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 strongly couple to external forces and fields, which makes them ideal for ultraprecise sensing and time keeping. All these factors call for generating nonclassical 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 the theory and the experiments with atomic ensembles that have demonstrated many-particle entanglement and quantum-enhanced metrology.

Quantum metrology with nonclassical states of atomic ensembles

Universal logic gates for two quantum bits (qubits) form an essential ingredient of quantum computation. Dynamical gates have been proposed in the context of trapped ions; however, geometric phase gates (which change only the phase of the physical qubits) offer potential practical advantages because they have higher intrinsic resistance to certain small errors and might enable faster gate implementation. Here we demonstrate a universal geometric pi-phase gate between two beryllium ion-qubits, based on coherent displacements induced by an optical dipole force. The displacements depend on the internal atomic states; the motional state of the ions is unimportant provided that they remain in the regime in which the force can be considered constant over the extent of each ion's wave packet. By combining the gate with single-qubit rotations, we have prepared ions in an entangled Bell state with 97% fidelity-about six times better than in a previous experiment demonstrating a universal gate between two ion-qubits. The particular properties of the gate make it attractive for a multiplexed trap architecture that would enable scaling to large numbers of ion-qubits.

Experimental demonstration of a robust, high-fidelity geometric two ion-qubit phase gate*

The authors review the history, current status, physical mechanisms, experimental methods, and applications of nonlinear magneto-optical effects in atomic vapors. They begin by describing the pioneering work of Macaluso and Corbino over a century ago on linear magneto-optical effects (in which the properties of the medium do not depend on the light power) in the vicinity of atomic resonances. These effects are then contrasted with various nonlinear magneto-optical phenomena that have been studied both theoretically and experimentally since the late 1960s. In recent years, the field of nonlinear magneto-optics has experienced a revival of interest that has led to a number of developments, including the observation of ultranarrow (1-Hz) magneto-optical resonances, applications in sensitive magnetometry, nonlinear magneto-optical tomography, and the possibility of a search for parity- and time-reversal-invariance violation in atoms.

Resonant nonlinear magneto-optical effects in atoms

We report the creation of thermal, Fock, coherent, and squeezed states of motion of a harmonically bound {sup 9}Be{sup +} ion. The last three states are coherently prepared from an ion which has been initially laser cooled to the zero point of motion. The ion is trapped in the regime where the coupling between its motional and internal states, due to applied (classical) radiation, can be described by a Jaynes-Cummings-type interaction. With this coupling, the evolution of the internal atomic state provides a signature of the number state distribution of the motion. {copyright} {ital 1996 The American Physical Society.}

Generation of Non-classical Motional States of a Trapped Atom

The technique of stimulated Raman adiabatic passage (STIRAP), which allows efficient and selective population transfer between quantum states without suffering loss due to spontaneous emission, was introduced in 1990 (Gaubatz \emph{et al.}, J. Chem. Phys. \textbf{92}, 5363, 1990). Since then STIRAP has emerged as an enabling methodology with widespread successful applications in many fields of physics, chemistry and beyond. This article reviews the many applications of STIRAP emphasizing the developments since 2000, the time when the last major review on the topic was written (Vitanov \emph{et al.}, Adv. At. Mol. Opt. Phys. \textbf{46}, 55, 2001). A brief introduction into the theory of STIRAP and the early applications for population transfer within three-level systems is followed by the discussion of several extensions to multi-level systems, including multistate chains and tripod systems. The main emphasis is on the wide range of applications in atomic and molecular physics (including atom optics, cavity quantum electrodynamics, formation of ultracold molecules, precision experiments, etc.), quantum information (including single- and two-qubit gates, entangled-state preparation, etc.), solid-state physics (including processes in doped crystals, nitrogen-vacancy centers, superconducting circuits, etc.), and even some applications in classical physics (including waveguide optics, frequency conversion, polarization optics, etc.). Promising new prospects for STIRAP are also presented (including processes in optomechanics, detection of parity violation in molecules, spectroscopy of core-nonpenetrating Rydberg states, and population transfer with X-ray pulses).

Stimulated Raman adiabatic passage in physics, chemistry, and beyond

In order to clarify factors determining the interface dipole, we have studied the electronic structures of pentacene adsorbed on Cu(111), Ag(111), and Au(111) by using first-principles density functional theoretical calculations. In the structural optimization, a semiempirical van der Waals (vdW) approach [S. Grimme, J. Comput. Chem. 27, 1787 (2006)] is employed to include long-range vdW interactions and is shown to reproduce pentacene-metal distances quite accurately. The pentacene-metal distances for Cu, Ag, and Au are evaluated to be 0.24, 0.29, and 0.32 nm, respectively, and work function changes calculated by using the theoretically optimized adsorption geometries are in good agreement with the experimental values, indicating the validity of the present approach in the prediction of the interface dipole at metal/organic interfaces. We examined systematically how the geometric factors, especially the pentacene-substrate distance (ZC), and the electronic properties of the metal substrates contribute to...

Density functional theoretical study of pentacene/noble metal interfaces with van der Waals corrections: Vacuum level shifts and electronic structures

We propose a method for quantum nondemolition (QND) measurement of one component of spin by the measurement of polarization rotation of the off-resonant light induced by a paramagnetic Faraday rotation effect We show that nonclassical states of spins such as the squeezed spin state, the Dicke state, and macroscopic quantum superposed state of spin can be realized corresponding to particular results of QND measurements Furthermore, it is shown that a nonclassical state of light such as the twin photon state can also be realized with this method

Quantum nondemolition measurement of spin via the paramagnetic Faraday rotation

The quantum statistics of bosons and fermions manifest themselves in the manner in which two indistinguishable particles interfere quantum mechanically. When two photons, which are bosonic particles, enter a beam-splitter with one photon in each input port, they bunch together at either of the two output ports. The corresponding disappearance of the coincidence count is the Hong-Ou-Mandel effect. Here we show the phonon counterpart of this effect in a system of trapped-ion phonons, which are collective excitations derived by quantizing vibrational motions that obey Bose-Einstein statistics. We realize a beam-splitter transformation of the phonons by employing the mutual Coulomb repulsion between ions, and perform a two-phonon quantum interference experiment using that transformation. We observe an almost perfect disappearance of the phonon coincidence between two ion sites, confirming that phonons can be considered indistinguishable bosonic particles. The two-particle interference demonstrated here is purely a quantum effect, without a classical counterpart, hence it should be possible to demonstrate the existence of entanglement on this basis. We attempt to generate an entangled state of phonons at the centre of the Hong-Ou-Mandel dip in the coincidence temporal profile, under the assumption that the entangled phonon state is successfully generated if the fidelity of the analysis pulses is taken into account adequately. Two-phonon interference, as demonstrated here, proves the bosonic nature of phonons in a trapped-ion system. It opens the way to establishing phonon modes as carriers of quantum information in their own right, and could have implications for the quantum simulation of bosonic particles and analogue quantum computation via boson sampling.

Hong–Ou–Mandel interference of two phonons in trapped ions

We have succeeded in magneto-optical trapping of Yb atoms decelerated by a Zeeman slower method. The number of the trapped atoms is more than about $1.3\ifmmode\times\else\texttimes\fi{}{10}^{6}$ measured by light absorption. We have found the evidence of the branching from the ${}^{1}{P}_{1}$ excited state to triplet states, and determined the lower limit on the branching ratio to be $1.2\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}7}.$

Magneto-optical trapping of Yb atoms and a limit on the branching ratio of the 1 P 1 state

We report an experimental realization of the Jaynes-Cummings-Hubbard model using the internal and radial phonon states of two trapped ions. An adiabatic transfer corresponding to a quantum phase transition from a localized insulator ground state to a delocalized superfluid (SF) ground state is demonstrated. The SF phase of polaritonic excitations characteristic of the interconnected Jaynes-Cummings (JC) system is experimentally explored, where a polaritonic excitation refers to a combination of an atomic excitation and a phonon interchanged via a JC coupling.

https://physics.aps.org/featured-article-pdf/10.1103/PhysRevLett.111.160501

Kenji Toyoda

Papers

Density functional theoretical study of pentacene/noble metal interfaces with van der Waals corrections: Vacuum level shifts and electronic structures

Quantum nondemolition measurement of spin via the paramagnetic Faraday rotation

Hong–Ou–Mandel interference of two phonons in trapped ions

Magneto-optical trapping of Yb atoms and a limit on the branching ratio of the 1 P 1 state

Experimental realization of a quantum phase transition of polaritonic excitations.