2> = < (<I1>+dI1>) (<I2>+dI2>) > / <I1><I2> Note: <I1> + dI1≥ 0 <I2> + dI2 ≥ 0 <dI1> = <dI2> = 0 g(2) = (<I1><I2>+<dI1><I2>+<dI2><I1>+<dI1dI2>)/<I1><I2> = 1 + <dI1dI2>)/<I1><I2> = 1 for uncorrelated <dI1dI2> = 0 > 1 for positive correlation <dI1dI2> > 0 e.g. dI1=dI2 <1 for anti-correlation <dI1dI2> < 0 Classical optics: viewing the same point, the intensities must be positively correlated. Hanbury-Brown and Twiss (1956) Correlation g(2) Tube position I Detectors view same point t I Detectors view different points I1= I0/2 I0 t I2= I0/2

  5. Kimble, Dagenais + Mandel 1977 PRL, v.39 p691 Correlation g(2) Classical: correlated I1= I0/2 I0 I2= I0/2 t1 - t2 Correlation g(2) Quantum: anti-correlated n1=0 or 1 n0=1 n2= 1- n1 t1 - t2

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

  7. Kimble, Dagenais + Mandel 1977 PRL, v.39 p691 Interpretation: g(2)(t)  < a+(t)a+(t+t)a(t+t)a(t)>  < E-(t) E-(t+t) E+(t+t)E+(t)> E+(t) =  a exp[i k.r – iwt] E-(t) =  a+ exp[-i k.r + iwt] Pe time t

  8. Kuhn, Hennrich and Rempe 2002

  9. Kuhn, Hennrich and Rempe 2002

  10. Pelton, et al. 2002

  11. Pelton, et al. 2002 InAs QD relax fs pulse emit

  12. Pelton, et al. 2002 Goal: make the pure state |> = a+|0> = |1> Accomplished: make the mixed state r 0.38 |1><1| + 0.62 |0><0|

  13. Holt + Pipkin / Clauser + Freedman / Aspect, Grangier + Roger 1973-1982 J=0 J=1 J=0 Total angular momentum is zero. For counter-propagating photons implies a singlet polarization state: |> =(|L>|R> - |R>|L>)/2

  14. 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.

  15. Holt + Pipkin / Clauser + Freedman / Aspect, Grangier + Roger 1973-1982 a b a' 22.5° b' |SQM| ≤ 22 = 2.828...

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

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

  18. “Classic” Photomultiplier Tube E Many valence electrons, each can be driven into the continuum wi. Broadband detection.

  19. Photocathode Response Broad wavelength range: 120 nm – 900 nm Lower efficiency: QE < 30%

  20. 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)

  21. Coincidence Detection with Parametric Downconversion Using MCPPMTs 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. FRIBERG S, HONG CK, MANDEL LMEASUREMENT OF TIME DELAYS IN THE PARAMETRIC PRODUCTION OF PHOTON PAIRS Phys. Rev. Lett. 54 (18): 2011-2013 1985

  22. Physical Picture of Parametric Downconversion phase matching conduction collinear non-collinear or k-vector conservation ks + ki = kp valence 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: ws + wi = wp ks + ki = kp Even so, can be large uncertainty in ws-wi Intermediate states (virtual states) don’t even approximately conserve energy. Thus must be very short-lived. Result: signal and idler produced at same time.

  23. Coincidence Detection with Parametric Downconversion TDC = time-to-digital converter. Measures delay from A detection to B detection. transit time through KDP ~400 ps Dt < 100 ps FRIBERG S, HONG CK, MANDEL LMEASUREMENT OF TIME DELAYS IN THE PARAMETRIC PRODUCTION OF PHOTON PAIRS Phys. Rev. Lett. 54 (18): 2011-2013 1985

  24. 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

  25. Quadrature Detection (Wu, Xiao, Kimble 1985)

  26. Quadrature Detection Electronics environmental noise P measurement frequency n Pn freq Spectrum analyzer time Wu, et. al. 1987 Slusher, et. al. 1985

  27. Quadrature Detection of Squeezed Vacuum Pn input is squeezed vacuum input is vacuum 63% VRMS (40% power) LO phase X2 X2 q q X1 X1 squeezed vacuum vacuum

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