Quantum-mechanical noise in an interferometer: Intrinsic uncertainty versus measurement uncertainty

Abstract

In many quantum-mechanical measurements, the total uncertainties (\ensuremath{\sigma}) are greater than or equal to the intrinsic uncertainties (${\ensuremath{\sigma}}_{I}$) of the quantities to be measured; the differences are due to the particular measurement processes chosen. In each of these situations, a measurement uncertainty ${\ensuremath{\sigma}}_{M}$ can be defined as ${\ensuremath{\sigma}}_{M}$=(${\ensuremath{\sigma}}^{2}$-${\ensuremath{\sigma}}_{I}$${\mathrm{}}^{2}$${)}^{1/2}$. A question to ask is whether ${\ensuremath{\sigma}}_{M}$ is independent of the initial quantum state of the system to be measured, i.e., whether ${\ensuremath{\sigma}}_{M}$ is only dependent on the measurement process chosen. For a Michelson interferometer, we extend Loudon's model to show that in the model ${\ensuremath{\sigma}}_{M}$ is only dependent on the measurement process chosen for the case with small radiation-pressure fluctuation. When the intensity and radiation-pressure fluctuation are high, there are cross-correlated terms. Some of these terms are negative and give hope to the possibility of uncertainty reductions for appropriate schemes.