By Arthur Cox
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To subtract out the contribution of the reflected local oscillator field balanced homodyne detection may be used. In this scheme the output from both ports of the beam splitter is directed to a photodetector and the resulting currents combined with appropriate phase shifts before subsequent analysis. 121. 83). 1 Classical Theory Consider radiation of intensity I ( t ) falling on a photo-electric counter. 9 Photon Counting Measurements 47 The parameter r is a measure of the sensitivity of the detector, and depends on the area of the detector and the spectral range of the incident light.
3. A phase convention for squeezed states. Direction I is thc direction of squeezing, d~rection 2 is the direction of coherent excitation. The error ellipse is aligned so that the squeezing direction is parallel to the X , d ~ r e c t ~ o n . 2%= ( X I ) + i(X2) with 0 = t a n number for this squeezed state is ( I - n2 - I r 12(cosh21. - C ((X2)/(X,)). 70) When 0 = 74'2, that is the squeezing is out of phase with the complex amplitude Thus this state with increased amplitude fluctuations has super-Poissonian statistics as expected.
3. Plot of the electric field versus t ~ m eshowing schematically the uncertainty in phase and amplitude for (a) a coherent state. (b) a squeezed state with reduced amplitude fluctuations. 61 where v = sinh re2'@, p = coshr, P = PC(+ V U * H,(x) are Hermite polynomials. The photon number distribution for a squeezed state may be broader or narrower than a Poissonian depending on whether the reduced fluctuations occur in the phase ( X , ) or amplitude ( X I )component of the field. This is illustrated in Fig.