The current status of studies in the physics of entangled states of atomic systems — an interdisciplinary field involving quantum optics, quantum information, and the foundations of quantum mechanics — is reviewed. In the first part of the review, an introduction to the theory of entangled states is given, their properties and applications are described. In the second part, experiments on the creation and detection of entangled states in atomic systems are discussed along with associated experimental proposals for their refinement. Today's most advanced experimental technique for creating entangled ion states in an ion trap is considered, and promising methods focussed on the analogous states of neutral atoms are analyzed.
The current status of studies in the physics of entangled states of atomic systems — an interdisciplinary field involving quantum optics, quantum information, and the foundations of quantum mechanics — is reviewed. In the first part of the review, an introduction to the theory of entangled states is given, their properties and applications are described. In the second part, experiments on the creation and detection of entangled states in atomic systems are discussed along with associated experimental proposals for their refinement. Today's most advanced experimental technique for creating entangled ion states in an ion trap is considered, and promising methods focussed on the analogous states of neutral atoms are analyzed.
In this chapter, we will discuss the central topic in the current quantum optics studies, that is, entanglement. We focus mostly on the problem of creation of entanglement between two atoms and address the question how one could create multi-atom entangled states. The term entanglement, one of themost intriguing properties of multi-particle systems, was introduced by Schro¨dinger in his discussions of the foundations of quantum mechanics. It describes a multi-particle system that has the astonishing property that the results of a measurement on one particle cannot be specified independently of the results of measurements on the other particles. Although entangled systems can be physically separated, they can no longer be considered as independent, even when they are very far from one another. Entanglement is not only at the heart of the distinction between quantum and classical mechanics, but is now regarded to be a resource central to the development of quantum technologies ranging from quantum information, quantum cryptography, teleportation and quantum computation to atomic and molecular spectroscopy. These practical implementations all stem from the realization that we may control and manipulate quantum systems at the level of single atoms and photons to store information and transfer the information between distant systems in a controlled way and with high fidelity. This field of study is a relatively new one, and considerable research activity is taking place at present. The most active ones are the studies of practical schemes for creation of entanglement between trapped atoms or ions [91, 94].
In the past decades, rapid advances in the experimental control of quantum systems have opened up unparalleled capabilities of engineering exotic quantum states. Nowadays, we may consider ourselves witnesses of a second quantum revolution as strongly correlated quantum matter is regularly created, on a daily basis, within the most diverse platforms, e.g. arrays of Rydberg atoms, ultra-cold atoms in optical lattices, superconducting qubits, trapped ions, and quantum dots. In this era, dubbed Noisy-Intermediate Scale Quantum (NISQ) era, the effort in pursuing research for realizing quantum technologies with practical purposes, such as quantum computing, simulations, communication and metrology, has greatly accelerated, and we are just starting to experience the immense progress that could be achieved. The remarkable breakthrough we are facing builds upon seminal theoretical and experimental advances in quantum physics. The key achievements in atomic, molecular, and optical (AMO) physics have opened up the possibility of controlling, trapping, and measuring single atoms, one by one, with high accuracy and reliability. In parallel, from a theoretical point of view, the study of quantum entanglement and correlations has bridged AMO physics and quantum information with crucial proposals for the realization of universal quantum computers. In this context, entanglement has emerged as one of the key tools to characterize and to exploit quantum many-body systems for quantum information purposes. We will study quantum entanglement in several scenarios to investigate and probe complex quantum many-body systems. We will consider examples ranging from generic mixed states in equilibrium to out-of-equilibrium dynamics, with and without dissipation, and topologically non-trivial systems. The leitmotif of this work will be how entanglement and correlations can be exploited to characterize the many-body quantum state describing a physical system and how entanglement can be detected in an experimentally efficient manner.
Quantum entanglement is a peculiar phenomenon in quantum information science, characterized by nonclassical correlations between quantum states of subsystems in a quantum system. Since the proposal of the Einstein-Podolsky-Rosen (EPR) paradox by Einstein, Podolsky, and Rosen, quantum entanglement has sparked intense debates on local realism. Bell’s inequality experiment established the nonlocality of quantum mechanics. Currently, high-dimensional quantum entanglement of both deterministic and random states can be realized in systems such as photons and cold atoms. Technologies such as quantum teleportation, quantum teleportation, quantum computing, and others rely on quantum entanglement to achieve effects beyond classical limitations. Current research focuses on the implementation of macroscopic quantum entanglement and its significance in fundamental problems of quantum mechanics. Quantum entanglement opens up a new paradigm for information processing with broad application prospects. It is necessary to conduct in-depth research on the nature of quantum entanglement and its advantages in information processing. This paper reviews the theoretical foundations of quantum entanglement, methods of generation and detection, and research progress in its applications in the field of quantum information. It discusses the important applications of quantum entanglement in quantum communication, computing, and sensing and provides an outlook on the future development prospects of quantum entanglement technologies.
Quantum technologies exploit entanglement to revolutionize computing, measurement, and communication. 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 forces and light fields, which makes them ideal for ultra-precise sensing and time keeping. All these factors call for generating non-classical atomic states designed for phase estimation in atomic clocks and atom interferometers, exploiting many-body entanglement to increase the sensitivity of precision measurements. The goal of this article is to review and illustrate successful theoretical proposals and experiments with atomic ensembles that have demonstrated many-particle entanglement and quantum-enhanced metrology.
Some of the quantum mechanical conceptual problems, their current status, and related theoretical developments are reviewed. The characteristics of the entangled quantum states are analyzed, and new experiments and quantum information applications involving such states are discussed. The well-known paradox of Schroedinger's cat (the impossibility of observing superpositions of macroscopically distinct states that are predicted by quantum mechanics) is discussed. It is shown that decoherence (arising when a quantum system is measured in such a way that some information about its state is recorded in its environment) prevents the distinguishing of a superposition and the corresponding mixture. This overcomes the difficulties associated with the paradoxical nature of quantum measurement provided we remain within the framework of the theory of open systems. Other conceptual difficulties, while actually lying outside physics, are now the subject of much research and have already led to new interesting interpretations of quantum mechanics. The suggestion of Wigner and others that the observer's consciousness be included in the theory of quantum measurement is discussed in this context. A hypothesis is put forward which might enable the functioning of consciousness to be described in quantum measurement terms.