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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 view same point t I Detectors view different points 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...

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