Remote Spins Research Articles

The Creation of Remote Spin Entanglement with a Nanomechanical Cantilever

We consider the creation of entanglement between remote electron spins using a magnetic nanoparticle attached to a cantilever tip (CT). We assume that the frequency of the CT vibrations matches the Larmor frequency of the spin (CT–spin resonance). Under the conditions of CT–spin resonance, the CT–spin system is described using the Jaynes–Cummings model. In this work, using the evolution operator of the Jaynes–Cummings model, we show that a movable CT can create an entangled state between remote spins. The most striking result is that the entanglement between the remote spins can be achieved without measuring the vibrational state of the CT.

Room-temperature polarization of individual nuclear spins in diamond via anisotropic hyperfine coupling and coherent population trapping

We employ the electronic spin of a single nitrogen-vacancy (NV) defect in diamond to detect and control the quantum state of remote nuclear spins coupled by hyperfine interaction. More precisely, our work focuses on individual ^{13}text {C} nuclei featuring a moderate hyperfine coupling strength (sim 1 MHz) with the NV’s electron spin. Two different methods providing an efficient room-temperature polarization of these peculiar ^{13}text {C} nuclear spins are described. The first one is based on a polarization transfer from the NV electron spin to the ^{13}text {C} nucleus, which is mediated by the anisotropic component of the hyperfine interaction. The second one relies on coherent population trapping (CPT) within a Lambda -type energy-level configuration in the microwave domain, which enables to initialize the ^{13}text {C} nuclear spin in any quantum state superposition on the Bloch sphere. This CPT protocol is performed in an unusual regime for which relaxation from the excited level of the Lambda -scheme is externally triggered by optical pumping and separated in time from coherent microwave excitations. For these two polarization techniques, we investigate the impact of optical illumination on the nuclear spin polarization efficiency. This work adds new methods to the quantum toolbox used for coherent control of individual nuclear spins in diamond, which might find applications in quantum metrology.Graphical

Sign switching of superexchange mediated by a few electrons in a nonuniform magnetic field

Long-range interaction between distant spins is an important building block for the realization of a large quantum-dot network in which couplings between pairs of spins can be selectively addressed. Recent experiments on the coherent oscillation of logical states between remote spins facilitated by intermediate electron states were the first step for large-scale quantum information processing. Reaching this ultimate goal requires extensive studies on the superexchange interaction in different quantum-dot spatial arrangements and electron configurations. Here, we consider a linear triple quantum dot with two antiparallel spins in the outer dots forming the logical states while varying numbers of electrons in the middle dot form a mediator, which facilitates the superexchange interaction. We show that the superexchange is enhanced when the number of mediating electrons increases. In addition, we show that forming a four-electron triplet in the mediator dot further enhances the superexchange strength. Our work can be a guide to scale up the quantum-dot array with controllable and dense connectivity.

Proposal for room-temperature quantum repeaters with nitrogen-vacancy centers and optomechanics

We propose a quantum repeater architecture that can operate under ambient conditions. Our proposal builds on recent progress towards non-cryogenic spin-photon interfaces based on nitrogen-vacancy centers, which have excellent spin coherence times even at room temperature, and optomechanics, which allows to avoid phonon-related decoherence and also allows the emitted photons to be in the telecom band. We apply the photon number decomposition method to quantify the fidelity and the efficiency of entanglement established between two remote electron spins. We describe how the entanglement can be stored in nuclear spins and extended to long distances via quasi-deterministic entanglement swapping operations involving the electron and nuclear spins. We furthermore propose schemes to achieve high-fidelity readout of the spin states at room temperature using the spin-optomechanics interface. Our work shows that long-distance quantum networks made of solid-state components that operate at room temperature are within reach of current technological capabilities.

Secular and semi-nonsecular models of cross-polarization kinetics for remote spins: an application for nano-structured calcium hydroxyapatite

The 1H → 31P cross-polarization (CP) kinetics in the nanostructured calcium hydroxyapatite (nano-CaHA) was measured under moderate (5 kHz) magic-angle spinning (MAS) rate. This material was chosen as it contains the distanced 1H–31P spin pairs and the interactions between them are characterized by a relatively low dipolar coupling (b) that could be comparable with the spin-diffusion rates (R). Therefore, the physical legitimacy to use the secular solution of the quantum Liouville–von Neumann equation is doubtful. The semi-nonsecular model of spin dynamics was applied, and the results were compared with those obtained by the secular approach. The comparable results obtained by both models show that the secular model is applicable, with certain reservation, also in the case of |b| ≈ R. The extremely high anisotropy of spin diffusion in the nano-CaHA was deduced. This can be a matter of the applied approach, as the interactions of the 31P spins with the proton bath were neglected in both models. The high anisotropy could also be caused by the physical reasons that stem from the structural and proton diffusion features of CaHA. This material belongs to low-dimensional proton conductors possessing a large motional freedom for protons along OH– chains.

Exchange Coupling in a Linear Chain of Three Quantum-Dot Spin Qubits in Silicon.

Quantum gates between spin qubits can be implemented leveraging the natural Heisenberg exchange interaction between two electrons in contact with each other. This interaction is controllable by electrically tailoring the overlap between electronic wave functions in quantum dot systems, as long as they occupy neighboring dots. An alternative route is the exploration of superexchange-the coupling between remote spins mediated by a third idle electron that bridges the distance between quantum dots. We experimentally demonstrate direct exchange coupling and provide evidence for second neighbor mediated superexchange in a linear array of three single-electron spin qubits in silicon, inferred from the electron spin resonance frequency spectra. We confirm theoretically, through atomistic modeling, that the device geometry only allows for sizable direct exchange coupling for neighboring dots, while next-nearest neighbor coupling cannot stem from the vanishingly small tail of the electronic wave function of the remote dots, and is only possible if mediated.

Cross-polarization kinetics and fractal nature of thermal equilibration in spin systems: From low-dimensional proton conductors to tripeptides

Cross-polarization with magic-angle spinning (CP MAS) kinetics (1H–13C and 1H–31P) between remote spins were studied in a series of selected materials: from poly-(vinyl phosphonic acid) (pVPA) to calcium hydroxyapatite (CaHA), poly(2-hydroxyethyl methacrylate) (pHEMA), glycine and ultimately to tripeptides (Gly-Pro-Gly, Gly-Phe-Gly and Gly-Gly-Gly). The selection was based on the working concept that the pathways of thermal equilibration in the proton bath should be linked to the structural features of materials. Therefore we attempted to cover the maximal range of dimensionality of conceivable fractal structures as depicted in numerous literature sources. The ‘stretched exponential’ decay was involved in a purely phenomenological way to describe the thermal equilibration during the polarization transfer between remote spins. Its ‘stretching’ index allowed determining the fractal dimensions (Dp) of equilibration pathways. The spin-diffusion model improved by the thermal equilibration in the proton bath was the most appropriate to describe the experimental CP kinetics in the studied series.The fractal dimensions obtained for studied compounds are very reasonable: CaHA and pVPA behave as one-dimensional systems, whereas pHEMA and glycine are close to 2D-systems, and tripeptides can be considered as ‘almost’ 3D-systems. This rational sequence allows us to state that the developed treatment of CP kinetics with included thermal equilibration can reproduce the fractal images of complex compounds. The thermal equilibration is mainly mediated through the strongest interatomic/intramolecular vibrations. In addition to elasticity, a peculiar role of high mobility of protons along H-bonds has to be stressed.

Interplay of exchange and superexchange in triple quantum dots

Recent experiments on semiconductor quantum dots have demonstrated the ability to utilize a large quantum dot to mediate superexchange interactions and generate entanglement between distant spins. This opens up a possible mechanism for selectively coupling pairs of remote spins in a larger network of quantum dots. Taking advantage of this opportunity requires a deeper understanding of how to control superexchange interactions in these systems. Here, we consider a triple-dot system arranged in linear and triangular geometries. We use configuration interaction calculations to investigate the interplay of superexchange and nearest-neighbor exchange interactions as the location, detuning, and electron number of the mediating dot are varied. We show that superexchange processes strongly enhance and increase the range of the net spin-spin exchange as the dots approach a linear configuration. Furthermore, we show that the strength of the exchange interaction depends sensitively on the number of electrons in the mediator. Our results can be used as a guide to assist further experimental efforts towards scaling up to larger, two-dimensional quantum dot arrays.

Strong polarization of individual nuclear spins weakly coupled to nitrogen-vacancy color centers in diamond

We experimentally demonstrate high degree of polarization of 13C nuclear spins weakly interacting with nitrogen-vacancy (NV) centers in diamond. We combine coherent microwave excitation pulses with optical illumination to provide controlled relaxation and achieve a polarity-tunable, fast nuclear polarization of degree higher than 85% at room temperature for remote 13C nuclear spins exhibiting hyperfine interaction strength with NV centers of the order of 600 kHz. We show with the aid of numerical simulation that the anisotropic hyperfine tensor components naturally provide a route to control spin mixing parameter so that highly efficient nuclear polarization is enabled through careful tuning of nuclear quantization axis by external magnetic field. We further discuss spin dynamics and wide applicability of this method to various target 13C nuclear spins around the NV center electron spin. The proposed control method demonstrates an efficient and versatile route to realize, for example, high-fidelity spin register initialization and quantum metrology using nuclear spin resources in solids.

Quasi-Equilibria and Polarization Transfer Between Adjacent and Remote Spins: 1H-13C CP MAS Kinetics in Glycine.

The 1H-13C CP MAS kinetic curves were measured in glycine powder sample at the MAS rates of 7, 10, and 12 kHz. Each experimental curve contained up to 1000 equidistant points over the whole contact time range of 10 μs - 10 ms. The CP kinetic data for CH2 group, i.e., for the system containing adjacent 1H-13C spin pairs with a definite dominant dipolar coupling can be described in the frame of the isotropic spin-diffusion approach. The local order parameter ⟨ S⟩ ≈ 1.0, determined as the ratio of the measured dipolar 1H-13C coupling constant and the calculated static dipolar coupling constant, is very close to the values deduced in series of other amino acids. The strong narrow peaks observed in the spin coupling spectrum at multiples of the MAS frequency can be considered as the confirmation that the periodic quasi-equilibrium state can appear also in the powder samples. The anisotropic spin-diffusion approach improved by the introducing of the thermal equilibration in the proton bath is the most proper model to describe the CP kinetics in the system containing remote spins. Very realistic values of the spin-cluster size ( N) have been obtained without any constraint on the flow of the nonlinear curve fitting. The finite values of N ≤ 4 means that CP transfer is located within one glycine molecule.

Engineering of entanglement and spin state transfer via quantum chains of atomic spins at large separations

Several recent experiments have shown that long-range exchange interactions can determine collective magnetic ground states of nanostructures in bulk and on surfaces. The ability to generate and control entanglement in a system with long-range interaction will be of great importance for future quantum technology. An important step forward to reach this goal is the creation of entangled states for spins of distant magnetic atoms. Herein, the generation of long-distance entanglement between remote spins at large separations in bulk and on surface is studied theoretically, based on a quantum spin Hamiltonian and time-dependent Schrödinger equation for experimentally realized conditions. We demonstrate that long-distance entanglement can be generated between remote spins by using an appropriate quantum spin chain (a quantum mediator), composed by sets of antiferromagnetically coupled spin dimers. Ground state properties and quantum spin dynamics of entangled atoms are studied. We demonstrate that one can increase or suppress entanglement by adding a single spin in the mediator. The obtained result is explained by monogamy property of entanglement distribution inside a quantum spin system. We present a novel approach for non-local sensing of remote magnetic adatoms via spin entanglement.

Cross-entangling electronic and nuclear spins of distant nitrogen-vacancy centers in noisy environments by means of quantum microwave radiation

Nitrogen-vacancy (NV) defect centers in diamond are strong candidates to generate entangled states in solid-state environments even at room temperature. Quantum correlations in spatially separated NV systems, for distances between NVs ranging from a few nanometers to a few kilometers, have been recently reported. In the present work we consider the entanglement transfer from two- mode microwave squeezed (entangled) photons, which are in resonance with the two lowest NV electron spin states, to initially unentangled NV centers. We first demonstrate that the entanglement transfer process from quantum microwaves to isolated NV electron spins is feasible. We then proceed to extend the previous results to more realistic scenarios where 13 C nuclear spin baths surrounding each NV are included, quantifying the entanglement transfer efficiency and robustness under the effects of dephasing/dissipation noisy nuclear baths. Finally, we address the issue of assessing the possibility of entanglement transfer from the squeezed microwave light to two remote nuclear spins closely linked to different NV centers.

Pulse-phase control for spectral disambiguation in quantum sensing protocols

We present a method to identify spurious signals generated by finite-width pulses in quantum sensing experiments and apply it to recently proposed dynamical decoupling sequences for accurate spectral interpretation. We first study the origin of these fake resonances and quantify their behavior in a situation that involves the measurement of a classical magnetic field. Here we show that a change of the initial phase of the sensor or, equivalently, of the decoupling pulses leads to oscillations in the spurious signal intensity while the real resonances remain intact. Finally we extend our results to the quantum regime for the unambiguous detection of remote nuclear spins by utilization of a nitrogen vacancy sensor in diamond.

Role of the electron spin in determining the coherence of the nuclear spins in a quantum dot.

A huge effort is underway to develop semiconductor nanostructures as low-noise qubits. A key source of dephasing for an electron spin qubit in GaAs and in naturally occurring Si is the nuclear spin bath. The electron spin is coupled to each nuclear spin by the hyperfine interaction. The same interaction also couples two remote nuclear spins via a common coupling to the delocalized electron. It has been suggested that this interaction limits both electron and nuclear spin coherence, but experimental proof is lacking. We show that the nuclear spin decoherence time decreases by two orders of magnitude on occupying an empty quantum dot with a single electron, recovering to its original value for two electrons. In the case of one electron, agreement with a model calculation verifies the hypothesis of an electron-mediated nuclear spin-nuclear spin coupling. The results establish a framework to understand the main features of this complex interaction in semiconductor nanostructures.

Subnanoscale Order and Spin Diffusion in Complex Solids through the Processing of Cross-Polarization Kinetics

The advanced strategy of processing of NMR cross-polarization (CP) data has been developed separating the short-range order- and the bulk effects in the manifold of spin interactions. The effectiveness of such treatment have been demonstrated on 1H–31P CP kinetics in the nanostructured calcium hydroxyapatite (nano-CaHA) and that containing amorphous phosphate phase (amorph-CaHA). This allowed to describe the oscillatory manner of CP kinetics, oscillation blurring phenomenon, and to determine the spin distribution at the short- and moderate internuclear distances. The contribution of the dipolar coupling with remote spins has been removed modeling their spatial distribution using a set of radial profiles. The short 31P–1H contact peak at 0.24–0.27 nm has been well resolved in the spatial distribution profile of the nano-CaHA sample and it is hardly noticeable in the case of amorph-CaHA. It reflects the differences in surface organization in nanostructured and amorphous materials. The spin diffusion process...

Resolving remote nuclear spins in a noisy bath by dynamical decoupling design

We experimentally resolve several weakly coupled nuclear spins in diamond using a series of novelly designed dynamical decoupling controls. Some nuclear spin signals, hidden by decoherence under ordinary dynamical decoupling controls, are shifted forward in time domain to the coherence time range and thus rescued from the fate of being submerged by the noisy spin bath. In this way, more and remoter single nuclear spins are resolved. Additionally, the field of detection can be continuously tuned on sub-nanoscale. This method extends the capacity of nanoscale magnetometry and may be applicable in other systems for high-resolution noise spectroscopy.

Heteronuclear transverse and longitudinal relaxation in AX4 spin systems: Application to 15N relaxations in 15NH4+

The equations that describe the time-evolution of transverse and longitudinal 15N magnetisations in tetrahedral ammonium ions, 15NH4+, are derived from the Bloch-Wangsness-Redfield density operator relaxation theory. It is assumed that the relaxation of the spin-states is dominated by (1) the intra-molecular 15N–1H and 1H–1H dipole–dipole interactions and (2) interactions of the ammonium protons with remote spins, which also include the contribution to the relaxations that arise from the exchange of the ammonium protons with the bulk solvent. The dipole–dipole cross-correlated relaxation mechanisms between each of the 15N–1H and 1H–1H interactions are explicitly taken into account in the derivations. An application to 15N-ammonium bound to a 41kDa domain of the protein DnaK is presented, where a comparison between experiments and simulations show that the ammonium ion rotates rapidly within its binding site with a local correlation time shorter than approximately 1ns. The theoretical framework provided here forms the basis for further investigations of dynamics of AX4 spin systems, with ammonium ions in solution and bound to proteins of particular interest.

Quantum information processing and metrology with color centers in diamonds

The Nitrogen-Vacancy (NV) center is becoming a promising qubit for quantum information processing. The defect has a long coherence time at room temperature and it allows spin state initialized and read out by laser and manipulated by microwave pulses. It has been utilized as a ultra sensitive probe for magnetic fields and remote spins as well. Here, we review the recent progresses in experimental demonstrations based on NV centers. We first introduce our work on implementation of the Deutsch-Jozsa algorithm with a single electronic spin in diamond. Then the quantum nature of the bath around the center spin is revealed and continuous wave dynamical decoupling has been demonstrated. By applying dynamical decoupling, a multi-pass quantum metrology protocol is realized to enhance phase estimation. In the final, we demonstrated NV center can be regarded as a ultra-sensitive sensor spin to implement nuclear magnetic resonance (NMR) imaging at nanoscale.

Quantum mechanical NMR simulation algorithm for protein-size spin systems

Nuclear magnetic resonance spectroscopy is one of the few remaining areas of physical chemistry for which polynomially scaling quantum mechanical simulation methods have not so far been available. In this communication we adapt the restricted state space approximation to protein NMR spectroscopy and illustrate its performance by simulating common 2D and 3D liquid state NMR experiments (including accurate description of relaxation processes using Bloch–Redfield–Wangsness theory) on isotopically enriched human ubiquitin – a protein containing over a thousand nuclear spins forming an irregular polycyclic three-dimensional coupling lattice. The algorithm uses careful tailoring of the density operator space to only include nuclear spin states that are populated to a significant extent. The reduced state space is generated by analysing spin connectivity and decoherence properties: rapidly relaxing states as well as correlations between topologically remote spins are dropped from the basis set.

Composite and shaped pulses for efficient and robust pumping of disconnected eigenstates in magnetic resonance

Hyperpolarization methods, which can enhance nuclear spin signals by orders of magnitude, open up important new opportunities in magnetic resonance. However, many of these applications are limited by spin lattice relaxation, which typically destroys the hyperpolarization in seconds. Significant lifetime enhancements have been found with "disconnected eigenstates" such as the singlet state between a pair of nearly equivalent spins, or the "singlet-singlet" state involving two pairs of chemically equivalent spins; the challenge is to populate these states (for example, from thermal equilibrium magnetization or hyperpolarization) and to later recall the population into observable signal. Existing methods for populating these states are limited by either excess energy dissipation or high sensitivity to inhomogeneities. Here we overcome the limitations by extending recent work using continuous-wave irradiation to include composite and adiabatic pulse excitations. Traditional composite and adiabatic pulses fail completely in this problem because the interactions driving the transitions are fundamentally different, but the new shapes we introduce can move population between accessible and disconnected eigenstates over a wide range of radio-frequency (RF) amplitudes and offsets while depositing insignificant amounts of power.