An account is given of noise in electrical circuits and its relation to quantum noise connected with Heisenberg’s uncertainty principle. A phase-insensitive amplifier must introduce noise (most commonly the spontaneous emission noise) in order to satisfy the constraint imposed by quantum mechanics on the simultaneous measurement of two observables represented by noncommuting operators. Nonstationary, phase-sensitive amplifiers can employ squeezed radiation and reduce the noise below that of phase-insensitive amplifiers. Experiments on squeezing in optical fibers and the attendant noise reduction are presented. The squeezing apparatus can also be employed as a quantum nondemolition measurement of photon number. A thought experiment of a two-slit interferometer is described, in which the fringes are washed out progressively with the accuracy of the photon number determination in one of its arms. Implications of measurements of this kind for the resolution of the Einstein–Podolsky–Rosen paradox are discussed.
A new scheme for generating an amplitude-squeezed state is proposed. The photon-flux fluctuation of a semiconductor-laser output wave is measured with a quantum nondemolition (QND) detector, and is negatively fed back to the laser pumping current. The operator Langevin equations are derived by combining the quantum-mechanical analyses on the laser internal-external field fluctuations, the quantum nondemolition detector based on an optical Kerr effect, and a negative-feedback circuit. The output wave features a reduced photon number noise below the standard quantum limit, 〈(\ensuremath{\Delta}n^
)2〉^〉, and an enhanced phase noise above that, 〈(\ensuremath{\Delta}\ensuremath{\psi}^
)2〉>(1/4)〈n^${〉}^{\mathrm{\ensuremath{-}}1}$, while the minimum uncertainty product is still preserved. The observed photoelectron statistics in a negative-feedback GaAs laser diode using a conventional p-i-n photodiode (not a QND detector) are shown to exhibit sub-Poissonian statistics with the variance 〈(\ensuremath{\Delta}n^
)2〉apeq20.26〈n^〉. The measured photocurrent fluctuation spectral density is also indicated to be below the standard quantum limit by a factor of 0.2 (=-7 dB). The experimental results also confirm that such amplitude squeezing is only observed inside the feedback loop and cannot be extracted from the loop unless a quantum nondemolition detector is used.