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Journal of Physics Conference Series

Quantum measurement limits to clock precision

Gerard J Milburn, Michael J. Kewming

Published Nov 1, 2024• 0 citations
Publisher

Abstract

Abstract The role of projection noise, an example of quantum measurement noise, in clock design has been well understood for some time. It is based on a particular measurement protocol — Ramsey interferometry. In this paper we discuss more general quantum measurement schemes to estimate the period/frequency of a clock system based on continuous readout of a driven quantum system. The measurement needs to be chosen so as to provide a precise counting signal. We give an example based on a superconducting circuit clock.

DOI
10.1088/1742-6596/2889/1/012060

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Abstract The role of projection noise, an example of quantum measurement noise, in clock design has been well understood for some time. It is based on a particular measurement protocol — Ramsey interferometry. In this paper we discuss more general quantum measurement schemes to estimate the period/frequency of a clock system based on continuous readout of a driven quantum system. The measurement needs to be chosen so as to provide a precise counting signal. We give an example based on a superconducting circuit clock.
We theoretically and experimentally study the precision of a quantum clock near zero temperature, explicitly accounting for the effect of continuous measurement. The clock is created by a superconducting transmon qubit dispersively coupled to an open coplanar resonator. The cavity and qubit are driven by coherent fields, and the cavity output is monitored with a quantum-noise-limited amplifier. When the continuous measurement is weak, it induces persistent coherent oscillations (with fluctuating periods) in the conditional moments of the qubit's energy probability distribution, which are manifest in the output of the resonator. On the other hand, strong continuous measurement leads to an incoherent cycle of quantum jumps. We theoretically find an equality for the precision of the clock in each regime. Independently from the equalities, we derive a kinetic uncertainty relation for the precision, and find that both equalities satisfy this uncertainty relation. Finally, we experimentally verify that our quantum clock obeys the kinetic uncertainty relation for the precision, thus making an explicit link between the (kinetic) thermodynamic behavior of the clock and its precision, and achieving an experimental test of a kinetic uncertainty relation in the quantum domain.
We investigate the ultimate quantum limits to the achievable uncertainty in the estimation of the transition frequency between two atomic levels. We focus on Rabi, Ramsey, and coherent-population-trapping (CPT) techniques, which are widely employed in experiments. We prove that in the Rabi and Ramsey schemes, measuring the atomic population allows one to reach the minimum uncertainty, but for the CPT setup, a measurement involving the coherences between the levels results in a further improvement of the estimation. As a paradigmatic example of possible noises, the effect of cavity coupling fluctuations is considered in the Rabi and Ramsey scenarios. As a figure of merit, we assess the Fisher information of the population measurement and compare its value with the maximum one given by the quantum Fisher information, which is achieved by optimizing over all the possible measurements allowed by quantum mechanics.
Frequency metrology is a cornerstone of modern precision measurements and optical atomic clocks have emerged as one of the most precise measurement devices. In this progress report, we explore various Ramsey interrogation schemes tailored to optical atomic clocks primarily limited by laser noise. To incorporate frequency fluctuations directly into the theoretical model, we consider a Bayesian framework. In this context, we review fundamental bounds arising in Bayesian estimation theory, which serve as a benchmark throughout this work. We investigate the trade-off between entanglement-enhanced sensitivity and robustness against laser noise in order to identify optimal initial states, measurement schemes and estimation strategies. Beside standard protocols based on coherent spin states, spin-squeezed states and Greenberger-Horne-Zeilinger states, we consider variational Ramsey protocols implemented via low-depth quantum circuits based on one-axis twisting operations to approach optimal stability. In particular, we review known and identify new optimal Ramsey interrogation schemes for a variety of scenarios, including different experimental platforms, ensemble sizes and regimes characterized by a wide range of interrogation durations and dead times. Hence, this work establishes a comprehensive theoretical framework for optimizing Ramsey interrogation schemes, providing guidance for the development of next-generation optical atomic clocks.
A driven linear oscillator and a feedback mechanism are two necessary elements of any classical periodic clock. Here, we introduce a fully quantum clock using a driven oscillator in the quantum regime and coherent quantum feedback. We show that if we treat the model semiclassically, this system supports limit cycles, or self-sustained oscillations, as needed for a periodic clock. We then analyze the noise of the system quantum mechanically and prove that the accuracy of this clock is higher compared with the clock implemented with the classical measurement feedback. We experimentally implement the model using two superconducting cavities with incorporated Josephson junctions and microwave circulators for the realization of the quantum feedback. We confirm the appearance of the limit cycle and study the clock accuracy both in frequency and time domains. Under specific conditions of noisy driving, we observe that the clock oscillations are more coherent than the drive, pointing towards the implementation of a quantum autonomous clock.
Abstract The frequency stability of many optical atomic clocks is limited by the coherence of their local oscillator. Here, we present a measurement protocol that overcomes the laser coherence limit. It relies on engineered dynamical decoupling of laser phase noise and near-synchronous interrogation of two clocks. One clock coarsely tracks the laser phase using dynamical decoupling; the other refines this estimate using a high-resolution phase measurement. While the former needs to have a high signal-to-noise ratio, the latter clock may operate with any number of particles. The protocol effectively enables minute-long Ramsey interrogation for coherence times of few seconds as provided by the current best ultrastable laser systems. We demonstrate implementation of the protocol in a realistic proof-of-principle experiment, where we interrogate for 0.5 s at a laser coherence time of 77 ms. Here, a single lattice clock is used to emulate synchronous interrogation of two separate clocks in the presence of artificial laser frequency noise. We discuss the frequency instability of a single-ion clock that would result from using the protocol for stabilisation, under these conditions and for minute-long interrogation, and find expected instabilities of σy(τ) = 8 × 10−16(τ/s)−1/2 and σy(τ) = 5 × 10−17(τ/s)−1/2, respectively.