Given a physical setup, what is the precision that can be obtained? In this paper, we firstly review the recently theoretical developments about the quantum parameter estimation. The measurement sensitivity can be improved from the Heisenberg limit (HL) to super-Heisenberg limit (SHL) by changing the coupling Hamiltonian from linear to nonlinear. Then we review some techniques which have been used to break through the standard quantum limit (SQL) and reach the HL in optical quantum metrology, and describe the experiment of nonlinear quantum metrology where the interaction among particles as a valuable resource can contribute to measurement sensitivity and give scaling beyond the HL. Finally, we introduce a potential new approach to the future developments of quantum metrology.
Given a physical setup, what is the precision that can be obtained? In this paper, we firstly review the recently theoretical developments about the quantum parameter estimation. The measurement sensitivity can be improved from the Heisenberg limit (HL) to super-Heisenberg limit (SHL) by changing the coupling Hamiltonian from linear to nonlinear. Then we review some techniques which have been used to break through the standard quantum limit (SQL) and reach the HL in optical quantum metrology, and describe the experiment of nonlinear quantum metrology where the interaction among particles as a valuable resource can contribute to measurement sensitivity and give scaling beyond the HL. Finally, we introduce a potential new approach to the future developments of quantum metrology.
Quantum metrology studies the use of entanglement and other quantum resources to improve precision measurement. An interferometer using N independent particles to measure a parameter χ can achieve at best the "standard quantum limit" (SQL) of sensitivity δχ ∝ N-1/2. The same interferometer using N entangled particles can achieve in principle the "Heisenberg limit" δχ ∝ N-1, using exotic states, e.g., NooN states. Recent theoretical work argues that interactions among particles may be a valuable resource for quantum metrology, allowing scaling beyond the Heisenberg limit. Specifically, a k-particle interaction will produce sensitivity δχ ∝ N-kwith appropriate entangled states and δχ ∝ N-(k-1/2)even without entanglement. Here we demonstrate this "super-Heisenberg" scaling in a nonlinear, non-destructive measurement of the magnetisation of an atomic ensemble.
Abstract The Heisenberg limit is acknowledged as the ultimate precision limit for parameter estimation in quantum metrology. Recent studies have demonstrated super-Heisenberg-scaling limits, where the root mean square errors of estimation decrease faster-than-linearly with the number of probes or evolution processes. This casts doubt on what the ultimate precision limit of quantum metrology really is and, in particular, whether there is a deeper connection with Heisenberg's uncertainty principle. By linking the dynamics of the metrological process with properties in parameter space, we construct a Heisenberg's uncertainty relation between the unknown parameter and its canonical momentum. We propose a novel quantum metrological scheme that utilizes a generating process with indefinite time direction to increase the canonical momentum nonlinearly. This approach achieves a nonlinear-scaling precision limit that improves quadratically with the increase in evolution time length or the number of processes, in accordance with Heisenberg's uncertainty relation. Then we experimentally demonstrate in quantum optical systems that this nonlinear-scaling enhancement can be achieved with a fixed amount of energy in the probes. Consequently, our results provide a deeper insight into the Heisenberg limit in quantum metrology, and shed new light on improving the precision of practical metrological and sensing tasks in realistic quantum systems.
Questions about quantum limits on measurement precision were once viewed from the perspective of how to reduce or avoid the effects of quantum noise. With the advent of quantum information science came a paradigm shift to proving rigorous bounds on measurement precision. These bounds have been interpreted as saying, first, that the best achievable sensitivity scales as 1/n, where n is the number of particles one has available for a measurement and, second, that the only way to achieve this Heisenberg-limited sensitivity is to use quantum entanglement. We review these results and show that using quadratic couplings of n particles to a parameter to be estimated, one can achieve sensitivities that scale as 1/n^2 if one uses entanglement, but even in the absence of any entanglement at any time during the measurement protocol, one can achieve a super-Heisenberg scaling of 1/n^(3/2)
Quantum precision measurement is based on the basic principle of quantum mechanics by using the interaction between light, atoms and magnetism to measure physical quantities, also known as precision measurements based on microscopic particle systems and their quantum states. As an important means of quantum precision measurement, interferometer precision measurement technology has great application value in quantum communication. The linear interferometer measures the magnitude of the physical quantity by using the phase change obtained from the measurements, but measurement accuracy is limited and unable to meet the requirements of today's scientific problems for the precision measurement of some physical quantities. On this basis, nonlinear interferometer is able to take advantage of the quantum entangled state, that is, using the two light fields of quantum correlation characteristics to realize quantum enhanced precision measurement, thus greatly improving the measurement sensitivity, Therefore, the scope of application is wider, but the preparation of quantum entangled states has many limitations in practical manipulation. With the maturity of experimental conditions and technology, how to use both of these interferometers to further improve the measurement accuracy of the phase signal so as to break the limitation to shot noise, breaking the standard quantum limit and even approaching to the Heisenberg limit has become a frontier research topic . In this paper, we introduce several methods to improve the accuracy of parameter evaluation in the measurement process by using linear (including an atomic/photon interferometer) and nonlinear interferometer to call quantum resources at different stages. High-precision measurement can be achieved by inputting non-classical states into the interferometer, such as compressed state, bi-fock state, and NOON state. And we also introduce the weak measurement developed for the direct observation of quantum states and its application to non-Hermitian systems, and the multiparameter measurement proposed to eliminate the accuracy balance between parameters. Compared with the first two measurement methods, weak measurement method is based on the weak value amplification principle of an indirect measurement. Measurements are performed virtually without perturbing the quantum system, which does not lead the wave function to collapse, the weak value of the real and virtual part have different physical significance, The combination of weak measurement theory and non-Hermitian system also further improves the measurement sensitivity. Multi-parameter measurement uses quantum entanglement, quantum control and other quantum resources to make the measurement progress reach the Heisenberg limit, which is the current research hotspot in the field of precision measurement. Furthermore, we present a conjecture whether there will be multi-atomic mixing measurements based on atomic spin effects or ultra-high sensitivity measurement instruments with precision of fT or even aT by using other particles detection. Finally, several measurement methods are analyzed and compared with each other, and the development prospect of quantum precision measurement is forecasted.
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.
Nonlinear interactions are recognized as potential resources for quantum metrology, facilitating parameter estimation precisions that scale as the exponential Heisenberg limit of ${2}^{\ensuremath{-}N}$. We explore such nonlinearity and propose an associated quantum measurement scenario based on the nonlinear interaction of N-probe entanglement-generating form. This scenario provides an enhanced precision scaling of ${D}^{\ensuremath{-}N}/(N\ensuremath{-}1)!$ with D>2 a tunable parameter. In addition, it can be readily implemented in a variety of experimental platforms and applied to measurements of a wide range of quantities, including local gravitational acceleration g, magnetic field, and its higher-order gradients.