Chains Of Ions Research Articles

Dynamical Hamiltonian engineering of 2D rectangular lattices in a one-dimensional ion chain

Controlling the interaction graph between spins or qubits in a quantum simulator allows user-controlled tailoring of native interactions to achieve a target Hamiltonian. Engineering long-ranged phonon-mediated spin–spin interactions in a trapped ion quantum simulator offers such a possibility. Trapped ions, a leading candidate for quantum simulation, are most readily trapped in a linear 1D chain, limiting their utility for readily simulating higher dimensional spin models. In this work, we introduce a hybrid method of analog-digital simulation for simulating 2D spin models which allows for the dynamic changing of interactions to achieve a new graph using a linear 1D chain. We focus this numerical work on engineering 2D rectangular nearest-neighbor spin lattices, demonstrating that the required control parameters scale linearly with ion number. This hybrid approach offers compelling possibilities for the use of 1D chains in the study of Hamiltonian quenches, dynamical phase transitions, and quantum transport in 2D and 3D.

More crystal field theory in action: the metal-4-picoline (pic)-sulfate [M(pic)x]SO4 complexes (M= Fe, Co, Ni, Cu, Zn, and Cd).

Seven crystal structures of five first-row (Fe, Co, Ni, Cu, and Zn) and one second-row (Cd) transition metal-4-picoline (pic)-sulfate complexes of the form [M(pic)x]SO4 are reported. These complexes are catena-poly[[tetrakis(4-methylpyridine-κN)metal(II)]-μ-sulfato-κ2O:O'], [M(SO4)(C6H7N)4]n, where the metal/M is iron, cobalt, nickel, and cadmium, di-μ-sulfato-κ4O:O-bis[tris(4-methylpyridine-κN)copper(II)], [Cu2(SO4)2(C6H7N)6], catena-poly[[bis(4-methylpyridine-κN)zinc(II)]-μ-sulfato-κ2O:O'], [Zn(SO4)(C6H7N)2]n, and catena-poly[[tris(4-methylpyridine-κN)zinc(II)]-μ-sulfato-κ2O:O'], [Zn(SO4)(C6H7N)3]n. The Fe, Co, Ni, and Cd compounds are isomorphous, displaying polymeric crystal structures with infinite chains of MII ions adopting an octahedral N4O2 coordination environment that involves four picoline ligands and two bridging sulfate anions. The Cu compound features a dimeric crystal structure, with the CuII ions possessing square-pyramidal N3O2 coordination environments that contain three picoline ligands and two bridging sulfate anions. Zinc crystallizes in two forms, one exhibiting a polymeric crystal structure with infinite chains of ZnII ions adopting a tetrahedral N2O2 coordination containing two picoline ligands and two bridging sulfate anions, and the other exhibiting a polymeric crystal structure with infinite chains of ZnII ions adopting a trigonal bipyramidal N3O2 coordination containing three picoline ligands and two bridging sulfate anions. The structures are compared with the analogous pyridine complexes, and the observed coordination environments are examined in relation to crystal field theory.

Absolute single-ion thermometry

We describe and experimentally implement a single-ion local thermometry technique with absolute sensitivity adaptable to all laser-cooled atomic ion species. The technique is based on the velocity-dependent spectral shape of a quasi-dark resonance tailored in a J $\rightarrow$ J transition such that the two driving fields can be derived from the same laser source leading to a negligible relative phase shift. We validated the method and tested its performances in an experiment on a single 88 Sr + ion cooled in a surface radio-frequency trap. We first applied the technique to characterise the heating-rate of the surface trap. We then measured the stationary temperature of the ion as a function of cooling laser detuning in the Doppler regime. The results agree with theoretical calculations, with an absolute error smaller than 100 $\mu$K at 500 $\mu$K, in a temperature range between 0.5 and 3 mK and in the absence of adjustable parameters. This simple-to-implement and reliable method opens the way to fast absolute measurements of single-ion temperatures in future experiments dealing with heat transport in ion chains or thermodynamics at the single-ion level.

Controlling systematic frequency uncertainties at the 10−19 level in linear Coulomb crystals

Trapped ions are ideally suited for precision spectroscopy, as is evident from the remarkably low systematic uncertainties of single-ion clocks. The major weakness of these clocks is the long averaging time, necessitated by the low signal of a single atom. An increased number of ions can overcome this limitation and allow for the implementation of novel clock schemes. However, this presents the challenge to maintain the excellent control over systematic shifts of a single particle in spatially extended and strongly coupled many-body systems. We measure and deduce systematic frequency uncertainties related to spectroscopy with ion chains in a newly developed rf trap array designed for precision spectroscopy on simultaneously trapped ion ensembles. For the example of an In${}^+$ clock, sympathetically cooled with Yb${}^+$ ions, we show in our system that the expected systematic frequency uncertainties related to multi-ion operation can be below $1\times10^{-19}$. Our results pave the way to advanced spectroscopy schemes such as entangled clock spectroscopy and cascaded clock operation.

Analytical treatment of Anderson localization in a chain of trapped ions experiencing laser Bessel beams**Project supported by the National Natural Science Foundation of China (Grant Nos. 11734018, 11674360, 11404377, and 91636220).

Trapped ions, under electromagnetic confinement and Coulomb repulsion, can behave as non-interacting particles in one-dimensional lattices. Here we explore analytically the possible effects regarding Anderson localization in a chain of trapped ions experiencing laser Bessel beams. Under an experimentally feasible condition, we predict an analytical form of the energy-dependent mobility edges, which is verified to be in good agreement with the exact numerical results except for the top band. Some other important properties regarding the phonon localization in the ion chain are also discussed both analytically and numerically. Our results are relevant to experimental observation of localization–delocalization transition in the ion trap and helpful for deeper understanding of the rich phenomena due to long-range phonon hopping.

Vibrational properties and magnetic specific heat of the covalent chain antiferromagnet RbFeSe2

The magnetic specific heat of $\mathrm{RbFeS}{\mathrm{e}}_{2}$ and the spin state of $\mathrm{F}{\mathrm{e}}^{3+}$ ions in the compound have been studied. Phonon dispersion and phonon density of states (PDOS), element specific and total, were evaluated from first-principles calculations. It is shown that iron atoms in quasi-one-dimensional chains have dramatically different vibrational properties against Rb and Se atoms: the Fe PDOS is mostly concentrated within two Einstein-like optical phonon peaks at high frequencies. Analysis of our M\ossbauer data for $\mathrm{RbFeS}{\mathrm{e}}_{2}$, utilizing the calculated Fe PDOS as well as our optical absorption measurements, have shown full agreement with the location of the high-frequency optical-type lattice vibrations within the $\mathrm{FeS}{\mathrm{e}}_{4}$ tetrahedra. The calculated PDOS was utilized to evaluate the lattice contribution to the specific heat. The phonon heat capacity has been used to evaluate the magnetic specific heat of the quasi-one-dimensional antiferromagnetically correlated $\mathrm{F}{\mathrm{e}}^{3+}$ ion chains in $\mathrm{RbFeS}{\mathrm{e}}_{2}$. An intermediate spin state $S=3/2$ has been found most closely relevant to our magnetic entropy analysis for $\mathrm{F}{\mathrm{e}}^{3+}$ ions in $\mathrm{RbFeS}{\mathrm{e}}_{2}$.

Quantum thermometry with trapped ions

We introduce the estimation protocol for detecting the temperature of the transverse vibrational modes of linear ion crystal. We show that thanks to the laser induced laser coupling between the vibrational modes and the collective spin states the estimation of the temperature is carried out by set of measurements of the spin populations. We show that temperature estimation protocol using single ion as a quantum probe is optimal in a sense that the set of state projective measurement saturates the fundamental Cramer-Rao bound. We find a plateau of the maximal temperature sensitivity using ion chain as a quantum probe. Moreover, we show that the non-classical part of the quantum Fisher information could leads to enhancement of the temperature sensitivity compared to the single ion case.

Charge-assisted hydrogen bonding in three diaminobenzene salts.

Hydrogen-bonding interactions play an important role in the rational design of crystal systems with desirable architectures. The crystal structures of benzene-1,2-diaminium sulfate sesquihydrate, C6H20N22+·SO42-·1.5H2O, (1), benzene-1,3-diaminium tetrachloridozincate(II), (C6H20N2)[ZnCl4], (3), and 3-aminoanilinium perchlorate, C6H9N2+·ClO4-, (4), are reported. Hydrated salt (1) is a polymorph (space group C2/c) of a previously reported [Anderson et al. (2011). Cryst. Growth Des. 11, 4904-4919] crystalline modification of salt (2) (space group P21/c). The contents of the asymmetric unit of (2) are twice that of (1). In each, the extended structures exhibit hydrogen bonds, resulting in chains of ions and hydrogen-bonded rings with an R44(8) motif involving water molecules. Hirshfeld surface analysis shows that a significant difference between the two is the degree of C...C interaction. Salt (3) exhibits an extended structure having hydrogen-bonded rings and parallel benzene rings, with a centroid-to-centroid separation of 3.860 (2) Å. Salt (4) displays a three-dimensional superstructure that results from linked planes of ions joined by an extensive hydrogen-bonding network involving N-H...O, N-H...N and C-H...π interactions. The cation-anion and N-H...N interaction energies in (4), determined using density functional theory (DFT), show significantly stronger aminium-perchlorate than amine-perchlorate interactions.

Cryogenic trapped-ion system for large scale quantum simulation

Trapped-ion systems are among the most promising hardware candidates for large scale quantum computing and quantum simulation. In order to scale up such devices, it is necessary to engineer extreme-high vacuum (XHV) environments to prevent background gas from disrupting the ion crystal. Here we present a new cryogenic ion trapping system designed for long time storage of large ion chains. Our apparatus is based on a segmented-blade ion trap enclosed in a 4 K cryostat, which enables us to routinely trap and hold over 100 171Yb+ ions for hours in a linear configuration, due to low background gas pressure from differential cryo-pumping. We characterize the XHV cryogenic environment measuring pressures below by recording both inelastic and elastic collisions between the ion chain and the molecular background gas. We also demonstrate coherent one and two-qubit operations and nearly equidistant ion spacing for chains of up to 44 ions using anharmonic axial potentials, in order to enable better detection and single ion addressing in large ion arrays. We anticipate that this reliable production and lifetime enhancement of large linear ion chains will enable quantum simulation of models that are intractable with classical computer modeling.

Entangling an arbitrary pair of qubits in a long ion crystal

It is well established that the collective motion of ion crystals can be used as a quantum bus for multi-qubit entanglement. However, as the number of ions increases, it becomes difficult to directly entangle ions far apart and resolve all motional modes of the ion crystal. We introduce a scalable and flexible scheme for efficient entanglement between any pair of ions within a large ion chain, using an evenly distributed 50-ion crystal as an example. By performing amplitude and frequency modulation, we find high-fidelity pulse sequences that primarily drive a transverse motional mode with a wavelength of 4 ion spacings. We present two $500 \mu s$ pulses that can in theory suppress gate errors due to residual motion to below $10^{-4}$, and observe a trade-off between gate power and robustness against unwanted frequency offsets.

Solvent‐ and Heat‐Dependent Binding Behaviors of HMeQ[6] with Alkyldiammonium Ions

AbstractBinding interactions between hexamethyl substituted cucurbit[6]uril (HMeQ[6]) and a series of alkyldiammonium ions both in water and organic solvent media (DMSO) were investigated by various techniques. In water, the alkyl chains of the alkyldiammonium ions were encapsulated into the hydrophobic cavity of the HMeQ[6] host to form inclusion complex. In DMSO, binding interactions of HMeQ[6] host with alkyldiammonium guests generate not only normal inclusion complexes, but also special head‐inclusion complexes, in which only the NH3+ groups of the guests were engulfed into the HMeQ[6] cavity while the alkyl chains of the guests reside outside of the HMeQ[6] portals. Interestingly, some of the head‐inclusion complexes can be switched to supramolecular polymers by heating.

Phonon localization in an ion chain under irradiation with a Bessel laser beam

Trapped ions offer an excellent platform to investigate fascinating phenomena in quantum physics. Here we propose an experimental scheme to achieve Anderson localization of phonons using an ion chain under irradiation of a laser Bessel beam. The quasiperiodicity comes from the characteristic of the Bessel beam, which is only relevant to the positions of the individual ions with respect to the standing wave of the Bessel beam, rather than the internal degrees of freedom of the ions. We demonstrate, by the inverse participation ratio, the delocalization-localization transition, which is sensitive to the strength and the phase of the Bessel beam laser. Our model involving long-range phonon hopping could present richer phenomena than the Aubry-Andr\'e model including only nearest-neighbor coupling.

Betaine (trimethylammonioacetate) binary compound with sodium iodide

In the title compound,catena-poly[[[bis[2-(trimethylazaniumyl)acetato-κO]sodium]-di-μ-aqua-[diaquasodium]-di-μ-aqua] diiodide], {[Na2(C5H11NO2)2(H2O)6]I2}n, both Na+ions have distorted octahedral environments (coordination number 6). The coordination polyhedra of the sodium ions are connected by common edges forming an infinite chain of ions along [100]. The chains and betaine zwitterions are assembled into infinitive layersviahydrogen bonds. These layers are connectedviaelectrostatic attraction between iodide ions and positive trimethylazanium groups in the crystal.

Pulsed dynamical decoupling for fast and robust two-qubit gates on trapped ions

We propose a pulsed dynamical decoupling protocol as the generator of tunable, fast, and robust quantum phase gates between two microwave-driven trapped ion hyperfine qubits. The protocol consists of sequences of $\pi$-pulses acting on ions that are oriented along an externally applied magnetic field gradient. In contrast to existing approaches, in our design the two vibrational modes of the ion chain cooperate under the influence of the external microwave driving to achieve significantly increased gate speeds. Our scheme is robust against the dominant noise sources, which are errors on the magnetic field and microwave pulse intensities, as well as motional heating, predicting two-qubit gates with fidelities above $99.9\%$ in tens of microseconds.

Optical Trapping of Ion Coulomb Crystals

The electronic and motional degrees of freedom of trapped ions can be controlled and coherently coupled on the level of individual quanta. Assembling complex quantum systems ion by ion while keeping this unique level of control remains a challenging task. For many applications, linear chains of ions in conventional traps are ideally suited to address this problem. However, driven motion due to the magnetic or radio-frequency electric trapping fields sometimes limits the performance in one dimension and severely affects the extension to higher dimensional systems. Here, we report on the trapping of multiple Barium ions in a single-beam optical dipole trap without radio-frequency or additional magnetic fields. We study the persistence of order in ensembles of up to six ions within the optical trap, measure their temperature and conclude that the ions form a linear chain, commonly called a one-dimensional Coulomb crystal. As a proof-of-concept demonstration, we access the collective motion and perform spectrometry of the normal modes in the optical trap. Our system provides a platform which is free of driven motion and combines advantages of optical trapping, such as state-dependent confinement and nano-scale potentials, with the desirable properties of crystals of trapped ions, such as long-range interactions featuring collective motion. Starting with small numbers of ions, it has been proposed that these properties would allow the experimental study of many-body physics and the onset of structural quantum phase transitions between one- and two-dimensional crystals.

Simulating the performance of a distance-3 surface code in a linear ion trap

We explore the feasibility of implementing a small surface code with 9 data qubits and 8 ancilla qubits, commonly referred to as surface-17, using a linear chain of 171Yb+ ions. Two-qubit gates can be performed between any two ions in the chain with gate time increasing linearly with ion distance. Measurement of the ion state by fluorescence requires that the ancilla qubits be physically separated from the data qubits to avoid errors on the data due to scattered photons. We minimize the time required to measure one round of stabilizers by optimizing the mapping of the two-dimensional surface code to the linear chain of ions. We develop a physically motivated Pauli error model that allows for fast simulation and captures the key sources of noise in an ion trap quantum computer including gate imperfections and ion heating. Our simulations showed a consistent requirement of a two-qubit gate fidelity of ≥99.9% for the logical memory to have a better fidelity than physical two-qubit operations. Finally, we perform an analysis of the error subsets from the importance sampling method used to bound the logical error rates to gain insight into which error sources are particularly detrimental to error correction.

Structural and vibrational study of diphenylhydrazine dihydrogenophosphate single crystal (C 6 H 9 N 2 ) 2 H 2 P 2 O 7 (DPHDP)

Abstract Chemical preparation, crystal structure and vibrational study are reported on a new diphenylhydrazine dihydrogenophosphate (C 6 H 9 N 2 ) 2 H 2 P 2 O 7 (DPHDP) single crystal. This organic cationic diphosphate compound was synthesized by the method of ion exchange resin . (C 6 H 9 N 2 ) 2 H 2 P 2 O 7 crystallizes in the monoclinic system. The structural resolution shows the existence of H 2 P 2 O 7 2− ion chains linked together by hydrogen bonds. The organic cations C 6 H 9 N 2 + and the phosphate chains are linked together by hydrogen bonds. The vibrational study by IR spectroscopy of the title compound reveals the presence of three bands and confirms the existence of non-equivalent positions of water molecules in the structure.

Comprehensive cluster-theory analysis of the magnetic structures and excitations in CoCl2·2H2O

The magnetic properties of ${\mathrm{CoCl}}_{2}\ifmmode\cdot\else\textperiodcentered\fi{}2{\mathrm{H}}_{2}\mathrm{O}$ are analyzed in the mean-field/random-phase approximation using a basis of clusters with four spins along the $c$-axis chains of Co ions. The model gives a unifying account of the bulk properties, the spin waves, and the higher-order cluster-spin excitations. The theory describes accurately the neutron scattering measurements of the excited doublet of the $S=3/2\phantom{\rule{4pt}{0ex}}{\mathrm{Co}}^{++}$ ions in both the antiferromagnetic and the paramagnetic phases. The theory has been applied by Larsen et al. [Phys. Rev. B 96, 174424 (2017)] for analyzing the quantum phase transition at a transverse field of 160 kOe and is found to agree closely with their observations.

Superprotonic conduction through one-dimensional ordered alkali metal ion chains in a lanthanide-organic framework.

Although no evident hydrogen-bond network appears, an ultrahigh proton conductivity of 2.91 × 10-2 S cm-1 at 363 K and 90% RH with an ultralow activation energy of 0.10 eV was observed in an anionic lanthanide-organic framework Na2[Eu(SDB)2(COO)]·0.375DMF·0.4H2O (1); both values approach the records among all reported proton-conducting MOF materials. This suggests that the proton conduction process in 1 is reminiscent of the Grotthuss mechanism, which together reveals an effective proton transportation pathway associated with aligned Na+ and their coordinated water.

Prethermal Strong Zero Modes and Topological Qubits

We prove that quantum information encoded in some topological excitations, including certain Majorana zero modes, is protected in closed systems for a time scale exponentially long in system parameters. This protection holds even at infinite temperature. At lower temperatures the decay time becomes even longer, with a temperature dependence controlled by an effective gap that is parametrically larger than the actual energy gap of the system. This non-equilibrium dynamical phenomenon is a form of prethermalization, and occurs because of obstructions to the equilibriation of edge or defect degrees of freedom with the bulk. We analyze the ramifications for ordered and topological phases in one, two, and three dimensions, with examples including Majorana and parafermionic zero modes in interacting spin chains. Our results are based on a non-perturbative analysis valid in any dimension, and they are illustrated by numerical simulations in one dimension. We discuss the implications for experiments on quantum-dot chains tuned into a regime supporting end Majorana zero modes, and on trapped ion chains.