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Many phenomena described in relativistic quantum field theory are inaccessible to direct observations, but analogue processes studied under well-defined laboratory conditions can present an alternative perspective. Recently, we demonstrated an analogy of particle creation using an intrinsically robust motional mode of two trapped atomic ions. Here, we substantially extend our classical control techniques by implementing machine-learning strategies in our platform and, consequently, increase the accessible parameter regime. As a proof of methodology, we present experimental results of multiple quenches and parametric modulation of an unprotected motional mode of a single ion, demonstrating the increased level of real-time control. In combination with previous results, we enable future experiments that may yield entanglement generation using a process in analogy to Hawking radiation. [ABSTRACT FROM AUTHOR]

Wepropose a method to simulate the dynamics of spin-boson models with small crystals of trapped ions where the electronic degree of freedom of one ion is used to encode the spin while the collective vibrational degrees of freedom are employed to form an effective harmonic environment. The key idea of our approach is that a single damped mode can be used to provide a harmonic environment with Lorentzian spectral density. More complex spectral functions can be tailored by combining several individually damped modes. The protocol is especially well-suited to simulate spin-boson models with structured environments. Wepropose to work with mixed-species crystals such that one species serves to encode the spin while the other species is used to cool the vibrational degrees of freedom to engineer the environment. The strength of the dissipation on the spin can be controlled by tuning the coupling between spin and vibrational degrees of freedom. In this way the dynamics of spin-boson models with macroscopic and non-Markovian environments can be simulated using only a few ions. Weillustrate the approach by simulating an experiment with realistic parameters and show by computing quantitative measures that the dynamics is genuinely non-Markovian. [ABSTRACT FROM AUTHOR]

We study discrete solitons (kinks) accessible in the state-of-theart trapped ion experiments, considering zigzag crystals and quasi-threedimensional configurations, both theoretically and experimentally. We first extend the theoretical understanding of different phenomena predicted and recently experimentally observed in the structure and dynamics of these topological excitations. Employing tools from topological degree theory, we analyze bifurcations of crystal configurations in dependence on the trapping parameters, and investigate the formation of kink configurations and the transformations of kinks between different structures. This allows us to accurately define and calculate the effective potential experienced by solitons within the Wigner crystal, and study how this (so-called Peierls-Nabarro) potential gets modified to a non-periodic globally trapping potential in certain parameter regimes. The kinks' rest mass (energy) and spectrum of modes are computed and the dynamics of linear and nonlinear kink oscillations are analyzed. We also present novel, experimentally observed, configurations of kinks incorporating a large-mass defect realized by an embedded molecular ion, and of pairs of interacting kinks stable for long times, offering the perspective for exploring and exploiting complex collective nonlinear excitations, controllable on the quantum level. [ABSTRACT FROM AUTHOR]

We introduce a scheme to perform dissipation-assisted quantum information processing in ion traps considering realistic decoherence rates, for example, due to motional heating. By means of continuous sympathetic cooling, we overcome the trap heating by showing that the damped vibrational excitations can still be exploited to mediate coherent interactions as well as collective dissipative effects. We describe how to control their relative strength experimentally, allowing for protocols of coherent or dissipative generation of entanglement. This scheme can be scaled to larger ion registers for coherent or dissipative many-body quantum simulations. [ABSTRACT FROM AUTHOR]

Two efficient and isotope-selective resonant two-photon ionization techniques for loading barium ions into radio-frequency (RF)-traps are demonstrated. The scheme of using the strong dipole-allowed transition 6 s S→6 s6 p P at λ=553 nm as a first step towards ionization is compared to the established technique of using a weak inter-combination line (6 s S→5 d6 p D, λ=413 nm). An increase of two orders of magnitude in the ionization efficiency is found favoring the transition at 553 nm. This technique can be implemented using commercial all-solid-state laser systems and is expected to be advantageous compared to other narrowband photo-ionization schemes of barium in cases where highest efficiency and isotope-selectivity are required. [ABSTRACT FROM AUTHOR]

We describe a versatile toolbox for the quantum simulation of manybody lattice models, capable of exploring the combined effects of background Abelian and non-Abelian gauge fields, bond and site disorder and strong onsite interactions. We show how to control the quantum dynamics of particles trapped in lattice potentials by the photon-assisted tunneling induced by periodic drivings. This scheme is general enough to be applied to either bosons or fermions with the additional advantage of being non-perturbative. It finds an ideal application in microfabricated ion trap arrays, where the quantized vibrational modes of the ions can be described by a quantum lattice model. We present a detailed theoretical proposal for a quantum simulator in that experimental setup, and show that it is possible to explore phases of matter that range from the fractional quantum Hall effect, to exotic strongly correlated glasses or flux-lattice models decorated with arbitrary patterns of localized defects. [ABSTRACT FROM AUTHOR]

We examine the prospects of discrete quantum walks (QWs) with trapped ions. In particular, we analyze in detail the limitations of the protocol of Travaglione and Milburn (2002 Phys. Rev. A 65 032310) that has been implemented by several experimental groups in recent years. Based on the first realization in our group (Schmitz et al 2009 Phys. Rev. Lett. 103 090504), we investigate the consequences of leaving the scope of the approximations originally made, such as the Lamb-Dicke approximation. We explain the consequential deviations from the idealized QW for different experimental realizations and an increasing number of steps by taking into account higherorder terms of the quantum evolution. It turns out that these already become significant after a few steps, which is confirmed by experimental results and is currently limiting the scalability of this approach. Finally, we propose a new scheme using short laser pulses, derived from a protocol from the field of quantum computation. We show that this scheme is not subject to the abovementioned restrictions and analytically and numerically evaluate its limitations, based on a realistic implementation with our specific setup. Implementing the protocol with state-of-the-art techniques should allow for substantially increasing the number of steps to 100 and beyond and should be extendable to higher-dimensional QWs. [ABSTRACT FROM AUTHOR]

Direct experimental access to some of the most intriguing quantum phenomena is not granted due to the lack of precise control of the relevant parameters in their naturally intricate environment. Their simulation on conventional computers is impossible, since quantum behaviour arising with superposition states or entanglement is not efficiently translatable into the classical language. However, one could gain deeper insight into complex quantum dynamics by experimentally simulating the quantum behaviour of interest in another quantum system, where the relevant parameters and interactions can be controlled and robust effects detected sufficiently well. Systems of trapped ions provide unique control of both the internal (electronic) and external (motional) degrees of freedom. The mutual Coulomb interaction between the ions allows for large interaction strengths at comparatively large mutual ion distances enabling individual control and readout. Systems of trapped ions therefore exhibit a prominent system in several physical disciplines, for example, quantum information processing or metrology. Here, we will give an overview of different trapping techniques of ions as well as implementations for coherent manipulation of their quantum states and discuss the related theoretical basics. We then report on the experimental and theoretical progress in simulating quantum many-body physics with trapped ions and present current approaches for scaling up to more ions and more-dimensional systems. [ABSTRACT FROM AUTHOR]

Isolating ions and atoms from the environment is essential in experiments on a quantum level. For decades, this has been achieved by trapping ions with radiofrequency fields and neutral particles with optical fields. Here we demonstrate the trapping of an ion by interaction with light. The lifetime in the optical trap is several milliseconds, allowing hundreds of oscillations in the optical potential, and could be enhanced by established methods. These results could form the starting point for combining the advantages of optical trapping and ions. Extending the approach to optical lattices could support developments in experimental quantum simulations. As well as simulating complex spin systems with trapped ions, a new class of quantum simulations could be enabled that combines atoms and ions in a common lattice (Cirac, J.I., personal communication; Zoller, P., personal communication). Furthermore, ions could be embedded into quantum degenerate gases, thereby avoiding the inevitable excess kinetic energy of ions in radiofrequency traps, which currently limits cold-chemistry experiments. [ABSTRACT FROM AUTHOR]

We cannot translate quantum behavior arising with superposition states or entanglement efficiently into the classical language of conventional computers (Feynman et al. in Int. J. Theor. Phys. 21:467, ). A universal quantum computer could describe and help to understand complex quantum systems. But it is envisioned to become functional only within the next decade(s). A shortcut was proposed via simulating the quantum behavior of interest in another quantum system, where all relevant parameters and interactions can be controlled and observables of interest detected sufficiently well. For example simulating quantum spin systems within an architecture of trapped ions (Porras and Cirac in Phys. Rev. Lett. 92:207901, ). Here we specify how we simulate the spin and all necessary interactions and how we calibrate their amplitudes. For example via a two-ion phase-gate operation on two axial motional modes simultaneously at a fidelity exceeding 95%. We explain the complete mode of operation of a quantum simulator on the basis of our simple model case—the proof of principle experiment of simulating the transition of a quantum magnet from paramagnetic into entangled ferromagnetic order (Friedenauer et al. in Nat. Phys. 4:757, ) and emphasize some of the similarities and differences with a quantum computer. [ABSTRACT FROM AUTHOR]

To gain deeper insight into the dynamics of complex quantum systems we need a quantum leap in computer simulations. We cannot translate quantum behaviour arising from superposition states or entanglement efficiently into the classical language of conventional computers. The solution to this problem, proposed in 1982 (ref. 1), is simulating the quantum behaviour of interest in a different quantum system where the interactions can be controlled and the outcome detected sufficiently well. Here we study the building blocks for simulating quantum spin Hamiltonians with trapped ions. We experimentally simulate the adiabatic evolution of the smallest non-trivial spin system from paramagnetic into ferromagnetic order with a quantum magnetization for two spins of 98%. We prove that the transition is not driven by thermal fluctuations but is of quantum-mechanical origin (analogous to quantum fluctuations in quantum phase transitions). We observe a final superposition state of the two degenerate spin configurations for the ferromagnetic order (|↑↑〉+|↓↓〉), corresponding to deterministic entanglement achieved with 88% fidelity. This method should allow for scaling to a higher number of coupled spins, enabling implementation of simulations that are intractable on conventional computers. [ABSTRACT FROM AUTHOR]

Experiments directed towards the development of an analogue quantum simulator based on trapped atomic magnesium ions are described. We report on the required initialization including ground state cooling of 25Mg+ ions for the first time - parallel to the group at NIST/Boulder. We discuss basic operations to implement quantum spin Hamiltonians like a one-dimensional quantum Ising model and some challenges to be addressed in reaching for larger scale and higher dimensional devices. [ABSTRACT FROM AUTHOR]

We describe the concept and experimental demonstration of the basic building blocks of a scalable quantum computer using trapped-ion qubits. The trap structure is divided into subregions where ion qubits can either be held as memory or subjected to individual rotations and multi-qubit gates in processor zones. Thus, ion qubits can become entangled in one trapping zone, then separated and distributed to separate zones (by switching control-electrode potentials) where subsequent single- and two-ion gates, and/or detection is performed. Recent work using these building blocks includes (1) demonstration of a dense-coding protocol, (2) demonstration of enhanced qubit-detection efficiency using quantum logic, (3) generation of GHZ states and their application to enhanced precision in spectroscopy, and (4) the realization of teleportation with atomic qubits. In the final section an analog quantum computer that could provide a shortcut towards quantum simulations under requirements less demanding than those for a universal quantum computer is also described. [ABSTRACT FROM AUTHOR]

Scalable quantum computation and communication require error control to protect quantum information against unavoidable noise. Quantum error correction protects information stored in two-level quantum systems (qubits) by rectifying errors with operations conditioned on the measurement outcomes. Error-correction protocols have been implemented in nuclear magnetic resonance experiments, but the inherent limitations of this technique prevent its application to quantum information processing. Here we experimentally demonstrate quantum error correction using three beryllium atomic-ion qubits confined to a linear, multi-zone trap. An encoded one-qubit state is protected against spin-flip errors by means of a three-qubit quantum error-correcting code. A primary ion qubit is prepared in an initial state, which is then encoded into an entangled state of three physical qubits (the primary and two ancilla qubits). Errors are induced simultaneously in all qubits at various rates. The encoded state is decoded back to the primary ion one-qubit state, making error information available on the ancilla ions, which are separated from the primary ion and measured. Finally, the primary qubit state is corrected on the basis of the ancillae measurement outcome. We verify error correction by comparing the corrected final state to the uncorrected state and to the initial state. In principle, the approach enables a quantum state to be maintained by means of repeated error correction, an important step towards scalable fault-tolerant quantum computation using trapped ions. [ABSTRACT FROM AUTHOR]

Isolating neutral and charged particles from the environment is essential in precision experiments. For decades, this has been achieved by trapping ions with radio-frequency (RF) fields and neutral particles with optical fields. Recently, the trapping of ions by interaction with light has been demonstrated. This might permit the advantages of optical trapping and ions to be combined. For example, we would benefit from superimposing optical traps to investigate ensembles of ions and atoms in the absence of any RF fields and from the versatile and scalable trapping geometries featured by optical lattices. In particular, ions provide individual addressability, and electronic and motional degrees of freedom that can be coherently controlled and detected via high-fidelity, state-dependent operations. Their long-range Coulomb interaction is significantly larger compared to those of neutral atoms and molecules. This enables ultra-cold interaction and the chemistry of trapped ions and atoms to be studied, as well as providing a novel platform for higher-dimensional experimental quantum simulations. The aim of this topical review is to present the current state of the art and to discuss the current challenges and prospects of the emerging field. [ABSTRACT FROM AUTHOR]

We introduce a theoretical scheme that exploits laser cooling and phonon-mediated spin–spin interactions in crystals of trapped atomic ions to explore the transport of energy through a quantum magnet. We show how to implement an effective transport window to control the flow of energy through the magnet even in the absence of fermionic statistics for the carriers. This is achieved by shaping the density of states of the effective thermal reservoirs that arise from the interaction with the external bath of the modes of the electromagnetic field, and can be experimentally controlled by tuning the laser frequencies and intensities appropriately. The interplay of this transport window with the spin–spin interactions is exploited to build an analogue of the Coulomb-blockade effect in nano-scale electronic devices, and opens new possibilities to study quantum effects in energy transport. [ABSTRACT FROM AUTHOR]

Laser-cooled and trapped ions can crystallize and feature discrete solitons that are nonlinear, topologically protected configurations of the Coulomb crystal. Such solitons, as their continuum counterparts, can move within the crystal, while their discreteness leads to the existence of a gap-separated, spatially localized motional mode of oscillation above the spectrum. Suggesting that these unique properties of discrete solitons can be used for generating entanglement between different sites of the crystal, we study a detailed proposal in the context of state-of-the-art experimental techniques. We analyze the interaction of periodically driven planar ion crystals with optical forces, revealing the effects of micromotion in radio-frequency traps inherent to such structures, as opposed to linear ion chains. The proposed method requires Doppler cooling of the crystal and sideband cooling of the soliton's localized modes alone. Since the gap separation of the latter is nearly independent of the crystal size, this approach could be particularly useful for producing entanglement and studying system-environment interactions in large, two- and possibly three-dimensional systems. [ABSTRACT FROM AUTHOR]

We demonstrate Floquet engineering in a basic yet scalable 2D architecture of individually trapped and controlled ions. Local parametric modulations of detuned trapping potentials steer the strength of long-range interion couplings and the related Peierls phase of the motional state. In our proof of principle, we initialize large coherent states and tune modulation parameters to control trajectories, directions, and interferences of the phonon flow. Our findings open a new pathway for future Floquet-based trapped-ion quantum simulators targeting correlated topological phenomena and dynamical gauge fields. [ABSTRACT FROM AUTHOR]

Quantum theory predicts intriguing dynamics during drastic changes of external conditions. We switch the trapping field of two ions sufficiently fast to tear apart quantum fluctuations, i.e., create pairs of phonons and, thereby, squeeze the ions' motional state. This process can be interpreted as an experimental analog to cosmological particle creation and is accompanied by the formation of spatial entanglement. Hence, our platform allows one to study the causal connections of squeezing, pair creation, and entanglement and might permit one to cross-fertilize between concepts in cosmology and applications of quantum information processing. [ABSTRACT FROM AUTHOR]

Trapped ions are a promising platform for envisioned quantum simulators, with outstanding results in one-dimensional ion crystals. However, theory requires not only interactions at long range, but also higher dimensionality. We operate a basic triangular array of three individually trapped ions based on scalable microfabrication technology. We demonstrate coherent coupling, tunable in real time and enabling interference in 2D, an essential building block for a reconfigurable quantum simulator. Mitigating motional heating will permit accessing the quantum regime and 2D experimental quantum simulations. [ABSTRACT FROM AUTHOR]

We study experimentally and theoretically discrete solitons in crystalline structures consisting of several tens of laser-cooled ions confined in a radio frequency trap. Resonantly exciting localized, spectrally gapped vibrational modes of the soliton, a nonlinear mechanism leads to a nonequilibrium steady state of the continuously cooled crystal. We find that the propagation and the escape of the soliton out of its quasi-one-dimensional channel can be described as a thermal activation mechanism. We control the effective temperature of the soliton's collective coordinate by the amplitude of the external excitation. Furthermore, the global trapping potential permits controlling the soliton dynamics and realizing directed transport depending on its topological charge. [ABSTRACT FROM AUTHOR]