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Advances in Photonics of Quantum Computing, Memory, and Communication

Time dependent metrology: improving precision through coherent control

Andrew N. Jordan

Published Mar 4, 2019• 0 citations
Publisher

Abstract

This paper will overview recent progress in time-dependent metrology. By applying coherent control to a quantum system, we will demonstrate that the amount of information about a parameter can be increased by typically a power law in the duration time of the experiment. Several examples will be given: measurement of an external oscillation frequency, the Landau-Zehner transition, and the details of a recent experiment realizing these physical predictions. A simple example will be analyzed in detail to illustrate the ingredients of the theory.

DOI
10.1117/12.2514947

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This paper will overview recent progress in time-dependent metrology. By applying coherent control to a quantum system, we will demonstrate that the amount of information about a parameter can be increased by typically a power law in the duration time of the experiment. Several examples will be given: measurement of an external oscillation frequency, the Landau-Zehner transition, and the details of a recent experiment realizing these physical predictions. A simple example will be analyzed in detail to illustrate the ingredients of the theory.
We investigate the fundamental limits in precision allowed by quantum mechanics from Landau-Zener transitions, concerning Hamiltonian parameters. While the Landau-Zener transition probabilities depend sensitively on the system parameters, much more precision may be obtained using the acquired phase, quantified by the quantum Fisher information. This information scales with a power of the elapsed time for the quantum case, whereas it is time independent if the transition probabilities alone are used. We add coherent control to the system and increase the permitted maximum precision in this time-dependent quantum system. The case of multiple passes before measurement, Landau-Zener-Stueckelberg interferometry, is considered, and we demonstrate that proper quantum control can cause the quantum Fisher information about the oscillation frequency to scale as T4{T}^{4}T4, where TTT is the elapsed time. These results are foundational for frequency standards and quantum clocks.
Precision measurements of frequency are critical to accurate time keeping and are fundamentally limited by quantum measurement uncertainties. While for time-independent quantum Hamiltonians the uncertainty of any parameter scales at best as 1/T, where T is the duration of the experiment, recent theoretical works have predicted that explicitly time-dependent Hamiltonians can yield a 1/T^{2} scaling of the uncertainty for an oscillation frequency. This quantum acceleration in precision requires coherent control, which is generally adaptive. We experimentally realize this quantum improvement in frequency sensitivity with superconducting circuits, using a single transmon qubit. With optimal control pulses, the theoretically ideal frequency precision scaling is reached for times shorter than the decoherence time. This result demonstrates a fundamental quantum advantage for frequency estimation.
Quantum metrology leverages the unique properties of quantum systems to enhance parameter estimation beyond classical limits. In this short review, we introduce the core concepts of quantum metrology, with a particular focus on its extension to multi-parameter estimation. We begin by outlining the foundational principles of quantum metrology and explore how quantum criticality can enhance measurement precision — especially near quantum phase transitions, where systems exhibit heightened sensitivity to external perturbations. Next, we consider the framework of multi-parameter quantum critical metrology, in which the simultaneous estimation of multiple parameters near criticality can lead to further improvements in accuracy. Finally, we discuss measurement-induced phase transitions, a phenomenon emerging in the context of continuous quantum measurements that introduces non-Hermitian dynamics and fundamentally alters the system’s behavior. This review provides a concise overview of these key developments and highlights their significance for future progress in quantum sensing technologies.
Recently new approaches for sensing the frequency of time dependent Hamiltonians have been presented, and it was shown that the optimal Fisher information scales as T4.{T}^{4}.T4. We present here our interpretation of this new scaling, where the relative phase is accumulated quadratically with time, and show that this can be produced by a variety of simple pulse sequences. Interestingly, this scaling has a limited duration, and we show that certain pulse sequences prolong the effect. The performance of these schemes is analyzed and we examine their relevance to state-of-the-art experiments. We analyze the T3{T}^{3}T3 scaling of the Fisher information which appears when multiple synchronized measurements are performed, and is the optimal scaling in the case of a finite coherence time.
Quantum metrology is supposed to significantly improve the precision of parameter estimation by utilizing suitable quantum resources. However, the predicted precision can be severely distorted by realistic noises. Here, we propose a control-enhanced quantum metrology scheme to defend against these noises to improve the metrology performance. Our scheme can automatically alter the parameter-encoding dynamics with adjustable controls, thus leading to optimal resultant states that are less sensitive to the noises under consideration. As a demonstration, we numerically apply it to the problem of frequency estimation under several typical Markovian noise channels. By comparing our control-enhanced scheme with the standard scheme and the ancilla-assisted scheme, we show that our scheme performs better and can improve the estimation precision up to around one order of magnitude. Furthermore, we conduct a proof-of-principle experiment in a nuclear magnetic resonance system to verify the effectiveness of the proposed scheme. The research here is helpful for current quantum platforms to harness the power of quantum metrology in realistic noise environments.
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