Uantum t heory p age a 9 r victor jones thus the

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UANTUM T HEORY P AGE A 9 R. Victor Jones, April 27, 2000 Thus the degree of first-order temporal coherence may be expressed directly in terms of well-defined experimentally observable quantities -- viz. γ 12 1 (29 s 2 - s 2 c = I Q ( 29 - I 1 Q ( 29 - I 2 Q ( 29 2 I 1 Q ( 29 I 2 Q ( 29 . [ VIA-21b ] where I Q ( 29 and I n Q ( 29 are, respectively, proportional to the intensity measured at Q with both pinholes open or with only the n th pinhole open. The visibility of the fringes given by V Q ( 29 = I max - I min I max + I min = 2 I 1` Q ( 29 I 2` Q ( 29 I 1` Q ( 29 + I 2` Q ( 29 γ 12 1 ( 29 s 2 - s 2 c [ VIA-22 ] M ODELS OF C HAOTIC L IGHT S OURCES A C OLLISION -B ROADENED S OURCE -- A N EXAMPLE OF HOMOGENEOUS - B ROADENING : Perhaps, the simplest model of a chaotic source is that of a collision interrupted oscillator. In this model one pictures an ensemble of atomic radiators each of which emits a field of constant amplitude, oscillating at a fixed frequency ϖ . The phase of the continuous output of each radiator is randomly modulated by the dephasing effect of collisions which occur random at some mean collision rate of τ 0 - 1 . The figures on the next page shows samples of the field radiated per atom (left-hand graphs) and the intensity radiated per atom (right-hand graphs) for ensembles of 50, 100, 200 and 300 collision interrupt atoms. 7 . This model is treated "experimentally' in the discussion entitled A "Toy" Model of a Randomly Fluctuating Optical Field which is located at 7 The figures show samples of the sums sin φ i i = 1 N N and sin φ i i = 1 N 2 N for N atoms with the phase radiated by each atom φ i distributed uniformly between 0 and 2 π .
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T HE I NTERACTION OF R ADIATION AND M ATTER : Q UANTUM T HEORY P AGE A 10 R. Victor Jones, April 27, 2000 . From that discussion, it is reasonable to write for a collision-broadened radiator γ 1 (29 ( τ ) = exp - i ϖ τ- τ τ 0 ( 29 [ ] [ VIA-23 ] (see a graph of this function below). From Equation [ VIA-15 ], we see that the spectrum of a collision-broadened source is given by the Lorentzian form F ϖ ( 29 = 1 πτ 0 ϖ- ϖ ( 29 2 + 1 τ 0 ( 29 2 - 1 [ VIA-24] F IELD AND I NTENSITY F LUCTUATIONS FOR C OLLISION - OR D OPPLER -B ROADENED S OURCES Mean = 0.00494765 50 Atoms Mean = 0.537517 50 Atoms Variance/Mean = 0.44 Variance/Mean = 0.95
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T HE I NTERACTION OF R ADIATION AND M ATTER : Q UANTUM T HEORY P AGE A 11 R. Victor Jones, April 27, 2000 Mean = 0.00715651 100 Atoms Mean = 0.65739 100 Atoms Variance/Mean = 0.62 Variance/Mean = 0.34 Mean = 0.00590588 200 Atoms 200 Atoms Mean = 0.570972 Variance/Mean = 1.35 Variance/Mean = 0.15
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T HE I NTERACTION OF R ADIATION AND M ATTER : Q UANTUM T HEORY P AGE A 12 R. Victor Jones, April 27, 2000 Mean = -0.00530774 300 Atoms Mean = 0.676839 300 Atoms Variance/Mean = 0.94 Variance/Mean = 0.16 D OPPLER -B ROADENED S OURCES -- A N EXAMPLE OF INHOMOGENEOUS -B ROADENING : A rather more intricate model of a chaotic source is that of a Doppler-broadening system of oscillators. In this model one pictures an ensemble of randomly moving atomic radiators each of which emits a field of constant amplitude, oscillating at a fixed frequency, but the observed frequency of a given atom is Doppler-shifted with respect to that fixed frequency.
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