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The ultimate precision limit in estimating the Larmor frequency of N unentangled qubits is well established, and is highly important for magnetometers, gyroscopes, and other types of quantum sensors. However, this limit assumes perfect projective measurements of the quantum registers. This requirement is not practical in many physical systems, such as NMR spectroscopy, where a weakly interacting external probe is used as a measurement device. Here, we show that in the framework of quantum nano-NMR spectroscopy, in which these limitations are inherent, the ultimate precision limit is still achievable using control and a finely tuned measurement.

Dynamical decoupling techniques are the method of choice for increasing gate fidelities. While these methods have produced very impressive results in terms of decreasing local noise and increasing the fidelities of single qubit operations, dealing with the noise of two qubit gates has proven more challenging. The main obstacle is that the noise time scale is shorter than the two qubit gate itself so that refocusing methods do not work. We present a measurement and feedback based method to refocus two qubit gates which cannot be refocused by conventional methods. We analyze in detail this method for an error model which is relevant for trapped ions quantum information.

Recently new approaches for sensing the frequency of time dependent Hamiltonians have been presented, and it was shown that the optimal Fisher information scales as ${T}^{4}.$ We present here our interpretation of this new scaling, where the relative phase is accumulated quadratically with time, and show that this can be produced by a variety of simple pulse sequences. Interestingly, this scaling has a limited duration, and we show that certain pulse sequences prolong the effect. The performance of these schemes is analyzed and we examine their relevance to state-of-the-art experiments. We analyze the ${T}^{3}$ scaling of the Fisher information which appears when multiple synchronized measurements are performed, and is the optimal scaling in the case of a finite coherence time.

Using long-range magnetic gradient induced coupling between three effective spins, a coherent QFT is efficiently realized with trapped Yb+ ions. With a single Yb+ ion, RF magnetic fields are measured close to the quantum limit.

Engineering entanglement between quantum systems often involves coupling through a bosonic mediator, which should be disentangled from the systems at the operation's end. The quality of such an operation is generally limited by environmental and control noise. One of the prime techniques for suppressing noise is by dynamical decoupling, where one actively applies pulses at a rate that is faster than the typical time scale of the noise. However, for boson-mediated gates, current dynamical decoupling schemes require executing the pulses only when the boson and the quantum systems are disentangled. This restriction implies an increase of the gate time by a factor of $\sqrt{N}$, with $N$ being the number of pulses applied. Here we propose and realize a method that enables dynamical decoupling in a boson mediated system where the pulses can be applied while spin-boson entanglement persists, resulting in an increase in time that is at most a factor of $\frac{\pi}{2}$, independently of the number of pulses applied. We experimentally demonstrate the robustness of our fast dynamically decoupled entangling gate to $\sigma_z$ noise with ions in a Paul trap.

Trapped ions are a promising tool for building a large-scale quantum computer. However, the number of required radiation fields for the realisation of quantum gates in any proposed ion-based architecture scales with the number of ions within the quantum computer, posing a major obstacle when imagining a device with millions of ions. Here we present a fundamentally different concept for trapped-ion quantum computing where this detrimental scaling entirely vanishes, replacing millions of radiation fields with only a handful of fields. The method is based on individually controlled voltages applied to each logic gate location to facilitate the actual gate operation analogous to a traditional transistor architecture within a classical computer processor. To demonstrate the key principle of this approach we implement a versatile quantum gate method based on long-wavelength radiation and use this method to generate a maximally entangled state of two quantum engineered clock-qubits with fidelity 0.985(12). This quantum gate also constitutes a simple-to-implement tool for quantum metrology, sensing and simulation.

The accumulation of quantum phase in response to a signal is the central mechanism of quantum sensing, as such, loss of phase information presents a fundamental limitation. For this reason approaches to extend quantum coherence in the presence of noise are actively being explored. Here we experimentally protect a room-temperature hybrid spin register against environmental decoherence by performing repeated quantum error correction whilst maintaining sensitivity to signal fields. We use a long-lived nuclear spin to correct multiple phase errors on a sensitive electron spin in diamond and realize magnetic field sensing beyond the timescales set by natural decoherence. The universal extension of sensing time, robust to noise at any frequency, demonstrates the definitive advantage entangled multi-qubit systems provide for quantum sensing and offers an important complement to quantum control techniques. In particular, our work opens the door for detecting minute signals in the presence of high frequency noise, where standard protocols reach their limits.

The experimental realization of many-body entangled states is one of the main goals of quantum technology as these states are a key resource for quantum computation and quantum sensing. However, increasing the number of photons in an entangled state has been proved to be a painstakingly hard task. This is a result of the non-deterministic emission of current photon sources and the distinguishability between photons from different sources. Moreover, the generation rate and the complexity of the optical setups hinder scalability. Here we present a new scheme that is compact, requires a very modest amount of components, and avoids the distinguishability issues by using only one single-photon source. States of any number of photons are generated with the same configuration, with no need for increasing the optical setup. The basic operation of this scheme is experimentally demonstrated and its sensitivity to imperfections is considered.

The use of long-wavelength radiation for gate operations is a promising approach for trapped-ion quantum computation. We demonstrate the key principle of this approach by generating a maximally entangled two-qubit Bell-state with fidelity of 0.985.

When incorporated in quantum sensing protocols, quantum error correction can be used to correct for high frequency noise, as the correction procedure does not depend on the actual shape of the noise spectrum. As such, it provides a powerful way to complement usual refocusing techniques. Relaxation imposes a fundamental limit on the sensitivity of state of the art quantum sensors which cannot be overcome by dynamical decoupling. The only way to overcome this is to utilize quantum error correcting codes. We present a superconducting magnetometry design that incorporates approximate quantum error correction, in which the signal is generated by a two qubit Hamiltonian term. This two-qubit term is provided by the dynamics of a tunable coupler between two transmon qubits. For fast enough correction, it is possible to lengthen the coherence time of the device beyond the relaxation limit.

Funding for Open Access provided by the UMD Libraries Open Access Publishing Fund., The physics of interacting integer-spin chains has been a topic of intense theoretical interest, particularly in the context of symmetry-protected topological phases. However, there has not been a controllable model system to study this physics experimentally. We demonstrate how spin-dependent forces on trapped ions can be used to engineer an effective system of interacting spin-1 particles. Our system evolves coherently under an applied spin-1 XY Hamiltonian with tunable, long-range couplings, and all three quantum levels at each site participate in the dynamics. We observe the time evolution of the system and verify its coherence by entangling a pair of effective three-level particles (“qutrits”) with 86% fidelity. By adiabatically ramping a global field, we produce ground states of the XY model, and we demonstrate an instance where the ground state cannot be created without breaking the same symmetries that protect the topological Haldane phase. This experimental platform enables future studies of symmetry-protected order in spin-1 systems and their use in quantum applications.

A fundamental goal of quantum technologies concerns the exploitation of quantum coherent dynamics for the realization of novel quantum applications such as quantum computing, quantum simulation, and quantum metrology. A key challenge on the way towards these goals remains the protection of quantum coherent dynamics from environmental noise. Here, we propose a concept of a hybrid dressed state from a pair of continuously driven systems. It allows sufficiently strong driving fields to suppress the effect of environmental noise while at the same time being insusceptible to both the amplitude and phase noise in the continuous driving fields. This combination of robust features significantly enhances coherence times under realistic conditions and at the same time provides new flexibility in Hamiltonian engineering that otherwise is not achievable. We demonstrate theoretically applications of our scheme for a noise-resistant analog quantum simulation in the well-studied physical systems of nitrogen-vacancy centers in diamond and of trapped ions. The scheme may also be exploited for quantum computation and quantum metrology.

We propose to experimentally explore the Haldane phase in spin-one XXZ antiferromagnetic chains using trapped ions. We show how to adiabatically prepare the ground states of the Haldane phase, demonstrate their robustness against sources of experimental noise, and propose ways to detect the Haldane ground states based on their excitation gap and exponentially decaying correlations, nonvanishing nonlocal string order, and doubly-degenerate entanglement spectrum.

A dialog with Asher Peres regarding the meaning of quantum teleportation is briefly reviewed. The Braunstein–Kimble method for teleportation of light is analyzed in the language of quantum wave functions. A pictorial example of continuous variable teleportation is presented using computer simulation.

In discrete models, such as spin chains, the entanglement between a pair of particles in a chain has been shown to vanish beyond a certain separation. In the continuum, a quantum field ⊘(x) at a point represents a single degree of freedom, thus at a region of finite size there are infinite separate degrees of freedom. We show that as a consequence, in contrast to discrete models, the ground state of a free, quantized and relativistic field exhibits entanglement between any pair of arbitrarily separated finite regions. We also provide a lower bound on the decay rate of the entanglement as a function of the separation length between the regions and briefly discuss the physical reasons behind this different behaviour of discrete and continuous systems.

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 propose a scheme that utilizes the collective enhancement of a photonic mode inside an atomic ensemble together with a proper Zeeman manifold in order to achieve a heralded polarization entangled Bell state. The entanglement is between two photons that are separated in time and can be used as a post selected deterministic source for applications such as quantum repeaters where a subsequent entanglement swapping measurement is employed. We present a detailed analysis of the practical limitation of the scheme., Comment: 6 pages, 5 figures

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.

We introduce a novel scheme that combines phonon-mediated quantum logic gates in trapped ions with the benefits of continuous dynamical decoupling. We demonstrate theoretically that a strong driving of the qubit decouples it from external magnetic-field noise, enhancing the fidelity of two-qubit quantum gates. Moreover, the scheme does not require ground-state cooling, and is inherently robust to undesired ac-Stark shifts. The underlying mechanism can be extended to a variety of other systems where a strong driving protects the quantum coherence of the qubits without compromising the two-qubit couplings., Comment: Slightly longer than the published version

We investigate the performance of inhomogeneously broadened spin ensembles as quantum memories under continuous dynamical decoupling. The role of the continuous driving field is twofold: firstly, it decouples individual spins from magnetic noise; secondly, and more importantly, it suppresses and reshapes the spectral inhomogeneity of spin ensembles. We show that a continuous driving field, which itself may also be inhomogeneous over the ensemble, can considerably enhance the decay of the tails of the inhomogeneous broadening distribution. This fact enables a spin-ensemble-based quantum memory to exploit the effect of cavity protection and achieve a much longer storage time. In particular, for a spin ensemble with a Lorentzian spectral distribution, our calculations demonstrate that continuous dynamical decoupling has the potential to improve its storage time by orders of magnitude for the state-of-the-art experimental parameters., publishedVersion

Trapped atomic ions have been successfully used for demonstrating basic elements of universal quantum information processing (QIP). Nevertheless, scaling up of these methods and techniques to achieve large scale universal QIP, or more specialized quantum simulations remains challenging. The use of easily controllable and stable microwave sources instead of complex laser systems on the other hand promises to remove obstacles to scalability. Important remaining drawbacks in this approach are the use of magnetic field sensitive states, which shorten coherence times considerably, and the requirement to create large stable magnetic field gradients. Here, we present theoretically a novel approach based on dressing magnetic field sensitive states with microwave fields which addresses both issues and permits fast quantum logic. We experimentally demonstrate basic building blocks of this scheme to show that these dressed states are long-lived and coherence times are increased by more than two orders of magnitude compared to bare magnetic field sensitive states. This changes decisively the prospect of microwave-driven ion trap QIP and offers a new route to extend coherence times for all systems that suffer from magnetic noise such as neutral atoms, NV-centres, quantum dots, or circuit-QED systems., Comment: 9 pages, 4 figures

We exploit the geometry of a zig-zag cold-ion crystal in a linear trap to propose the quantum simulation of a paradigmatic model of long-ranged magnetic frustration. Such a quantum simulation would clarify the complex features of a rich phase diagram that presents ferromagnetic, dimerized antiferromagnetic, paramagnetic, and floating phases, together with previously unnoticed features that are hard to assess by numerics. We analyze in detail its experimental feasibility, and provide supporting numerical evidence on the basis of realistic parameters in current ion-trap technology., replaced with published version

We investigate the entanglement between two spatially separated intervals in the vacuum state of a free one-dimensional Klein-Gordon field by means of explicit computations in the continuum limit of the linear harmonic chain. We demonstrate that the entanglement, which we quantify by the logarithmic negativity, is finite with no further need for renormalization. We find that in the critical regime, the quantum correlations are scale invariant as they depend only on the ratio of distance to length. They decay much faster than the classical correlations as in the critical limit long-range entanglement decays exponentially for separations larger than the size of the blocks, while classical correlations follow a power-law decay. With decreasing distance of the blocks, the entanglement diverges as a power law in the distance. The noncritical regime manifests richer behavior, as the entanglement depends both on the size of the blocks and on their separation. In correspondence with the von Neumann entropy also long-range entanglement distinguishes critical from noncritical systems.

We seek the first indications that a nanoelectromechanical system (NEMS) is entering the quantum domain as its mass and temperature are decreased. We find them by studying the transition from classical to quantum behavior of a driven nonlinear Duffing resonator. Numerical solutions of the equations of motion, operating in the bistable regime of the resonator, demonstrate that the quantum Wigner function gradually deviates from the corresponding classical phase-space probability density. These clear differences that develop due to nonlinearity can serve as experimental signatures, in the near future, that NEMS resonators are entering the quantum domain.

Much experimental effort is invested these days in fabricating nanoelectromechanical systems (NEMS) that are sufficiently small, cold and clean, so as to approach quantum mechanical behavior as their typical quantum energy scale becomes comparable with that of the ambient thermal energy kBT. Such systems will hopefully enable one to observe the quantum behavior of human-made objects, and test some of the basic principles of quantum mechanics. Here, we expand and elaborate on our recent suggestion (Katz et al 2007?Phys. Rev. Lett.?99?040404) to exploit the nonlinear nature of a nanoresonator in order to observe its transition into the quantum regime. We study this transition for an isolated resonator, as well as one that is coupled to a heat bath at either zero or finite temperature. We argue that by exploiting nonlinearities, quantum dynamics can be probed using technology that is almost within reach. Numerical solutions of the equations of motion display the first quantum corrections to classical dynamics that appear as the classical-to-quantum transition occurs. This provides practical signatures to look for in future experiments with NEMS resonators.

We present a method of generating collective multi-qubit entanglement via global addressing of an ion chain following the guidelines of the Tavis-Cummings model, where several qubits are coupled to a collective motional mode. We show that a wide family of Dicke states and irradiant states can be generated by single global laser pulses, unitarily or helped with suitable postselection techniques., 6 pages, 3 figures. Accepted for publication in Physical Review A

We discuss the consequences of the Aharonov-Bohm (AB) effect in setups involving several charged particles, wherein none of the charged particles encloses a closed loop around the magnetic flux. We show that in such setups, the AB phase is encoded either in the relative phase of a bipartite or multipartite entangled photons states, or alternatively, gives rise to an overall AB phase that can be measured relative to another reference system. These setups involve processes of annihilation or creation of electron-hole pairs. We discuss the relevance of such effects in ``vacuum birefringence" in QED, and comment on their connection to other known effects.

We employ an approach wherein the ground state entanglement of a relativistic free scalar field is directly probed in a controlled manner. The approach consists of having a pair of initially nonentangled detectors locally interact with the vacuum for a finite duration $T$, such that the two detectors remain causally disconnected, and then analyzing the resulting detector mixed state. We show that the correlations between arbitrarily far-apart regions of the vacuum cannot be reproduced by a local hidden-variable model, and that as a function of the distance $L$ between the regions, the entanglement decreases at a slower rate than $\ensuremath{\sim}\mathrm{exp}[\ensuremath{-}{(L∕cT)}^{3}]$.

We propose and study a method for detecting ground-state entanglement in a chain of trapped ions, which realizes a suggested scheme for detecting vacuum entanglement in quantum field theory. We show that the entanglement between single ions or groups of ions can be swapped to the internal levels of two ions by sending laser pulses that couple the internal and motional degrees of freedom. This allows to entangle two ions without actually doing gates. A proof of principle of the effect can be realized with two trapped ions and is feasible with current technology., 4 pages 8 figures

We present a detailed study on the possibility of manipulating quantum information encoded in the "radial" modes of arrays of trapped ions (i.e., in the ions' oscillations orthogonal to the trap's main axis). In such systems, because of the tightness of transverse confinement, the radial modes pertaining to different ions can be addressed individually. In the first part of the paper we show that, if local control of the radial trapping frequencies is available, any linear optical and squeezing operation on the locally defined modes - on single as well as on many modes - can be reproduced by manipulating the frequencies. Then, we proceed to describe schemes apt to generate unprecedented degrees of bipartite and multipartite continuous variable entanglement under realistic noisy working conditions, and even restricting only to a global control of the trapping frequencies. Furthermore, we consider the transmission of the quantum information encoded in the radial modes along the array of ions, and show it to be possible to a remarkable degree of accuracy, for both finite-dimensional and continuous variable quantum states. Finally, as an application, we show that the states which can be generated in this setting allow for the violation of multipartite non-locality tests, by feasible displaced parity measurements. Such a demonstration would be a first test of quantum non-locality for "massive" degrees of freedom (i.e., for degrees of freedom describing the motion of massive particles)., 21 pages; this paper, presenting a far more extensive and detailed analysis, completely supersedes arXiv:0708.0851