Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

Quantum-mechanical noise in an interferometer: intrinsic uncertainty vs measurement uncertainty

Wei-Tou Ni

Published Jun 9, 1986• 0 citations
OpenAlex

Abstract

The ultimate limits of accuracies of interferometers come from quantum-mechanical noise according to the quantum theory of measurement. There are two sources of quantum-mechanical measurement noise—the error due to photoncounting statistics and the disturbance of the end mirror positions produced by fluctuating radiation pressure. Photon-counting error decreases with the square root of power. Fluctuating radiation pressure disturbance increases with the square root of power.

Related papers

Quantum-mechanical noise in an interferometer

Carlton M. Caves

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.

Physical review. D. Particles, fields, gravitation, and cosmology/Physical review. D. Particles and fields•Apr 15, 1981•3,202 citations

Quantum-Mechanical Measurement Noise in a Michelson Interferometer Using General Squeezed-State Light Sources

Wei-Tou Nit

Two types of quantum-mechanical measurement noise - the photon-counting error and the radiation-pressure error - are analyzed for a Michelson interferometer with two general incoming squeezed states for the two input ports.

Chinese Journal of Physics•Mar 1, 1987•0 citations

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

Ohad Assaf, Y. Ben-Aryeh

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.

Journal of Optics B Quantum and Semiclassical Optics•Jan 14, 2002•12 citations

Quantum measurements of position, detection of weak classical forces, and interferometric noise

Wei-Tou Ni

We discuss quantum measurements of position and repeated-measurement schemes for monitoring free-mass position to an arbitrary accuracy. Using these schemes, weak classical forces can be monitored to an arbitrary accuracy. To illustrate various measurement uncertainties and intrinsic uncertainties, we consider the case of a Michelson interferometer. In the low-intensity limit, two measurement uncertainties, photon counting error and radiation pressure error, are independent of the intrinsic uncertainty. The uses of squeezed states and number eigenstates are discussed.

IEEE Transactions on Instrumentation and Measurement•Jun 1, 1987•0 citations

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

Wei-Tou Ni

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.

Physical review. D. Particles, fields, gravitation, and cosmology/Physical review. D. Particles and fields•May 15, 1987•7 citations

Force metrology using quantum correlations of light due to a room-temperature mechanical oscillator

Vivishek Sudhir, Ryan Schilling, Sergey A. Fedorov +3 more

The radiation pressure interaction of light with a mechanical oscillator leads to a fundamental disturbance on the oscillator. This disturbance - measurement backaction - is due to the quantum fluctuations in the amplitude of the light. When the phase of the light is detected to infer the mechanical position, quantum fluctuations in the phase - measurement imprecision - leads to a further uncertainty in the estimate of the position. In this conventional measurement strategy, these two noise sources impose a fundamental limit on the ability to estimate the position of the mechanical object - the so-called standard quantum limit [1]. However, the two noise contributions are in general correlated. The fluctuations in the amplitude quadrature drive the mechanical oscillator, and this backaction driven motion is transduced into the phase quadrature. Correlations thus established [2] form a valuable quantum mechanical resource that can be directly employed for back-action cancellation in the measurement record via “variational measurements” [3].

Conference on Lasers and Electro-Optics Europe & European Quantum Electronics Conference (CLEO/Europe-EQEC)•Jun 1, 2017•1 citation
The ultimate limits of accuracies of interferometers come from quantum-mechanical noise according to the quantum theory of measurement. There are two sources of quantum-mechanical measurement noise—the error due to photoncounting statistics and the disturbance of the end mirror positions produced by fluctuating radiation pressure. Photon-counting error decreases with the square root of power. Fluctuating radiation pressure disturbance increases with the square root of power.
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 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.
We discuss quantum measurements of position and repeated-measurement schemes for monitoring free-mass position to an arbitrary accuracy. Using these schemes, weak classical forces can be monitored to an arbitrary accuracy. To illustrate various measurement uncertainties and intrinsic uncertainties, we consider the case of a Michelson interferometer. In the low-intensity limit, two measurement uncertainties, photon counting error and radiation pressure error, are independent of the intrinsic uncertainty. The uses of squeezed states and number eigenstates are discussed.
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}$2{\mathrm{}}^{2}2)1/2{)}^{1/2})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.
The radiation pressure interaction of light with a mechanical oscillator leads to a fundamental disturbance on the oscillator. This disturbance - measurement backaction - is due to the quantum fluctuations in the amplitude of the light. When the phase of the light is detected to infer the mechanical position, quantum fluctuations in the phase - measurement imprecision - leads to a further uncertainty in the estimate of the position. In this conventional measurement strategy, these two noise sources impose a fundamental limit on the ability to estimate the position of the mechanical object - the so-called standard quantum limit [1]. However, the two noise contributions are in general correlated. The fluctuations in the amplitude quadrature drive the mechanical oscillator, and this backaction driven motion is transduced into the phase quadrature. Correlations thus established [2] form a valuable quantum mechanical resource that can be directly employed for back-action cancellation in the measurement record via “variational measurements” [3].