The realization of scalable arrangements of nitrogen vacancy (NV) centers in diamond remains a key challenge on the way towards efficient quantum information processing, quantum simulation and quantum sensing applications. Although technologies based on implanting NV-centers in bulk diamond crystals or hybrid device approaches have been developed, they are limited by the achievable spatial resolution and by the intricate technological complexities involved in achieving scalability. We propose and demonstrate a novel approach for creating an arrangement of NV-centers, based on the self-assembling capabilities of biological systems and their beneficial nanometer spatial resolution. Here, a self-assembled protein structure serves as a structural scaffold for surface functionalized nanodiamonds, in this way allowing for the controlled creation of NV-structures on the nanoscale and providing a new avenue towards bridging the bio–nano interface. One-, two- as well as three-dimensional structures are within the scope of biological structural assembling techniques. We realized experimentally the formation of regular structures by interconnecting nanodiamonds using biological protein scaffolds. Based on the achievable NV-center distances of 11 nm, we evaluate the expected dipolar coupling interaction with neighboring NV-centers as well as the expected decoherence time. Moreover, by exploiting these couplings, we provide a detailed theoretical analysis on the viability of multiqubit quantum operations, suggest the possibility of individual addressing based on the random distribution of the NV intrinsic symmetry axes and address the challenges posed by decoherence and imperfect couplings. We then demonstrate in the last part that our scheme allows for the high-fidelity creation of entanglement, cluster states and quantum simulation applications.

We propose an all-optical scheme to prolong the quantum coherence of a negatively charged nitrogen-vacancy (NV) center in diamond at cryogenic temperatures. Optical control of the NV spin suppresses energy fluctuations of the  ground states and forms an energy gap protected subspace. By optical control, the spectral linewidth of magnetic resonance is much narrower and the measurement of the frequencies of magnetic field sources has higher resolution. The optical control also improves the sensitivity of the magnetic field detection and can provide measurement of the directions of signal sources.

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.

The signal to noise ratio of quantum sensing protocols scales with the square root of the coherence time. Thus, increasing this time is a key goal in the field. By utilizing quantum error correction, we present a novel way of prolonging such coherence times beyond the fundamental limits of current techniques. We develop an implementable sensing protocol that incorporates error correction, and discuss the characteristics of these protocols in different noise and measurement scenarios. We examine the use of entangled versue untangled states, and error correction’s reach of the Heisenberg limit. The effects of error correction on coherence times are calculated and we show that measurement precision can be enhanced for both one-directional and general noise.

A proposal to use trapped ions to implement spin-one XXZ antiferromagnetic chains as an experimental tool to explore the Haldane phase is presented. We explain how to reach the Haldane phase adiabatically, demonstrate the robustness of the ground states to noise in the magnetic field and Rabi frequencies, and propose a way to detect them using their characteristics: an excitation gap and exponentially decaying correlations, a nonvanishing nonlocal string order, and a double degenerate entanglement spectrum. Scaling up to higher dimensions and more frustrated lattices, we obtain richer phase diagrams, and we can reach spin liquid phase, which can be detected by its entanglement entropy which obeys the boundary law.

We present a new robust decoupling scheme suitable for levels with either half-integer or integer angular momentum states. Through continuous dynamical decoupling techniques, we create a protected qubit subspace, utilizing a multistate qubit construction. Remarkably, the multistate system can also be composed of multiple substates within a single level. Our scheme can be realized with state-of-the-art experimental setups and thus has immediate applications for quantum information science. While the scheme is general and relevant for a multitude of solid-state and atomic systems, we analyze its performance for the case composed of trapped ions. Explicitly, we show how single qubit gates and an ensemble coupling to a cavity mode can be implemented efficiently. The scheme predicts a coherence time of ∼1  s, as compared to typically a few milliseconds for the bare states.

The development of statistical mechanics over the last century represents a major advance in the Natural Sciences. It is capable of describing a wide range of phenomena including the properties of phase transitions by reducing the complexity of quantum-many-body systems to simple general principles rooted in statistical methods that hold true in macroscopic systems. These principles apply to a broad range of physical theories, encompassing phenomena that are for example governed by classical, relativistic or quantum physics. While many of these predictions have been confirmed experimentally, the exploration, under highly controlled conditions, of the statistical mechanics of mesoscopic systems and the theoretical prediction of their behavior does still represent a challenge for both theory and experiment. A new avenue towards the controlled exploration of the classical and quantum statistical mechanics of mesoscopic systems has opened up in recent years thanks to the remarkable achievements in ion trap physics, which is pursued mainly for the realization of quantum information processing and precision metrology, in controlling and manipulating ion crystals.

We study experimentally and theoretically the properties of structural defects (kink solitons) in two-dimensional ion Coulomb crystals. We show how different types of kink solitons with different physical properties can be realized, and transformed from one type into another by varying the aspect ratio of the trap confinement. Further, we discuss how impurities in ion Coulomb crystals, such as mass defects, can modify the dynamics of kink creation and their stability. For both pure and impure crystals, the experimentally observed kink dynamics are analysed in detail and explained theoretically by numerical simulations and calculations of the Peierls–Nabarro potential. Finally, we demonstrate that static electric fields provide a handle to vary the influence of mass defects on kinks in a controlled way and allow for deterministic manipulation and creation of kinks.

Traversal of a symmetry-breaking phase transition at finite rates can lead to causally separated regions with incompatible symmetries and the formation of defects at their boundaries, which has a crucial role in quantum and statistical mechanics, cosmology and condensed matter physics. This mechanism is conjectured to follow universal scaling laws prescribed by the Kibble–Zurek mechanism. Here we determine the scaling law for defect formation in a crystal of 16 laser-cooled trapped ions, which are conducive to the precise control of structural phases and the detection of defects. The experiment reveals an exponential scaling of defect formation γ^β, where γ is the rate of traversal of the critical point and β=2.68±0.06. This supports the prediction of β=8/3≈2.67 for finite inhomogeneous systems. Our result demonstrates that the scaling laws also apply in the mesoscopic regime and emphasizes the potential for further tests of non-equilibrium thermodynamics with ion crystals.

Traversal of a symmetry-breaking phase transition at finite rates can lead to causally separated regions with incompatible symmetries and the formation of defects at their boundaries, which has a crucial role in quantum and statistical mechanics, cosmology and condensed matter physics. This mechanism is conjectured to follow universal scaling laws prescribed by the Kibble–Zurek mechanism. Here we determine the scaling law for defect formation in a crystal of 16 laser-cooled trapped ions, which are conducive to the precise control of structural phases and the detection of defects. The experiment reveals an exponential scaling of defect formation γ^β, where γ is the rate of traversal of the critical point and β=2.68±0.06. This supports the prediction of β=8/3≈2.67 for finite inhomogeneous systems. Our result demonstrates that the scaling laws also apply in the mesoscopic regime and emphasizes the potential for further tests of non-equilibrium thermodynamics with ion crystals.

Symmetry breaking phase transitions play an important role in nature. When a system traverses such a transition at a finite rate, its causally disconnected regions choose the new broken symmetry state independently. Where such local choices are incompatible, topological defects can form. The Kibble–Zurek mechanism predicts the defect densities to follow a power law that scales with the rate of the transition. Owing to its ubiquitous nature, this theory finds application in a wide field of systems ranging from cosmology to condensed matter. Here we present the successful creation of defects in ion Coulomb crystals by a controlled quench of the confining potential, and observe an enhanced power law scaling in accordance with numerical simulations and recent predictions. This simple system with well-defined critical exponents opens up ways to investigate the physics of non-equilibrium dynamics from the classical to the quantum regime.

Realizing controlled quantum dynamics via the magnetic interactions between colour centres in diamond remains a challenge despite recent demonstrations for nanometre separated pairs. Here we propose to use the intrinsic acoustical phonons in diamond as a data bus for accomplishing this task. We show that for nanodiamonds the electron–phonon coupling can take significant values that together with mode frequencies in the THz range can serve as a resource for conditional gate operations. Based on these results, we analyse how to use this phonon-induced interaction for constructing quantum gates among the electron-spin triplet ground states, introducing the phonon dependence via Raman transitions. Combined with decoupling pulses this offers the possibility for creating entangled states within nanodiamonds on the scale of several tens of nanometres, a promising prerequisite for quantum sensing applications.

We report the detection and polarization of nuclear spins in diamond at room temperature by using a single nitrogen-vacancy (NV) center. We use Hartmann-Hahn double resonance to coherently enhance the signal from a single nuclear spin while decoupling from the noisy spin bath, which otherwise limits the detection sensitivity. As a proof of principle, we (i) observe coherent oscillations between the NV center and a weakly coupled nuclear spin and (ii) demonstrate nuclear-bath cooling, which prolongs the coherence time of the NV sensor by more than a factor of 5. Our results provide a route to nanometer scale magnetic resonance imaging and novel quantum information processing protocols.

Strongly correlated quantum many-body systems may exhibit exotic phases, such as spin liquids and supersolids. Although their numerical simulation becomes intractable for as few as 50 particles, quantum simulators offer a route to overcome this computational barrier. However, proposed realizations either require stringent conditions such as low temperature/ultra-high vacuum, or are extremely hard to scale. Here, we propose a new solid-state architecture for a scalable quantum simulator that consists of strongly interacting nuclear spins attached to the diamond surface. Initialization, control and read-out of this quantum simulator can be accomplished with nitrogen-vacancy centers implanted in diamond. The system can be engineered to simulate a wide variety of strongly correlated spin models. Owing to the superior coherence time of nuclear spins and nitrogen-vacancy centers in diamond, our proposal offers new opportunities towards large-scale quantum simulation at ambient conditions of temperature and pressure.

The detection of a nuclear spin in an individual molecule represents a key challenge in physics and biology whose solution has been pursued for many years. The small magnetic moment of a single nucleus and the unavoidable environmental noise present the key obstacles for its realization. In this paper, we demonstrate theoretically that a single nitrogen-vacancy center in diamond can be used to construct a nano-scale single-molecule spectrometer that is capable of detecting the position and spin state of a single nucleus and can determine the distance and alignment of a nuclear or electron spin pair. The proposed device would find applications in single-molecule spectroscopy in chemistry and biology, for example in determining the protein structure or in monitoring macromolecular motions, and can thus provide a tool to help unravel the microscopic mechanisms underlying bio-molecular function.

The accurate characterization of eigenmodes and eigenfrequencies of two-dimensional ion crystals provides the foundation for the use of such structures for quantum simulation purposes. We present a combined experimental and theoretical study of two-dimensional ion crystals. We demonstrate that standard pseudopotential theory accurately predicts the positions of the ions and the location of structural transitions between different crystal configurations. However, pseudopotential theory is insufficient to determine eigenfrequencies of the two-dimensional ion crystals accurately but shows significant deviations from the experimental data obtained from resolved sideband spectroscopy. Agreement at the level of 2.5×10−3 is found with the full time-dependent Coulomb theory using the Floquet-Lyapunov approach and the effect is understood from the dynamics of two-dimensional ion crystals in the Paul trap. The results represent initial steps towards an exploitation of these structures for quantum simulation schemes.

The loss of coherence is one of the main obstacles for the implementation of quantum information processing. The efficiency of dynamical decoupling schemes, which have been introduced to address this problem, is limited itself by the fluctuations in the driving fields which will themselves introduce noise. We address this challenge by introducing the concept of concatenated continuous dynamical decoupling, which can overcome not only external magnetic noise but also noise due to fluctuations in driving fields. We show theoretically that this approach can achieve relaxation limited coherence times, and demonstrate experimentally that already the most basic implementation of this concept yields an order of magnitude improvement to the decoherence time for the electron spin of nitrogen vacancy centers in diamond. The proposed scheme can be applied to a wide variety of other physical systems, including trapped atoms and ions and quantum dots, and may be combined with other quantum technologies challenges such as quantum sensing and quantum information processing.

We expand the solutions of linearly coupled Mathieu equations in terms of infinite-continued matrix inversions, and use it to find the modes which diagonalize the dynamical problem. This allows obtaining explicitly the (Floquet–Lyapunov) transformation to coordinates in which the motion is that of decoupled linear oscillators. We use this transformation to solve the Heisenberg equations of the corresponding quantum-mechanical problem, and find the quantum wavefunctions for stable oscillations, expressed in configuration space. The obtained transformation and quantum solutions can be applied to more general linear systems with periodic coefficients (coupled Hill equations, periodically driven parametric oscillators), and to nonlinear systems as a starting point for convenient perturbative treatment of the nonlinearity.

Setting off from the classic input–output formalism, we develop a theoretical framework to characterize the Gaussian quantum channels relating the initial correlations of an open bosonic system to those of properly identified output modes. We then proceed to apply our formalism to the case of quantum harmonic oscillators, such as the motional degrees of freedom of trapped ions or nanomechanical oscillators, interacting with travelling electromagnetic modes through cavity fields and subject to external white noise. We thus determine the degree of squeezing that can be transferred from an intra-cavity oscillator to light and show that the intra-cavity squeezing can be transformed into distributed optical entanglement if one can access both output fields of a two-sided cavity.

The quest for experimental platforms that allow for the exploration, and even control, of the interplay of low dimensionality and frustration is a fundamental challenge in several fields of quantum many-body physics, such as quantum magnetism. Here, we propose the use of cold crystals of trapped ions to study a variety of frustrated quantum spin ladders. By optimizing the trap geometry, we show how to tailor the low dimensionality of the models by changing the number of legs of the ladders. Combined with a method for selectively hiding ions provided by laser addressing, it becomes possible to synthesize stripes of both triangular and Kagome lattices. Besides, the degree of frustration of the phonon-mediated spin interactions can be controlled by shaping the trap frequencies. We support our theoretical considerations by initial experiments with planar ion crystals, where a high and tunable anisotropy of the radial trap frequencies is demonstrated. We take into account an extensive list of possible error sources under typical experimental conditions, and describe explicit regimes that guarantee the validity of our scheme.