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Journal of Optics B Quantum and Semiclassical Optics

Quantum mechanical noise in coherent-state and squeezed-state Michelson interferometers

Ohad Assaf, Y. Ben-Aryeh

Published Jan 14, 2002• 12 citations

Abstract

In the present study we extend and generalize previous results for coherent-state and squeezed-state Michelson interferometer quantum mechanical uncertainties (or fluctuations), which are commonly referred to as `quantum noise'. The calculation of photon counting (PC) fluctuations in the squeezed-state interferometer is extended to fourth-order correlation functions used as the measured signal. We also generalize a `unified model' for treating both PC and radiation pressure fluctuations in the coherent-state interferometer, by using mathematical methods which apply to Kerr-type interactions. The results are more general than those reported previously in two ways. First, we obtain exact expressions, which lead to previous results under certain approximations. Second, we deal with cases in which the responses of the two mirrors to radiation pressure are not equal.

DOI: 10.1088/1464-4266/4/1/308

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In the present study we extend and generalize previous results for coherent-state and squeezed-state Michelson interferometer quantum mechanical uncertainties (or fluctuations), which are commonly referred to as

quantum noise'. The calculation of photon counting (PC) fluctuations in the squeezed-state interferometer is extended to fourth-order correlation functions used as the measured signal. We also generalize a

unified model' for treating both PC and radiation pressure fluctuations in the coherent-state interferometer, by using mathematical methods which apply to Kerr-type interactions. The results are more general than those reported previously in two ways. First, we obtain exact expressions, which lead to previous results under certain approximations. Second, we deal with cases in which the responses of the two mirrors to radiation pressure are not equal.

The interferometers now being developed to detect gravitational waves work by measuring the relative positions of widely separated masses. Two fundamental sources of quantum-mechanical noise determine the sensitivity of such an interferometer: (i) fluctuations in number of output photons (photon-counting error) and (ii) fluctuations in radiation pressure on the masses (radiation-pressure error). Because of the low power of available continuous-wave lasers, the sensitivity of currently planned interferometers will be limited by photon-counting error. This paper presents an analysis of the two types of quantum-mechanical noise, and it proposes a new technique---the "squeezed-state" technique---that allows one to decrease the photon-counting error while increasing the radiation-pressure error, or vice versa. The key requirement of the squeezed-state technique is that the state of the light entering the interferometer's normally unused input port must be not the vacuum, as in a standard interferometer, but rather a "squeezed state"---a state whose uncertainties in the two quadrature phases are unequal. Squeezed states can be generated by a variety of nonlinear optical processes, including degenerate parametric amplification.

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.