Entanglement is recognized as a key resource for quantum computation and quantum cryptography. For quantum metrology, the use of entangled states has been discussed and demonstrated as a means of improving the signal-to-noise ratio. In addition, entangled states have been used in experiments for efficient quantum state detection and for the measurement of scattering lengths. In quantum information processing, manipulation of individual quantum bits allows for the tailored design of specific states that are insensitive to the detrimental influences of an environment. Such 'decoherence-free subspaces' protect quantum information and yield significantly enhanced coherence times. Here we use a decoherence-free subspace with specifically designed entangled states to demonstrate precision spectroscopy of a pair of trapped Ca+ ions; we obtain the electric quadrupole moment, which is of use for frequency standard applications. We find that entangled states are not only useful for enhancing the signal-to-noise ratio in frequency measurements - a suitably designed pair of atoms also allows clock measurements in the presence of strong technical noise. Our technique makes explicit use of non-locality as an entanglement property and provides an approach for 'designed' quantum metrology.
We describe nonlinear quantum atom-light interfaces and nonlinear quantum metrology in the collective continuous variable formalism. We develop a nonlinear effective Hamiltonian in terms of spin and polarization collective variables and show that model Hamiltonians of interest for nonlinear quantum metrology can be produced in $^{87}$Rb ensembles. With these Hamiltonians, metrologically relevant atomic properties, e.g. the collective spin, can be measured better than the "Heisenberg limit" $\propto 1/N$. In contrast to other proposed nonlinear metrology systems, the atom-light interface allows…
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. T…
Precision metrology and quantum measurement often demand matter be prepared in well defined quantum states for both internal and external degrees of freedom. Laser-cooled neutral atoms localized in a deeply confining optical potential satisfy this requirement. With an appropriate choice of wavelength and polarization for the optical trap, two electronic states of an atom can experience the same trapping potential, permitting coherent control of electronic transitions independent of the atomic center-of-mass motion. We review a number of recent experiments that use this approach to investigate …
We use a small atomic Bose-Einstein condensate as an interferometric scanning probe to map out a microwave field near a chip surface with a few micrometers resolution. Using entanglement between the atoms we overcome the standard quantum limit of interferometry by 4 dB and maintain enhanced performance for interrogation times up to 20 ms. This demonstrates the usefulness of quantum metrology with entangled states when the particle number is limited due to the small probe size. Extending atom interferometry to micrometer spatial resolution enables new applications in electromagnetic field sensi…
We discuss theoretically the ground state of a Bose-Einstein condensate with attractive atom-atom interactions in a double-well trap as a starting point of Heisenberg-limited atom interferometry. The dimensionless parameter governing the quality of the ground state for this purpose is identified. The near-degeneracy between the ground state and the first excited state severely curtails the prospects of the thermally prepared ground state in quantum metrology.
We propose and analyze a probabilistic but heralded scheme to generate pure, entangled, non-Gaussian states of collective spin in large atomic ensembles by means of single-photon detection. One photon announces the preparation of a Dicke state, while two or more photons announce Schrödinger cat states. The method produces pure states even for finite photon detection efficiency and weak atom-photon coupling. The entanglement generation can be made quasi-deterministic by means of repeated trial and feedback, enabling metrology beyond the standard quantum limit.
An entangled state prepared in the decoherence free sub-space together with a Ramsey type measurement can probe parity violation in heavy alkali ions like Ba+ or Ra+. Here we propose an experiment with Ba+ ions as an example to measure the small parity violating effect in this system.
This chapter reviews recent developments in the use of mixed-species ion chains in quantum information science, frequency metrology and spectroscopy. A growing number of experiments have demonstrated new methods in this area, opening up new possibilities for quantum state generation, quantum control of previously inaccessible ions, and the ability to maintain quantum control over extended periods. I describe these methods, providing details of the techniques which are required in order to work with such systems. In addition, I present perspectives on possible future uses of quantum logic spect…
We propose a quantum metrology scheme in a cavity QED setup to achieve the Heisenberg limit. In our scheme, a series of identical two-level atoms randomly pass through and interact with a dissipative single-mode cavity. Different from the entanglement based Heisenberg limit metrology scheme, we do not need to prepare the atomic entangled states before they enter into the cavity. We show that the initial atomic coherence will induce an effective driving to the cavity field, whose steady state is an incoherent superposition of orthogonal states, with the superposition probabilities being depende…
Atom chips provide a versatile `quantum laboratory on a microchip' for experiments with ultracold atomic gases. They have been used in experiments on diverse topics such as low-dimensional quantum gases, cavity quantum electrodynamics, atom-surface interactions, and chip-based atomic clocks and interferometers. A severe limitation of atom chips, however, is that techniques to control atomic interactions and to generate entanglement have not been experimentally available so far. Such techniques enable chip-based studies of entangled many-body systems and are a key prerequisite for atom chip app…
Quantum technologies exploit entanglement to revolutionize computing, measurements, and communications. This has stimulated the research in different areas of physics to engineer and manipulate fragile many-particle entangled states. Progress has been particularly rapid for atoms. Thanks to the large and tunable nonlinearities and the well developed techniques for trapping, controlling and counting, many groundbreaking experiments have demonstrated the generation of entangled states of trapped ions, cold and ultracold gases of neutral atoms. Moreover, atoms can couple strongly to external forc…
Bragg interferometers, operating using pseudospin-1/2 systems composed of two momentum states, have become a mature technology for precision measurements. State-of-the-art Bragg interferometers are rapidly surpassing technical limitations and are soon expected to operate near the projection noise limit set by uncorrelated atoms. Despite the use of large numbers of atoms, their operation is governed by single-atom physics. Motivated by recent proposals and demonstrations of Raman gravimeters in cavities, we propose a scheme to squeeze directly on momentum states for surpassing the projection no…
An entangled state prepared in a decoherence free sub-space together with a Ramsey type measurement can probe parity violation in heavy alkali ions like Ba+ or Ra+. Here we propose an experiment with Ba+ as an example to measure the small parity violating effect in this system. It has been shown that a measurement on a maximally correlated system will reduce the uncertainty as compared to that on a single ion measurement. In addition it also provides a feasible solution to measure the nuclear spin dependent part of the total parity violating light shift in an ionic system which has so far not …
A promising practical application of entanglement is metrology, where quantum states can be used to make measurements beyond the shot noise limit. Here we consider how metrology schemes could be realised using atomic Bose-Einstein condensates (BECs) trapped in different potentials. In particular, we show that if a trapped BEC is rotated at just the right frequency, it can undergo a quantum phase transition characterised by large-scale entanglement spreading across the system. This simple process of stirring can generate interesting quantum states such as macroscopic superpositions of all the a…
In quantum metrology, entanglement represents a valuable resource that can be used to overcome the Standard Quantum Limit (SQL) that bounds the precision of sensors that operate with independent particles. Measurements beyond the SQL are typically enabled by relatively simple entangled states (squeezed states with Gaussian probability distributions), where quantum noise is redistributed between different quadratures. However, due to both fundamental limitations and the finite measurement resolution achieved in practice, sensors based on squeezed states typically operate far from the true funda…
Quantum metrology allows us to attain a measurement precision that surpasses the classically achievable limit by using quantum characters. The metrology precision is raised from the standard quantum limit (SQL) to the Heisenberg limit (HL) by using entanglement. However, it was reported that the HL returns to the SQL in the presence of local dephasing environments under the long encoding-time condition. We evaluate here the exact impacts of local dissipative environments on quantum metrology, based on the Ramsey interferometer. It is found that the HL is asymptotically recovered under the long…
National Institute of Standards and Technology（美国国家标准与技术研究院）；British Columbia Institute of Technology（不列颠哥伦比亚理工学院）；University of Bremen（不来梅大学）；Physikalisch-Technische Bundesanstalt（德国联邦物理技术研究院）；University of Maryland（马里兰大学）；University of British Columbia（不列颠哥伦比亚大学）
Spin Grid States for Quantum Metrology in Atomic Clocks Limited by Spontaneous Emission
Leibniz Universität Hannover（汉诺威莱布尼茨大学）；University of Innsbruck（因斯布鲁克大学）；Institute for Quantum Optics and Quantum Information of the Austrian Academy of Sciences（奥地利科学院量子光学与量子信息研究所）
Spin-polarised atomic ensembles probed by light based on the Faraday interaction are a versatile platform for numerous applications in quantum metrology and quantum information processing. Here we consider an ensemble of Alkali atoms that are continuously optically pumped and probed. Due to the collective scattering of photons at large optical depth, the steady state of atoms does not correspond to an uncorrelated tensor-product state, as is usually assumed. We introduce a self-consistent method to approximate the steady state including the pair correlations, taking into account the multilevel…
We study the impact of many-body effects on the fundamental precision limits in quantum metrology. On the one hand such effects may lead to non-linear Hamiltonians, studied in the field of non-linear quantum metrology, while on the other hand they may result in decoherence processes that cannot be described using single-body noise models. We provide a general reasoning that allows to predict the fundamental scaling of precision in such models as a function of the number of atoms present in the system. Moreover, we describe a computationally efficient approach that allows for a simple derivatio…
We have previously shown that quantum-enhanced atom interferometry can be achieved by mapping the quantum state of squeezed optical vacuum to one of the atomic inputs via a beamsplitter-like process [Phys.~Rev.~A \textbf{90}, 063630 (2014)]. Here we ask the question: is a better phase sensitivity possible if the quantum state transfer (QST) is described by a three-mode-mixing model, rather than a beamsplitter? The answer is yes, but only if the portion of the optical state not transferred to the atoms is incorporated via information recycling. Surprisingly, our scheme gives a better sensitivit…
We propose a stroboscopic method to dynamically decouple the effects of two-body atom-atom interactions for ultracold atoms, and realize a system dominated by elastic three-body interactions. Using this method, we show that it is possible to achieve the optimal scaling behavior predicted for interaction-based quantum metrology with three-body interactions. Specifically, we show that for ultracold atoms quenched in an optical lattice, we can measure the three-body interaction strength with a precision proportional to ${\bar n}^{-5/2}$ using homodyne quadrature interferometry, and ${\bar n}^{-7/…
The dynamics of the quantum Fisher information of the parameters of the initial atomic state and atomic transition frequency is studied, in the framework of open quantum systems, for a static polarizable two-level atom coupled in the multipolar scheme to a bath of fluctuating vacuum electromagnetic fields without and with the presence of a reflecting boundary. Our results show that in the case without a boundary, the electromagnetic vacuum fluctuations always cause the quantum Fisher information of the initial parameters and thus the precision limit of parameter estimation to decrease. Remarka…
We propose a versatile Loschmidt echo protocol to detect and quantify multiparticle entanglement. It allows us to extract the quantum Fisher information for arbitrary pure states, and finds direct application in quantum metrology. In particular, the protocol applies to states that are generally difficult to characterize, as non-Gaussian states, and states that are not symmetric under particle exchange. We focus on atomic systems, including trapped ions, polar molecules, and Rydberg atoms, where entanglement is generated dynamically via long-range interaction, and show that the protocol is stab…
Laser noise is a decisive limiting factor in high precision spectroscopy of narrow lines using atomic ensembles. In an idealized Doppler and differential light shift free magic wavelength lattice configuration, it remains as one distinct principal limitation beyond collective atomic decay. In this work we study the limitations originating from laser phase and amplitude noise in an idealized Ramsey pulse interrogation scheme with uncorrelated atoms. Phase noise leads to a saturation of the frequency sensitivity with increasing atom number while amplitude noise implies a scaling $1/\sqrtτ$ with …
Quantum-enhanced metrology can be achieved by entangling a probe with an auxiliary system, passing the probe through an interferometer, and subsequently making measurements on both the probe and auxiliary system. Conceptually, this corresponds to performing metrology with the purification of a (mixed) probe state. We demonstrate via the quantum Fisher information how to design mixed states whose purifications are an excellent metrological resource. In particular, we give examples of mixed states with purifications that allow (near) Heisenberg-limited metrology, and provide example entangling H…
We show that far field diffraction image of spontaneously scattered Stokes photons can be used for detection of spin entanglement and for metrology of fields gradients in cold atomic ensembles. For many-body states with small or maximum uncertainty in spin-excitation number, entanglement is simply witnessed by the presence of a sharp diffraction peak or dip. Gradient vector of external fields is measured by the displacement of a diffraction peak due to inhomogeneous spin precessions, which suggests a new possibility for precision measurement beyond the standard quantum limit without entangleme…
This review summarizes experimental works performed over the last decade by several groups on the manipulation of a few individual interacting Rydberg atoms. These studies establish arrays of single Rydberg atoms as a promising platform for quantum state engineering, with potential applications to quantum metrology, quantum simulation and quantum information.
We show that continuous quantum nondemolition (QND) measurement of an atomic ensemble is able to improve the precision of frequency estimation even in the presence of independent dephasing acting on each atom. We numerically simulate the dynamics of an ensemble with up to N = 150 atoms initially prepared in a (classical) spin coherent state, and we show that, thanks to the spin squeezing dynamically generated by the measurement, the information obtainable from the continuous photocurrent scales superclassically with respect to the number of atoms N. We provide evidence that such superclassical…
Enhancement of the sensitivities of optical magnetometers, atomic clocks and atom interferometers and other quantum metrology devices requires introducing new physical processes to improve on their present achievements. Many body collective correlations among the atoms, spins or, in general, quantum systems may prove to be a suitable method. As these correlations introduce interference terms in the intensity of the scattering amplitudes, they may enhance the signal as $N(N-1)$ for N correlated quantum systems. These correlations enhance the signal to noise ratio by a factor of $N^2$ and contri…
The aggressive scaling of silicon-based nanoelectronics has reached the regime where device function is affected not only by the presence of individual dopants, but more critically their position in the structure. The quantitative determination of the positions of subsurface dopant atoms is an important issue in a range of applications from channel doping in ultra-scaled transistors to quantum information processing, and hence poses a significant challenge. Here, we establish a metrology combining low-temperature scanning tunnelling microscopy (STM) imaging and a comprehensive quantum treatmen…
Chemical chain reactions are known to enable extremely sensitive detection schemes in chemical, biological, and medical analysis, and have even been used in the search for dark matter. Here we show that coherent, ultracold chemical reactions harbor great potential for quantum metrology: In an atom-molecule Bose-Einstein condensate (BEC), a weak external perturbation can modify the reaction dynamics and lead to the coherent creation of molecules in an atom-dominant regime which can be selectively detected with modern spectroscopic techniques. This promises to substantially improve the viability…
In its simplest form, decoherence occurs when a quantum state is entangled with a second state, but the results of measurements made on the second state are not accessible. As the second state has effectively "measured" the first, in this paper we argue that the quantum Fisher information is the relevant metric for predicting and quantifying this kind of decoherence. The quantum Fisher information is usually used to determine an upper bound on how precisely measurements on a state can be used to estimate a classical parameter, and as such it is an important resource. Quantum enhanced metrology…
In 1949, Ramsey's method of separated oscillating fields was elaborated boosting over many decades metrological performances of atomic clocks and becoming the standard technique for very high precision spectroscopic measurements. A generalization of this interferometric method is presented replacing the two single coherent excitations by arbitrary composite laser pulses. The rotation of the state vector of a two-level system under the effect of a single pulse is described using the Pauli matrices basis of the SU(2) group. It is then generalized to multiple excitation pulses by a recursive Eule…
We demonstrate that a many-body nonlocality is a resource for ultra-precise metrology. This result is achieved by linking the sensitivity of a quantum sensor with a combination of many-body correlation functions that witness the nonlocality. We illustrate our findings with some prominent examples---a collection of spins forming an Ising chain and a gas of ultra-cold atoms in any two-mode configuration.
In quantum metrology, one typically creates correlations among atoms or photons to enhance measurement precision. Here, we show how one can use other excitations to perform quantum-enhanced measurements on the example of center-of-mass excitations of a spin-orbit coupled Bose-Einstein condensate and a Coulomb crystal. We also present a method to simulate a homodyne detection of center-of-mass excitations in these systems, which is required for optimal estimation.
Squeezed states, a special kind of entangled states, are known as a useful resource for quantum metrology. In interferometric sensors they allow to overcome the "classical" projection noise limit stemming from the independent nature of the individual photons or atoms within the interferometer. Motivated by the potential impact on metrology as wells as by fundamental questions in the context of entanglement, a lot of theoretical and experimental effort has been made to study squeezed states. The first squeezed states useful for quantum enhanced metrology have been proposed and generated in quan…
Quantum-mechanically correlated (entangled) states of many particles are of interest in quantum information, quantum computing and quantum metrology. Metrologically useful entangled states of large atomic ensembles have been experimentally realized, but these states display Gaussian spin distribution functions with a non-negative Wigner function. Non-Gaussian entangled states have been produced in small ensembles of ions, and very recently in large atomic ensembles. Here, we generate entanglement in a large atomic ensemble via the interaction with a very weak laser pulse; remarkably, the detec…
We propose an experiment, where the Bell inequality is violated in a many-body system of massive particles. The source of correlated atoms is a spinor $F=1$ Bose-Einstein condensate residing in an optical lattice. We characterize the complete experimental procedure--- the local operations, the measurements and the inequality---necessary to run the Bell test. We show how the degree of violation of the Bell inequality depends on the strengths of the two-body correlations and on the number of scattered pairs. We show that the system can be used to demonstrate the Einstein-Podolsky-Rosen paradox. …
