Quantum metrology is the science that aims to achieve precision measurements by making use of quantum principles. Attribute to the well-developed techniques of manipulating and detecting cold atoms, cold atomic systems provide an excellent platform for implementing precision quantum metrology. In this chapter, we review the general procedures of quantum metrology and some experimental progresses in quantum metrology with cold atoms. Firstly, we give the general framework of quantum metrology and the calculation of quantum Fisher information, which is the core of quantum parameter estimation. Then, we introduce the quantum interferometry with single and multiparticle states. In particular, for some typical multiparticle states, we analyze their ultimate precision limits and show how quantum entanglement could enhance the measurement precision beyond the standard quantum limit. Further, we review some experimental progresses in quantum metrology with cold atomic systems.
Quantum metrology is the science that aims to achieve precision measurements by making use of quantum principles. Attribute to the well-developed techniques of manipulating and detecting cold atoms, cold atomic systems provide an excellent platform for implementing precision quantum metrology. In this chapter, we review the general procedures of quantum metrology and some experimental progresses in quantum metrology with cold atoms. Firstly, we give the general framework of quantum metrology and the calculation of quantum Fisher information, which is the core of quantum parameter estimation. Then, we introduce the quantum interferometry with single and multiparticle states. In particular, for some typical multiparticle states, we analyze their ultimate precision limits and show how quantum entanglement could enhance the measurement precision beyond the standard quantum limit. Further, we review some experimental progresses in quantum metrology with cold atomic systems.
Entanglement-enhanced quantum metrology explores the utilization of quantum entanglement to enhance measurement precision. When particles in a probe are prepared into a suitable quantum entangled state, they may collectively accumulate information about the physical quantity to be measured, leading to an improvement in measurement precision beyond the standard quantum limit and approaching the Heisenberg limit. The rapid advancement of techniques for quantum manipulation and detection has enabled the generation, manipulation, and detection of multi-particle entangled states in synthetic quantum systems such as cold atoms and trapped ions. This article aims to review and illustrate the fundamental principles and experimental progresses that demonstrate multi-particle entanglement for quantum metrology, as well as discuss the potential applications of entanglement-enhanced quantum sensors.
Quantum metrology is the interdisciplinary of investigating how to utilize the principles of quantum mechanics to perform parameter estimation and improve the measurement precision by quantum effects. With the experimental developments of ultracold atoms, ultracold atomic ensemble provides an excellent platform for implementing quantum metrology. Attributed to well-developed techniques of quantum control, one can prepare several exotic non-Gaussian multi-particle entangled states in the ensembles of ultracold atoms. Based on many-body quanum interferometry, and using these non-Gaussian entangled states as probe, the high-precision measurement beyond the standard quantum limit can be realized. This article introduces the background and advancement of this field.
Quantum entanglement offers powerful opportunities for enhancing measurement sensitivity beyond classical limits, with optical atomic clocks serving as a leading platform for such advances. This chapter introduces the principles of entanglement-enhanced quantum metrology and explores their applications to timekeeping. We review the theoretical framework of quantum phase estimation, comparing frequentist and Bayesian approaches, and discuss paradigmatic entangled states such as spin-squeezed and GHZ states. Particular emphasis is placed on the challenges posed by decoherence, which constrain the practical advantages that can be realized in large-scale devices. The discussion then turns to frequency estimation in atomic clocks, highlighting how experimental constraints shape the translation of abstract quantum limits into real performance gains. Finally, we outline emerging directions of contemporary quantum metrology. Together, these developments underscore the increasingly close interplay between quantum information processing and precision metrology.
We summarise important recent advances in quantum metrology, in connection to experiments in cold gases, trapped cold atoms and photons. First we review simple metrological setups, such as quantum metrology with spin squeezed states, with Greenberger-Horne-Zeilinger states, Dicke states and singlet states. We calculate the highest precision achievable in these schemes. Then, we present the fundamental notions of quantum metrology, such as shot-noise scaling, Heisenberg scaling, the quantum Fisher information and the Cram´er-Rao bound. Using these, we demonstrate that entanglement is needed to surpass the shot-noise scaling in very general metrological tasks with a linear interferometer. We discuss some applications of the quantum Fisher information, such as how it can be used to obtain a criterion for a quantum state to be a macroscopic superposition. We show how it is related to the the speed of a quantum evolution, and how it appears in the theory of the quantum Zeno effect. Finally, we explain how uncorrelated noise limits the highest achievable precision in very general metrological tasks.
We summarize important recent advances in quantum metrology, in connection to experiments in cold gases, trapped cold atoms and photons. First we review simple metrological setups, such as quantum metrology with spin squeezed states, with Greenberger–Horne–Zeilinger states, Dicke states and singlet states. We calculate the highest precision achievable in these schemes. Then, we present the fundamental notions of quantum metrology, such as shot-noise scaling, Heisenberg scaling, the quantum Fisher information and the Cramér–Rao bound. Using these, we demonstrate that entanglement is needed to surpass the shot-noise scaling in very general metrological tasks with a linear interferometer. We discuss some applications of the quantum Fisher information, such as how it can be used to obtain a criterion for a quantum state to be a macroscopic superposition. We show how it is related to the speed of a quantum evolution, and how it appears in the theory of the quantum Zeno effect. Finally, we explain how uncorrelated noise limits the highest achievable precision in very general metrological tasks. This article is part of a special issue of Journal of Physics A: Mathematical and Theoretical devoted to '50 years of Bell's theorem'.
The measurement of physical quantities and measurement units standard promote the development of metrology. Especially, the developments of laser interference and atomic frequency standard bring a revolutionary leap for metrology. Many precision measurement techniques have been proposed and experimentally demonstrated, such as gravitational wave measurements and laser gyroscopes based on laser interferometry, and atomic clocks and atomic gyroscopes based on the atom interferometry. Recently, a new branch of science, quantum metrology, has grown up to further explore and exploit the quantum techniques for precision measurement of physical quantities.#br#This paper will focus on recent developments in quantum metrology and interference based on coherence and correlation of light and atom. Firstly, we briefly review the development of metrology. Then, we introduce our own researches in recent years, including quantum-correlation SU(1,1) optical interferometer based on four wave mixing process in atomic vapor and the atom-light hybrid interferometer based on Raman scattering in atomic vapor.#br#Interferometer is a powerful tool to measure physical quantities sensitive to the inference wave with high precision, and has been widely used in scientific research, industry test, navigation and guidance system. For example, the laser interferometer is able to measure optical phase sensitive quantities, including length, angular velocity, gravitational wave and so on. Meanwhile, the atom interferometer is sensitive to the change of atomic phase caused by the light, gravity, electric and magnetic fields. As a new type of interferometry, the atom-light hybrid interferometer, is sensitive to both the optical phase and atomic phase. Furthermore, SU(1,1) interferometer and nonlinear atom-light hybrid interferometer have the ability to beat the standard quantum limit of phase sensitivity. Quantum interference technology, whose phase measurement accuracy can break through the limit of standard quantum limit, is the core of quantum metrology and quantum measurement technology.