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arXiv:1305.1051

Coherently enhanced measurements in classical mechanics

Daniel Braun, Sandu Popescu

Published May 5, 2013• 0 citations
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Abstract

We show that the recently discovered quantum-enhanced measurement protocol of coherent averaging that is capable of achieving Heisenberg-limited sensitivity without using entanglement, has a classical analogue. The classical protocol uses N harmonic oscillators coupled to a central oscillator and one measures the signal from the latter. We propose an application to the measurement of very weak interactions, and, in particular, a novel route to measuring the gravitational constant with enhanced precision.

DOI
10.48550/arxiv.1305.1051

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We show that the recently discovered quantum-enhanced measurement protocol of coherent averaging that is capable of achieving Heisenberg-limited sensitivity without using entanglement, has a classical analogue. The classical protocol uses N harmonic oscillators coupled to a central oscillator and one measures the signal from the latter. We propose an application to the measurement of very weak interactions, and, in particular, a novel route to measuring the gravitational constant with enhanced precision.
Abstract In all quantitative sciences, it is common practice to increase the signal-to-noise ratio of noisy measurements by measuring identically prepared systems N times and averaging the measurement results. This leads to a scaling of the sensitivity as 1/√N, known in quantum measurement theory as the “standard quantum limit” (SQL). It is known that if one puts the N systems into an entangled state, a scaling as 1/N can be achieved, the socalled “Heisenberg limit” (HL), but decoherence problems have so far prevented implementation of such protocols for large N. Here we show that a method of coherent averaging inspired by a recent entanglement-free quantum enhanced measurement protocol is capable of achieving a sensitivity that scales as 1/N in a purely classical setup. This may substantially improve the measurement of very weak interactions in the classical realm, and, in particular, open a novel route to measuring the gravitational constant with enhanced precision.
We propose a sensing scheme for detecting weak forces that achieves Heisenberg-limited sensitivity without relying on entanglement or other non-classical resources. Our scheme utilizes coherent averaging across a chain of N optomechanical cavities, unidirectionally coupled via a laser beam. As the beam passes through the cavities, it accumulates phase shifts induced by a common external force acting on the mechanical elements. Remarkably, this fully classical approach achieves the sensitivity scaling typically associated with quantum-enhanced protocols, providing a robust and experimentally feasible route to precision sensing. Potential applications range from high-sensitivity gravitational field measurements at the Large Hadron Collider to probing dark matter interactions and detecting gravitational waves. This work opens a new pathway for leveraging coherent light-matter interactions for force sensing.
We investigate in detail a recently introduced “coherent averaging scheme” in terms of its usefulness for achieving Heisenberg limited sensitivity in the measurement of different parameters. In the scheme, N quantum probes in a product state interact with a quantum bus. Instead of measuring the probes directly and then averaging as in classical averaging, one measures the quantum bus or the entire system and tries to estimate the parameters from these measurement results. Combining analytical results from perturbation theory and an exactly solvable dephasing model with numerical simulations, we draw a detailed picture of the scaling of the best achievable sensitivity with N , the dependence on the initial state, the interaction strength, the part of the system measured, and the parameter under investigation. In particular, we identify the situations allowing one to reach Heisenberg‐limited scaling of the sensitivity.
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]
The limitations of the detectability of extremely weak signals (gravitational radiation for instance) imposed by Heisenberg's uncertainty principle on the sequential determination of those signals have been explored recently. A variety of schemes have been proposed to circumvent these limitations. Although all of the earlier attempts have been proven fruitless a recent proposal seems to be quite promising. The scheme, consisting of two harmonic oscillators interacting with each other in a peculiar way, allows for an exact analytical solution which is derived here. If it can be assumed that the expectation value of one of the canonical variables of the total system suffices to monitor the weak signal it can be shown that, in the absence of thermal noise, arbitrarily weak signals can in principle be measured without interference from the uncertainty principle.
We present an enhanced entangled-quantum-clock protocol that incorporates a quantum phase estimation algorithm to directly estimate proper-time differences as an unknown phase. By employing highly entangled multi-clock states, the achievable uncertainty scales inversely with the total number of quantum clocks, achieving the Heisenberg limit O(1/N)O(1/N)O(1/N) while remaining completely immune to dynamical phase noise. Furthermore, we discuss the feasibility of utilizing this ultra-high precision protocol for gravitational wave detection, highlighting its potential for quantum-enhanced relativistic sensing and fundamental physics tests.