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arXiv:2212.08523 · Physical Review A

Enhancing precision of atomic clocks by tuning disorder in accessories

Aparajita Bhattacharyya, Ahana Ghoshal, Ujjwal Sen

Published Jul 26, 2024• 7 citations
arXivHTMLPDF

Abstract

We find that a quantum device having an accessory involving precision measurement can have an enhancement of its metrological precision in estimating an unknown parameter of the quantum system by insertion of glassy disorder, accidental or engineered. We clearly mention how an unbiased estimator can also be identified in a disordered situation and how the precision thereof can be bounded by the quantum Cr\'amer-Rao inequality. We compare the Fisher information-based lower bound of the minimum standard deviation of an unbiased estimator, in the presence of glassy disorder in the system, with the same of an ideal, viz. disorder-free, situation. The phenomenon can boost the efficiency of certain measuring devices, such as atomic clocks. The precision of these clocks, when measuring time, hinges on the precise determination of the frequency of a two-level atom. In cases where impurities are present in the atom, and can be modeled as a disorder parameter, it is possible for the measurement of frequency to be more accurate than in an ideal, disorder-free scenario. Moreover, disorder insertion can reduce the requirement of entanglement content of the initial probes, which are copies of two-qubit states, along with providing a disorder-induced enhancement.

DOI
10.1103/physreva.110.012620

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We find that a quantum device having an accessory involving precision measurement can have an enhancement of its metrological precision in estimating an unknown parameter of the quantum system by insertion of glassy disorder, accidental or engineered. We clearly mention how an unbiased estimator can also be identified in a disordered situation and how the precision thereof can be bounded by the quantum Cr'amer-Rao inequality. We compare the Fisher information-based lower bound of the minimum standard deviation of an unbiased estimator, in the presence of glassy disorder in the system, with the same of an ideal, viz. disorder-free, situation. The phenomenon can boost the efficiency of certain measuring devices, such as atomic clocks. The precision of these clocks, when measuring time, hinges on the precise determination of the frequency of a two-level atom. In cases where impurities are present in the atom, and can be modeled as a disorder parameter, it is possible for the measurement of frequency to be more accurate than in an ideal, disorder-free scenario. Moreover, disorder insertion can reduce the requirement of entanglement content of the initial probes, which are copies of two-qubit states, along with providing a disorder-induced enhancement.
Abstract This letter shows how incoherent dynamics can lead to metrological advantages in quantum sensing. The results rely on the fact that incoherent dynamics lead to an additive contribution to the quantum Fisher information about time. Such an additive contribution can reduce the error of optimal estimation protocols, as implied by the quantum Cramér–Rao bound. I characterize regimes in which the estimation of a time interval or a frequency is enhanced by decoherence, thereby identifying cases in which incoherent dynamics serve as a metrological resource. The decoherence processes that yield enhanced precision of quantum sensors can be engineered by randomized Hamiltonian dynamics. I illustrate the results with protocols that display improved sensing of time intervals or global fields by qubit and photonic sensors. Enhanced precision of time intervals is achieved with Hamiltonians that include randomized global parameters. Enhanced precision in field estimation is obtained by randomized sensing times.
Disorder is ubiquitous in quantum devices including quantum probes designed and fabricated for quantum parameter estimation and sensing. We investigate the robustness of a quantum probe against the presence of glassy disorder. We define a disorder marker quantifying the effect of the disorder by expanding the quantum Fisher information in terms of different orders of the standardized central moments of the disorder-distributions. We classify the quantum probes in terms of the possible values of the disorder marker, and analytically show, for a disorder-sensitive probe with identical and weak disorder on all or a subset of the parameters of the probe-Hamiltonian, that the absolute value of the disorder marker exhibits a quadratic dependence on the disorder strength. We derive a robustness scale intrinsic to the probe that competes with the disorder, and provide a prescription for estimating the maximum disorder strength that the probe can withstand from the disorder-free probe-Hamiltonian for a given initial state of the probe, which can be computed without the disorder averaging. We demonstrate our results in the case of a single-qubit probe under disordered magnetic field, and a multi-qubit probe described by a disordered one-dimensional Kitaev model with nearest-neighbor interactions.
This is a tutorial aimed at illustrating some recent developments in quantum parameter estimation beyond the Cramèr–Rao bound, as well as their applications in quantum metrology. Our starting point is the observation that there are situations in classical and quantum metrology where the unknown parameter of interest, besides determining the state of the probe, is also influencing the operation of the measuring devices, e.g. the range of possible outcomes. In those cases, nonregular statistical models may appear, for which the Cramèr–Rao theorem does not hold. In turn, the achievable precision may exceed the Cramèr–Rao bound, opening new avenues for enhanced metrology. We focus on quantum estimation of Hamiltonian parameters and show that an achievable bound to precision (beyond the Cramèr–Rao) may be obtained in a closed form for the class of so-called controlled energy measurements. Examples of applications of the new bound to various estimation problems in quantum metrology are worked out in some details.
This is a tutorial aimed at illustrating some recent developments in quantum parameter estimation beyond the Cramèr–Rao bound, as well as their applications in quantum metrology. Our starting point is the observation that there are situations in classical and quantum metrology where the unknown parameter of interest, besides determining the state of the probe, is also influencing the operation of the measuring devices, e.g. the range of possible outcomes. In those cases, nonregular statistical models may appear, for which the Cramèr–Rao theorem does not hold. In turn, the achievable precision may exceed the Cramèr–Rao bound, opening new avenues for enhanced metrology. We focus on quantum estimation of Hamiltonian parameters and show that an achievable bound to precision (beyond the Cramèr–Rao) may be obtained in a closed form for the class of so-called controlled energy measurements. Examples of applications of the new bound to various estimation problems in quantum metrology are worked out in some details.
While quantum metrology enables measurement precision beyond classical limits, its performance is often susceptible to experimental imperfections. Most prior studies have focused on imperfections in quantum states and operations. Here, we investigate the effect of coarse graining in quantum measurement through both theoretical analysis and experimental demonstration. Using an interferometer with a squeezed vacuum and a laser input, we analyze how coarse graining in homodyne detection affects the precision of phase estimation. We evaluate the Fisher information under various coarse-graining conditions and determine, in each case, an optimal estimation strategy that saturates the Cramér-Rao bound. Remarkably, even extremely coarse-grained measurement -- with only two bins -- enables phase estimation beyond the standard quantum limit and even achieves a precision that follows the Heisenberg scaling. We experimentally demonstrate quantum-enhanced phase estimation under coarse-grained homodyne detection. To determine an optimal estimation strategy, we employ the method of moments and present calibration procedures that enable its application to general experimental settings. Using only two bins, we observe a quantum enhancement of 1.2 dB compared to the classical method using the ideal measurement, improving towards 3.8 dB as the bin number increases. These results highlight a practical pathway to achieving quantum enhancement under the presence of severe experimental imperfections.
A usual assumption in quantum estimation is that the unknown parameter labels the possible states of the system, while it influences neither the sample space of outcomes nor the measurement aimed at extracting information on the parameter itself. This assumption is crucial to prove the quantum Cram\'er-Rao theorem and to introduce the quantum Fisher information as an upper bound to the Fisher information of any possible measurement. However, there are relevant estimation problems where this assumption does not hold and an alternative approach should be developed to find the genuine ultimate bound to precision of quantum measurements. We investigate physical situations where there is an intrinsic dependence of the measurement strategy on the parameter and find that quantum-enhanced measurements may be more precise than previously thought.