On the measurement of a weak classical force coupled to a harmonic oscillator: experimental progress

Abstract

Several high-precision physics experiments are approaching a level of sensitivity at which the intrinsic quantum nature of the experimental apparatus is the dominant source of fluctuations limiting the sensitivity of the measurements. This quantum limit is embodied by the Heisenberg uncertainty principle, which prohibits arbitrarily precise simultaneous measurements of two conjugate observables of a system but allows one-time measurements of a single observable with any precision. The dynamical evolution of a system immediately following a measurement limits the class of observables that may be measured repeatedly with arbitrary precision, with the influence of the measurement apparatus on the system being confined strictly to the conjugate observables. Observables having this feature, and the corresponding measurements performed on them, have been named quantum nondemolition or back-action evasion observables. In a previous review (Caves et al., 1980, Rev. Mod. Phys. 52, 341) a quantum-mechanical analysis of quantum nondemolition measurements of a harmonic oscillator was presented. The present review summarizes the experimental progress on quantum nondemolition measurements and the classical models developed to describe and guide the development of practical implementations of quantum nondemolition measurements. The relationship between the classical and quantum theoretical models is also reviewed. The concept of quantum nondemolition and back-action evasion measurements originated in the context of measurements on a macroscopic mechanical harmonic oscillator, though these techniques may be useful in other experimental contexts as well, as is discussed in the last part of this review. [S0034-6861(96)00103-1] CONTENTS

Mirror quiescence and high-sensitivity position measurements with feedback

“…In these applications one needs a very high resolution for position measurements and a good control of the various noise sources, because one has to detect the effect of a very weak force [3,4]. As shown by the pioneering work of Braginsky [5], even though all classical noise sources had been minimized, the detection of gravitational waves would be ultimately determined by quantum fluctuations and the Heisenberg uncertainty principle.…”

“…What is more important, expecially for gravitational wave detection [1], or for metrology applications [20], is to improve the sensitivity, i.e., the signal to noise ratio (SNR) of position measurements [4]. Both the stochastic cooling scheme of Ref.…”

Continuous quantum measurement of a Bose-Einstein condensate: A stochastic Gross-Pitaevskii equation

“…As we will see in this paper, the effect of the measurement can also be intentionally amplified to allow for unusual manipulation of the condensate itself. Dispersive imaging, in its more idealized form, is preserving the number of atoms and therefore represent a particular example of quantum nondemolition (QND) measurement [2,15,16]. We know that even quantum nondemolition measurements affect the state of the observed system, their unique feature being that the nondemolitive observable maintains the same average value, albeit the probability distribution of its outcome can be affected as well as the average values of all the conjugate observables.…”

Measuring a Photonic Qubit without Destroying It

“…A quantum non-demolition (QND) scheme seeks to make a measurement such that this inherent back-action feeds only into unwanted observables [1,2]. Such a measurement should satisfy the following criteria [3]: (1) The measurement outcome is correlated with the input; (2) The measurement does not alter the value of the measured observable; and (3) Repeated measurement yields the same result -quantum state preparation (QSP).…”