Quantum Computing Experiments with Cold Trapped Ions

Rydberg excitation of trapped cold ions: a detailed case study

We provide a detailed theoretical and conceptual study of a planned experiment to excite Rydberg states of ions trapped in a Paul trap. The ultimate goal is to exploit the strong state dependent interactions between Rydberg ions to implement quantum information processing protocols and to simulate the dynamics of strongly interacting spin systems. We highlight the promises of this approach when combining the high degree of control and readout of quantum states in trapped ion crystals with the novel and fast gate schemes based on interacting giant Rydberg atomic dipole moments. We discuss anticipated theoretical and experimental challenges on the way towards its realization.

Spin Heat Engine Coupled to a Harmonic-Oscillator Flywheel

We realize a heat engine using a single electron spin as a working medium. The spin pertains to the valence electron of a trapped $^{40}$Ca$^+$ ion, and heat reservoirs are emulated by controlling the spin polarization via optical pumping. The engine is coupled to the ion's harmonic-oscillator degree of freedom via spin-dependent optical forces. The oscillator stores the work produced by the heat engine and therefore acts as a flywheel. We characterize the state of the flywheel by reconstructing the Husimi $\mathcal{Q}$ function of the oscillator after different engine runtimes. This allows us to infer both the deposited energy and the corresponding fluctuations throughout the onset of oper…

Accumulation of positrons from a LINAC based source

International audience; The GBAR experiment aims to measure the gravitational acceleration of antihydrogen H̅. It will use H̅+ ions formed by the interaction of antiprotons with a dense positronium cloud, which will require about 1010 positrons to produce one H̅+. We present the first results on the positron accumulation, reaching 3.8±0.4×108 e+ collected in 560 s.

Trapped Rydberg ions: a new platform for quantum information processing

In this chapter, we present an overview of experiments with trapped Rydberg ions and outline the advantages and challenges of developing applications of this new platform for quantum computing, sensing and simulation. Trapped Rydberg ions feature several important properties, unique in their combination: they are tightly bound in a harmonic potential of a Paul trap, in which their internal and external degrees of freedom can be controlled in a precise fashion. High fidelity state preparation of both internal and motional states of the ions has been demonstrated, and the internal states have been employed to store and manipulate qubit information. Furthermore, strong dipolar interactions can…

Precision measurement of the ionization energy of a single trapped $^{40}$Ca$^+$ ion by Rydberg series excitation

A complete set of spectroscopic data is indispensable when using Rydberg states of trapped ions for quantum information processing. We carried out Rydberg series spectroscopy for $nS_{1/2}$ states with $38 \leq n \leq 65$ and for $nD_{5/2}$ states with $37\leq n \leq 50$ on a single trapped $^{40}$Ca$^+$ ion. From a nonlinear regression to resonance frequencies, we determined the ionization energy of 2 870 575.582(15) GHz, measured 60 times more accurately as compared to the accepted value and contradicting it by 7.5 standard deviations. We confirm quantum defect values of $\delta_{S_{1/2}}=1.802995(5)$ and $\delta_{D_{5/2}}=0.626888(9)$ for $nS_{1/2}$ and $nD_{5/2}$ states respectively, wh…

Stern-Gerlach splitting of low-energy ion beams

We present a feasibility study with several magnetic field configurations for creating spin-dependent forces that can split a low-energy ion beam by the Stern-Gerlach effect. To the best of our knowledge, coherent spin-splittings of charged particles have yet to be realised. Our proposal is based on ion source parameters taken from a recent experiment that demonstrated single-ion implantation from a high-brightness ion source combined with a radio-frequency Paul trap. The inhomogeneous magnetic fields can be created by permanently magnetised microstructures or from current-carrying wires with sizes in the micron range, such as those recently used in a successful implementation of the Stern-…

Trapping and sympathetic cooling of single thorium ions for spectroscopy

Precision optical spectroscopy of exotic ions reveals accurate information about nuclear properties such as charge radii and magnetic and quadrupole moments. Thorium ions exhibit unique nuclear properties with high relevance for testing symmetries of nature. We report loading and trapping of single $^{232}$Th$^+$ ions in a linear Paul trap, embedded into and sympathetically cooled by small crystals of trapped $^{40}$Ca$^+$ ions. Trapped Th ions are identified in a non-destructive manner from the voids in the laser-induced Ca fluorescence pattern emitted by the crystal, and alternatively, by means of a time-of-flight signal when extracting ions from the Paul trap and steering them into an ex…

Fabrication of a planar micro Penning trap and numerical investigations of versatile ion positioning protocols

We describe a versatile planar Penning trap structure, which allows one to dynamically modify the trapping configuration almost arbitrarily. The trap consists of 37 hexagonal electrodes, each with a circumcircle diameter of 300 μm, fabricated in a gold-on-sapphire lithographic technique. Every hexagon can be addressed individually, thus shaping the electric potential. The fabrication of such a device with clean room methods is demonstrated. We illustrate the variability of the device by a detailed numerical simulation of a lateral and a vertical transport and simulate trapping in racetrack and artificial crystal configurations. The trap may be used for ions or electrons, as a versatile cont…

Experimental verification of position-dependent angular-momentum selection rules for absorption of twisted light by a bound electron

We analyze the multipole excitation of atoms with twisted light, i.e., by a vortex light field that carries orbital angular momentum. A single trapped $^{40}$Ca$^+$ ion serves as a localized and positioned probe of the exciting field. We drive the $S_{1/2} \to D_{5/2}$ transition and observe the relative strengths of different transitions, depending on the ion's transversal position with respect to the center of the vortex light field. On the other hand, transition amplitudes are calculated for a twisted light field in form of a Bessel beam, a Bessel-Gauss and a Gauss-Laguerre mode. Analyzing experimental obtained transition amplitudes we find agreement with the theoretical predictions at a…

Cryogenic setup for trapped ion quantum computing

We report on the design of a cryogenic setup for trapped ion quantum computing containing a segmented surface electrode trap. The heat shield of our cryostat is designed to attenuate alternating magnetic field noise, resulting in 120~dB reduction of 50~Hz noise along the magnetic field axis. We combine this efficient magnetic shielding with high optical access required for single ion addressing as well as for efficient state detection by placing two lenses each with numerical aperture 0.23 inside the inner heat shield. The cryostat design incorporates vibration isolation to avoid decoherence of optical qubits due to the motion of the cryostat. We measure vibrations of the cryostat of less t…

A pulsed high-voltage decelerator system to deliver low-energy antiprotons

International audience; The GBAR (Gravitational Behavior of Antihydrogen at Rest) experiment at CERN requires efficient deceleration of 100 keV antiprotons provided by the new ELENA synchrotron ring to synthesize antihydrogen. This is accomplished using electrostatic deceleration optics and a drift tube that is designed to switch from -99 kV to ground when the antiproton bunch is inside – essentially a charged particle “elevator” – producing a 1 keV pulse. We describe the simulation, design, construction and successful testing of the decelerator device at -92 kV on-line with antiprotons from ELENA.

Quantum gate in the decoherence-free subspace of trapped ion qubits

We propose a geometric phase gate in a decoherence-free subspace with trapped ions. The quantum information is encoded in the Zeeman sublevels of the ground-state and two physical qubits to make up one logical qubit with ultra long coherence time. Single- and two-qubit operations together with the transport and splitting of linear ion crystals allow for a robust and decoherence-free scalable quantum processor. For the ease of the phase gate realization we employ one Raman laser field on four ions simultaneously, i.e. no tight focus for addressing. The decoherence-free subspace is left neither during gate operations nor during the transport of quantum information.

Feel the force

An approach based on quantum sensing, in which controlled quantum systems serve as precision sensors, has enabled measurement of the weak magnetic interaction between two electrons bound to two separate ions. See Letter p.376 Every electron carries an intrinsic magnetic dipole moment, so any two electrons should therefore exert magnetic forces on one another. The forces involved are very small, and at atomic scale Coulomb interaction is dominant, so it is extremely difficult to observe the magnetic interaction. However, Shlomi Kotler et al. have now done just that, measuring the interaction between two electrons, in separate trapped strontium-88 ions. The two electrons exhibit spin entangle…

Nanoscale Heat Engine Beyond the Carnot Limit

We consider a quantum Otto cycle for a time-dependent harmonic oscillator coupled to a squeezed thermal reservoir. We show that the efficiency at maximum power increases with the degree of squeezing, surpassing the standard Carnot limit and approaching unity exponentially for large squeezing parameters. We further propose an experimental scheme to implement such a model system by using a single trapped ion in a linear Paul trap with special geometry. Our analytical investigations are supported by Monte Carlo simulations that demonstrate the feasibility of our proposal. For realistic trap parameters, an increase of the efficiency at maximum power of up to a factor of 4 is reached, largely ex…

Measurement of Dipole Matrix Elements with a Single Trapped Ion.

We demonstrate a new method for the direct measurement of atomic dipole transition matrix elements based on techniques developed for quantum information purposes. The scheme consists of measuring dispersive and absorptive off-resonant light-ion interactions and is applicable to many atomic species. We determine the dipole matrix element pertaining to the Ca II H line, i.e. the 4$^2$S$_{1/2} \leftrightarrow $ 4$^2$P$_{1/2}$ transition of $^{40}$Ca$^+$, for which we find the value 2.8928(43) ea$_0$. Moreover, the method allows us to deduce the lifetime of the 4$^2$P$_{1/2}$ state to be 6.904(26) ns, which is in agreement with predictions from recent theoretical calculations and resolves a lon…

Phase-stable free-space optical lattices for trapped ions

We demonstrate control of the absolute phase of an optical lattice with respect to a single trapped ion. The lattice is generated by off-resonant free-space laser beams, we actively stabilize its phase by measuring its ac-Stark shift on a trapped ion. The ion is localized within the standing wave to better than 2\% of its period. The locked lattice allows us to apply displacement operations via resonant optical forces with a controlled direction in phase space. Moreover, we observe the lattice-induced phase evolution of spin superposition states in order to analyze the relevant decoherence mechanisms. Finally, we employ lattice-induced phase shifts for inferring the variation of the ion pos…

Experimental realization of fast ion separation in segmented Paul traps

We experimentally demonstrate fast separation of a two-ion crystal in a microstructured segmented Paul trap. By the use of spectroscopic calibration routines for the electrostatic trap potentials, we achieve the required precise control of the ion trajectories near the critical point, where the harmonic confinement by the external potential vanishes. The separation procedure can be controlled by three parameters: a static potential tilt, a voltage offset at the critical point, and the total duration of the process. We show how to optimize the control parameters by measurements of ion distances, trap frequencies, and the final motional excitation. We extend the standard measurement technique…

Generalised Kronig-Penney model for ultracold atomic quantum systems

We study the properties of a quantum particle interacting with a one dimensional structure of equidistant scattering centres. We derive an analytical expression for the dispersion relation and for the Bloch functions in the presence of both even and odd scattering waves within the pseudopotential approximation. This generalises the well-known solid-state physics text-book result known as the Kronig-Penney model. Our generalised model can be used to describe systems such as degenerate Fermi gases interacting with ions or with another neutral atomic species confined in an optical lattice, thus enabling the investigation of polaron or Kondo physics within a simple formalism. We focus our atten…

Single-Ion Heat Engine at Maximum Power

We propose an experimental scheme to realize a nanoheat engine with a single ion. An Otto cycle may be implemented by confining the ion in a linear Paul trap with tapered geometry and coupling it to engineered laser reservoirs. The quantum efficiency at maximum power is analytically determined in various regimes. Moreover, Monte Carlo simulations of the engine are performed that demonstrate its feasibility and its ability to operate at a maximum efficiency of 30% under realistic conditions.

Excitation of E1-forbidden Atomic Transitions with Electric, Magnetic or Mixed Multipolarity in Light Fields Carrying Orbital and Spin Angular Momentum

Photons carrying a well-defined orbital angular momentum have been proven to modify spectroscopic selection rules in atomic matter. Excitation profiles of electric quadrupole transitions have been measured with single trapped $^{40}$Ca$^+$ ions for varying polarizations. We further develop the photo-absorption formalism to study the case of arbitrary alignment of the beam's optical axis with respect to the ion's quantization axis and mixed multipolarity. Thus, predictions for M1-dominated $^{40}Ar^{13+}$, E3-driven $^{171}Yb^+$ and $^{172}Yb^+$, and B-like $^{20}Ne^{5+}$ are presented. The latter case displays novel effects, coming from the presence of a strong photon -- magnetic dipole cou…

Positron production using a 9 MeV electron linac for the GBAR experiment

For the GBAR (Gravitational Behaviour of Antihydrogen at Rest) experiment at CERN's Antiproton Decelerator (AD) facility we have constructed a source of slow positrons, which uses a low-energy electron linear accelerator (linac). The driver linac produces electrons of 9 MeV kinetic energy that create positrons from bremsstrahlung-induced pair production. Staying below 10 MeV ensures no persistent radioactive activation in the target zone and that the radiation level outside the biological shield is safe for public access. An annealed tungsten-mesh assembly placed directly behind the target acts as a positron moderator. The system produces $5\times10^7$ slow positrons per second, a performan…

Rydberg Excitation of a Single Trapped Ion.

We demonstrate excitation of a single trapped cold $^{40}$Ca$^+$ ion to Rydberg levels by laser radiation in the vacuum-ultraviolet at 122 nm wavelength. Observed resonances are identified as 3d$^2$D$_{3/2}$ to 51 F, 52 F and 3d$^2$D$_{5/2}$ to 64F. We model the lineshape and our results imply a large state-dependent coupling to the trapping potential. Rydberg ions are of great interest for future applications in quantum computing and simulation, in which large dipolar interactions are combined with the superb experimental control offered by Paul traps.

Efficient and robust photo-ionization loading of beryllium ions

We demonstrate the efficient generation of Be$^+$ ions with a 60 ns and 150 nJ laser pulse near 235 nm for two-step photo-ionization, proven by subsequent counting the number of ions loaded into a linear Paul trap. The bandwidth and power of the laser pulse are chosen in such a way that a first, resonant step fully saturates the entire velocity distribution of beryllium atoms effusing from a thermal oven. The second excitation step is driven by the same light field causing efficient non-resonant ionization. Our ion-loading scheme is more than 15 times more efficient as compared to former pathways using two-photon continuous wave laser excitation.

Single Ion Thermal Wave Packet Analyzed Via Time-Of-Flight Detection

Abstract A single 40Ca ion is confined in the harmonic potential of a Paul trap and cooled to a temperature of a few mK, with a wave packet of sub-μm spatial and sub-m s−1 velocity uncertainty. Deterministically extracted from the Paul trap, the single ion is propagating over a distance of 0.27 m and detected. By engineering the ion extraction process on the initial wave packet, theoretically modeling the ion trajectories, and studying experimentally the time-of-flight distribution, we directly infer the state of the previously trapped ion. This analysis allows for accurate remote sensing of the previous motional excitation in the trap potential, both coherently or incoherently. Our method …

Designing spin-spin interactions with one and two dimensional ion crystals in planar micro traps

We discuss the experimental feasibility of quantum simulation with trapped ion crystals, using magnetic field gradients. We describe a micro structured planar ion trap, which contains a central wire loop generating a strong magnetic gradient of about 20 T/m in an ion crystal held about 160 \mu m above the surface. On the theoretical side, we extend a proposal about spin-spin interactions via magnetic gradient induced coupling (MAGIC) [Johanning, et al, J. Phys. B: At. Mol. Opt. Phys. 42 (2009) 154009]. We describe aspects where planar ion traps promise novel physics: Spin-spin coupling strengths of transversal eigenmodes exhibit significant advantages over the coupling schemes in longitudin…

Isotope shift measurements in the 2s1/2→ 2p3/2transition of Be+and extraction of the nuclear charge radii for7, 10, 11Be

International audience; shift measurements in the 2s 1/2 → 2p 3/2 transition of Be + and extraction of the nuclear charge radii for 7, 10, 11 Be Abstract. We have performed isotope shift measurements in the 2s 1/2 → 2p 3/2 transition of Be + ions using advanced collinear laser spectroscopy with two counterpropagating laser beams. Measurements involving a frequency comb for laser stabilization and absolute frequency determination allowed us to determine the isotope shifts with an accuracy of 2 MHz. From the isotope shifts between 9 Be and 7, 10, 11 Be, high-accuracy mass shift calculations and the charge radius of the reference isotope 9 Be we determined nuclear charge radii for the isotopes…

Frustrated quantum spin models with cold coulomb crystals

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.

Light of Two Atoms in Free Space: Bunching or Antibunching?

Photon statistics divides light sources into three different categories, characterized by bunched, antibunched, or uncorrelated photon arrival times. Single atoms, ions, molecules, or solid state emitters display antibunching of photons, while classical thermal sources exhibit photon bunching. Here we demonstrate a light source in free space, where the photon statistics depends on the direction of observation, undergoing a continuous crossover between photon bunching and antibunching. We employ two trapped ions, observe their fluorescence under continuous laser light excitation, and record spatially resolved the autocorrelation function ${g}^{(2)}(\ensuremath{\tau})$ with a movable Hanbury …

Emulating Solid-State Physics with a Hybrid System of Ultracold Ions and Atoms

We propose and theoretically investigate a hybrid system composed of a crystal of trapped ions coupled to a cloud of ultracold fermions. The ions form a periodic lattice and induce a band structure in the atoms. This system combines the advantages of scalability and tunability of ultracold atomic systems with the high fidelity operations and detection offered by trapped ion systems. It also features close analogies to natural solid-state systems, as the atomic degrees of freedom couple to phonons of the ion lattice, thereby emulating a solid-state system. Starting from the microscopic many-body Hamiltonian, we derive the low energy Hamiltonian including the atomic band structure and give an…

Precise experimental investigation of eigenmodes in a planar ion crystal.

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 …

Assessing the progress of trapped-ion processors towards fault-tolerant quantum computation

41 pags., 32 figs., 7 tabs. -- Open Access funded by Creative Commons Atribution Licence 4.0

Phonon-to-spin mapping in a system of a trapped ion via optimal control

We propose a protocol for measurement of the phonon number distribution of a harmonic oscillator based on selective mapping to a discrete spin-1/2 degree of freedom. We consider a system of a harmonically trapped ion, where a transition between two long-lived states can be driven with resolved motional sidebands. The required unitary transforms are generated by amplitude-modulated polychromatic radiation fields, where the time-domain ramps are obtained from numerical optimization by application of the chopped random basis algorithm (CRAB). We provide a detailed analysis of the scaling behavior of the attainable fidelities and required times for the mapping transform with respect to the size…

Visibility of Young's interference fringes: Scattered light from small ion crystals

We observe interference in the light scattered from trapped $^{40}$Ca$^+$ ion crystals. By varying the intensity of the excitation laser, we study the influence of elastic and inelastic scattering on the visibility of the fringe pattern and discriminate its effect from that of the ion temperature and wave-packet localization. In this way we determine the complex degree of coherence and the mutual coherence of light fields produced by individual atoms. We obtain interference fringes from crystals consisting of two, three and four ions in a harmonic trap. Control of the trapping potential allows for the adjustment of the interatomic distances and thus the formation of linear arrays of atoms s…

Fast ion swapping for quantum-information processing

We demonstrate a swap gate between laser-cooled ions in a segmented microtrap via fast physical swapping of the ion positions. This operation is used in conjunction with qubit initialization, manipulation, and readout and with other types of shuttling operations such as linear transport and crystal separation and merging. Combining these operations, we perform quantum process tomography of the swap gate, obtaining a mean process fidelity of 99.5(5)%. The swap operation is demonstrated with motional excitations below 0.05(1) quantum for all six collective modes of a two-ion crystal for a process duration of $42\ensuremath{\mu}\mathrm{s}$. Extending these techniques to three ions, we reverse …

Focus on atom optics and its applications

Atom optics employs the modern techniques of quantum optics and laser cooling to enable applications which often outperform current standard technologies. Atomic matter wave interferometers allow for ultra-precise sensors; metrology and clocks are pushed to an extraordinary accuracy of 17 digits using single atoms. Miniaturization and integration are driven forward for both atomic clocks and atom optical circuits. With the miniaturization of information-storage and -processing devices, the scale of single atoms is approached in solid state devices, where the laws of quantum physics lead to novel, advantageous features and functionalities. An upcoming branch of atom optics is the control of …

Colloquium: Trapped ions as quantum bits -- essential numerical tools

Trapped, laser-cooled atoms and ions are quantum systems which can be experimentally controlled with an as yet unmatched degree of precision. Due to the control of the motion and the internal degrees of freedom, these quantum systems can be adequately described by a well known Hamiltonian. In this colloquium, we present powerful numerical tools for the optimization of the external control of the motional and internal states of trapped neutral atoms, explicitly applied to the case of trapped laser-cooled ions in a segmented ion-trap. We then delve into solving inverse problems, when optimizing trapping potentials for ions. Our presentation is complemented by a quantum mechanical treatment of…

Observation of the Kibble-Zurek scaling law for defect formation in 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 …

Corrigendum: Fabrication and heating rate study of microscopic surface electrode ion traps

We report heating rate measurements in a microfabricated goldon-sapphire surface electrode ion trap with a trapping height of approximately 240 μm. Using the Doppler recooling method, we characterize the trap heating rates over an extended region of the trap. The noise spectral density of the trap falls in the range of noise spectra reported in ion traps at room temperature. We find that during the first months of operation, the heating rates increase by approximately one order of magnitude. The increase in heating rates is largest in the ion-loading region of the trap, providing a strong hint that surface contamination plays a major role for excessive heating rates. We discuss data found i…

Transmission Microscopy with Nanometer Resolution Using a Deterministic Single Ion Source.

We realize a single particle microscope by using deterministically extracted laser-cooled ^{40}Ca^{+} ions from a Paul trap as probe particles for transmission imaging. We demonstrate focusing of the ions to a spot size of 5.8±1.0  nm and a minimum two-sample deviation of the beam position of 1.5 nm in the focal plane. The deterministic source, even when used in combination with an imperfect detector, gives rise to a fivefold increase in the signal-to-noise ratio as compared with conventional Poissonian sources. Gating of the detector signal by the extraction event suppresses dark counts by 6 orders of magnitude. We implement a Bayes experimental design approach to microscopy in order to ma…

Experimental and theoretical challenges for the trapped electron quantum computer

We discuss quantum information processing with trapped electrons. After recalling the operation principle of planar Penning traps we sketch the experimental conditions to load, cool and detect single electrons. Here we present a detailed investigation of a scalable scheme including feasibility studies and the analysis of all important elements, relevant for the experimental stage. On the theoretical side, we discuss different methods to couple electron qubits. We estimate the relevant qubit coherence times and draw implications for the experimental setting. A critical assessment of quantum information processing with trapped electrons is concluding the article.

Entanglement-Based dc magnetometry with separated ions

We demonstrate sensing of inhomogeneous dc magnetic fields by employing entangled trapped ions, which are shuttled in a segmented Paul trap. As sensor states, we use Bell states of the type j↑↓i þ eiφj↓↑i encoded in two 40Caþ ions stored at different locations. The linear Zeeman effect leads to the accumulation of a relative phase φ, which serves for measuring the magnetic-field difference between the constituent locations. Common-mode magnetic-field fluctuations are rejected by the entangled sensor state, which gives rise to excellent sensitivity without employing dynamical decoupling and therefore enables accurate dc sensing. Consecutive measurements on sensor states encoded in the S1=2 g…

Rydberg Series Excitation of a Single Trapped Ca+40 Ion for Precision Measurements and Principal Quantum Number Scalings

A complete set of spectroscopic data is indispensable when using Rydberg states of trapped ions for quantum information processing. We carried out Rydberg series spectroscopy for $n{S}_{1/2}$ states with $38\ensuremath{\le}n\ensuremath{\le}65$ and for $n{D}_{5/2}$ states with $37\ensuremath{\le}n\ensuremath{\le}50$ on a single trapped $^{40}{\mathrm{Ca}}^{+}$ ion. We determined the ionization energy of 2 870 575.582(15) GHz, 60 times more accurately as compared to the accepted value and contradicting it by 7.5 standard deviations. We confirm quantum defect values of ${\ensuremath{\delta}}_{{S}_{1/2}}=1.802\text{ }995(5)$ and ${\ensuremath{\delta}}_{{D}_{5/2}}=0.626\text{ }888(9)$ for $n{S}_…

Observing the phase space trajectory of an entangled matter wave packet

We observe the phase space trajectory of an entangled wave packet of a trapped ion with high precision. The application of a spin dependent light force on a superposition of spin states allows for coherent splitting of the matter wave packet such that two distinct components in phase space emerge. We observe such motion with a precision of better than 9% of the wave packet extension in both momentum and position, corresponding to a 0.8 nm position resolution. We accurately study the effect of the initial ion temperature on the quantum entanglement dynamics. Furthermore, we map out the phonon distributions throughout the action of the displacement force. Our investigation shows corrections t…

Development of a PbWO 4 detector for single-shot positron annihilation lifetime spectroscopy at the GBAR experiment

International audience; We have developed a PbWO 4 (PWO) detector with a large dynamic range to measure the intensity of a positron beam and the absolute density of the ortho-positronium (o-Ps) cloud it creates. A simulation study shows that a setup based on such detectors may be used to determine the angular distribution of the emission and reflection of o-Ps to reduce part of the uncertainties of the measurement. These will allow to improve the precision in the measurement of the cross section for the (anti) hydrogen formation by (anti) proton-positronium charge exchange and to optimize the yield of antihydrogen ion which is an essential parameter in the GBAR experiment.

Determination of quantum defect for the Rydberg P series of Ca II

We present an experimental investigation of the Rydberg 23 P$_{1/2}$ state of laser-cooled $^{40}$Ca$^+$ ions in a radiofrequency ion trap. Using micromotion sideband spectroscopy on a narrow quadrupole transition, the oscillating electric field at the ion position was precisely characterised, and the modulation of the Rydberg transition due to this field was minimised. From a correlated fit to this P line and previously measured P and F level energies of Ca II, we have determined the ionization energy of 95 751.916(32) $\rm {cm}^{-1}$, in agreement with the accepted value, and the quantum defect for the $n$ P$_{1/2}$ states.

Fast thermometry for trapped ions using dark resonances

We experimentally demonstrate a method to determine the temperature of trapped ions which is suitable for monitoring fast thermalization processes. We show that observing and analyzing the lineshape of dark resonances in the fluorescence spectrum provides a temperature measurement which accurate over a large dynamic range, applied to single ions and small ion crystals. Laser induced fluorescence is detected over a time of only $20\,\mu$s allowing for rapid determination of the ion temperature. In the measurement range of $10^{-1}-10^{+2}\,$mK we reach better than $15\,\%$ accuracy. Tuning the cooling laser to selected resonance features allows for controlling the ion temperatures between $0…

A single-atom heat engine

Making a teeny tiny engine Steam locomotives, cars, and the drinking bird toy all convert heat into useful work as it cycles between two reservoirs at different temperatures. Usually, the working substance where the heat-work conversion occurs is a liquid or a gas, consisting of many molecules. Roβnagel et al. have made a working substance of a single calcium ion in a tapered ion trap. A laser-cooling beam plays the part of a cold reservoir for the calcium ion, and in turn, electric field noise acts as a hot reservoir. Science , this issue p. 325

Imaging Trapped Ion Structures via Fluorescence Cross-Correlation Detection

Cross-correlation signals are recorded from fluorescence photons scattered in free space off a trapped ion structure. The analysis of the signal allows for unambiguously revealing the spatial frequency, thus the distance, as well as the spatial alignment of the ions. For the case of two ions we obtain from the cross-correlations a spatial frequency ${f}_{\text{spatial}}=1490\ifmmode\pm\else\textpm\fi{}{2}_{\mathrm{stat}}\ifmmode\pm\else\textpm\fi{}{8}_{\mathrm{syst}}\text{ }\text{ }{\mathrm{rad}}^{\ensuremath{-}1}$, where the statistical uncertainty improves with the integrated number of correlation events as ${N}^{\ensuremath{-}0.51\ifmmode\pm\else\textpm\fi{}0.06}$. We independently deter…

Entangled states of trapped ions allow measuring the magnetic field gradient produced by a single atomic spin

Using trapped ions in an entangled state we propose detecting a magnetic dipole of a single atom at distance of a few $\mu$m. This requires a measurement of the magnetic field gradient at a level of about 10$^{-13}$ Tesla/$\mu$m. We discuss applications e.g. in determining a wide variation of ionic magnetic moments, for investigating the magnetic substructure of ions with a level structure not accessible for optical cooling and detection,and for studying exotic or rare ions, and molecular ions. The scheme may also be used for measureing spin imbalances of neutral atoms or atomic ensembles trapped by optical dipole forces. As the proposed method relies on techniques well established in ion t…

Scalable Creation of Long-Lived Multipartite Entanglement.

We demonstrate the deterministic generation of multipartite entanglement based on scalable methods. Four qubits are encoded in Ca+40, stored in a microstructured segmented Paul trap. These qubits are sequentially entangled by laser-driven pairwise gate operations. Between these, the qubit register is dynamically reconfigured via ion shuttling operations, where ion crystals are separated and merged, and ions are moved in and out of a fixed laser interaction zone. A sequence consisting of three pairwise entangling gates yields a four-ion Greenberger-Horne-Zeilinger state |ψ=(1/2)(|0000+|1111), and full quantum state tomography reveals a state fidelity of 94.4(3)%. We analyze the decoherence o…

Quantum algorithm for simulating an experiment: Light interference from single ions and their mirror images

We widen the range of applications for quantum computing by introducing digital quantum simulation methods for coherent light-matter interactions: We simulate an experiment where the emitted light from a single ion was interfering with its mirror image [Eschner et al., Nature (London) 413, 495 (2001)]. Using the quantum simulation software q1tsim, we accurately reproduce the interference pattern which had been observed experimentally and also show the effect of the mirror position on the spontaneous-emission rate of the ion. In order to minimize the number of required qubits, we implement a qubit-reinitialization technique. We show that a digital quantum simulation of complex experiments in…

Deterministic Single-Ion Implantation of Rare-Earth Ions for Nanometer-Resolution Color-Center Generation

Single dopant atoms or dopant-related defect centers in a solid state matrix provide an attractive platform for quantum simulation of topological states, for quantum computing and communication, due to their potential to realize a scalable architecture compatible with electronic and photonic integrated circuits. The production of such quantum devices calls for deterministic single atom doping techniques because conventional stochastic doping techniques are cannot deliver appropriate architectures. Here, we present the fabrication of arrays of praseodymium color centers in YAG substrates, using a deterministic source of single laser-cooled Pr$^+$ ions. The beam of single Pr$^+$ ions is extra…

Two-dimensional spectroscopy for the study of ion Coulomb crystals

Ion Coulomb crystals are currently establishing themselves as a highly controllable test-bed for mesoscopic systems of statistical mechanics. The detailed experimental interrogation of the dynamics of these crystals however remains an experimental challenge. In this work, we show how to extend the concepts of multi-dimensional nonlinear spectroscopy to the study of the dynamics of ion Coulomb crystals. The scheme we present can be realized with state-of-the-art technology and gives direct access to the dynamics, revealing nonlinear couplings even in the presence of thermal excitations. We illustrate the advantages of our proposal showing how two-dimensional spectroscopy can be used to detec…

Fabrication of $^{15}\textrm{NV}^{-}$ centers in diamond using a deterministic single ion implanter

Nitrogen Vacancy (NV) centers in diamond are a platform for several important quantum technologies, including sensing, communication and elementary quantum processors. In this letter we demonstrate the creation of NV centers by implantation using a deterministic single ion source. For this we sympathetically laser-cool single $^{15}\textrm{N}_2^+$ molecular ions in a Paul trap and extract them at an energy of 5.9\,keV. Subsequently the ions are focused with a lateral resolution of 121(35)\,nm and are implanted into a diamond substrate without any spatial filtering by apertures or masks. After high-temperature annealing, we detect the NV centers in a confocal microscope and determine a conve…

Transfer of optical orbital angular momentum to a bound electron

Photons can carry angular momentum, not only due to their spin, but also due to their spatial structure. This extra twist has been used, for example, to drive circular motion of microscopic particles in optical tweezers as well as to create vortices in quantum gases. Here we excite an atomic transition with a vortex laser beam and demonstrate the transfer of optical orbital angular momentum to the valence electron of a single trapped ion. We observe strongly modified selection rules showing that an atom can absorb two quanta of angular momentum from a single photon: one from the spin and another from the spatial structure of the beam. Furthermore, we show that parasitic ac-Stark shifts from…

Controlling Fast Transport of Cold Trapped Ions

We realize fast transport of ions in a segmented micro-structured Paul trap. The ion is shuttled over a distance of more than 10^4 times its groundstate wavefunction size during only 5 motional cycles of the trap (280 micro meter in 3.6 micro seconds). Starting from a ground-state-cooled ion, we find an optimized transport such that the energy increase is as low as 0.10 $\pm$ 0.01 motional quanta. In addition, we demonstrate that quantum information stored in a spin-motion entangled state is preserved throughout the transport. Shuttling operations are concatenated, as a proof-of-principle for the shuttling-based architecture to scalable ion trap quantum computing.

Engineering NonBinary Rydberg Interactions via Phonons in an Optical Lattice

Coupling electronic and vibrational degrees of freedom of Rydberg atoms held in optical tweezer arrays offers a flexible mechanism for creating and controlling atom-atom interactions. We find that the state-dependent coupling between Rydberg atoms and local oscillator modes gives rise to two- and three-body interactions which are controllable through the strength of the local confinement. This approach even permits the cancellation of two-body terms such that three-body interactions become dominant. We analyze the structure of these interactions on two-dimensional bipartite lattice geometries and explore the impact of three-body interactions on system ground state on a square lattice. Focus…

Shuttling of Rydberg ions for fast entangling operations

We introduce a scheme to entangle Rydberg ions in a linear ion crystal, using the high electric polarizability of the Rydberg electronic states in combination with mutual Coulomb coupling of ions that establishes common modes of motion. After laser-initialization of ions to a superposition of ground- and Rydberg-state, the entanglement operation is driven purely by applying a voltage pulse that shuttles the ion crystal back and forth. This operation can achieve entanglement on a sub-$\mu$s timescale, more than two orders of magnitude faster than typical gate operations driven by continuous-wave lasers. Our analysis shows that the fidelity achieved with this protocol can exceed $99.9\%$ with…

Quantum simulation of the cooperative Jahn-Teller transition in 1D Ion crystals

The Jahn-Teller effect explains distortions and nondegenerate energy levels in molecular and solid-state physics via a coupling of effective spins to collective bosons. Here we propose and theoretically analyze the quantum simulation of a many-body Jahn-Teller model with linear ion crystals subjected to magnetic field gradients. We show that the system undergoes a quantum magnetic structural phase transition which leads to a reordering of particle positions and the formation of a spin-phonon quasicondensate in mesoscopic ion chains.

Twisted-Light-Ion Interaction: The Role of Longitudinal Fields.

The propagation of light beams is well described using the paraxial approximation, where field components along the propagation direction are usually neglected. For strongly inhomogeneous or shaped light fields, however, this approximation may fail, leading to intriguing variations of the light-matter interaction. This is the case of twisted light having opposite orbital and spin angular momenta. We compare experimental data for the excitation of a quadrupole transition in a single trapped $^{40}$Ca$^+$ ion by Schmiegelow et al, Nat.\ Comm.\ 7, 12998 (2016), with a complete model where longitudinal components of the electric field are taken into account. Our model matches the experimental d…

Maximizing the information gain of a single ion microscope using bayes experimental design

We show nanoscopic transmission microscopy, using a deterministic single particle source and compare the resulting images in terms of signal-to-noise ratio, with those of conventional Poissonian sources. Our source is realized by deterministic extraction of laser-cooled calcium ions from a Paul trap. Gating by the extraction event allows for the suppression of detector dark counts by six orders of magnitude. Using the Bayes experimental design method, the deterministic characteristics of this source are harnessed to maximize information gain, when imaging structures with a parametrizable transmission function. We demonstrate such optimized imaging by determining parameter values of one and …

Millicharged dark matter detection with ion traps

We propose the use of trapped ions for detection of millicharged dark matter. Millicharged particles will scatter off the ions, giving a signal either in individual events or in the overall heating rate of the ions. Ion traps have several properties which make them ideal detectors for such a signal. First, ion traps have demonstrated significant isolation of the ions from the environment, greatly reducing the background heating and event rates. Second, ion traps can have low thresholds for detection of energy deposition, down to $\sim \text{neV}$. Third, since the ions are charged, they naturally have large cross sections for scattering with the millicharged particles, further enhanced by t…

Optical super-resolution sensing of a trapped ion's wave packet size

We demonstrate super-resolution optical sensing of the size of the wave packet of a single trapped ion. Our method extends the well known ground state depletion (GSD) technique to the coherent regime. Here, we use a hollow beam to strongly saturate a coherently driven dipole-forbidden transition around a sub-diffraction limited area at its center and observe state dependent fluorescence. By spatially scanning this laser beam over a single trapped $^{40}\mathrm{Ca}^+$ ion, we are able to measure the wave packet sizes of cooled ions. Using a depletion beam waist of $4.2(1)\,\mu$m we reach a spatial resolution which allows us to determine a wave packet size of $39(9)\,$nm for a near ground sta…

Quantum magnetism of spin-ladder compounds with trapped-ion crystals

Abstract 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 frustrat…

A single ion as a shot noise limited magnetic field gradient probe

It is expected that ion trap quantum computing can be made scalable through protocols that make use of transport of ion qubits between sub-regions within the ion trap. In this scenario, any magnetic field inhomogeneity the ion experiences during the transport, may lead to dephasing and loss of fidelity. Here we demonstrate how to measure, and compensate for, magnetic field gradients inside a segmented ion trap, by transporting a single ion over variable distances. We attain a relative magnetic field sensitivity of \Delta B/B_0 ~ 5*10^{-7} over a test distance of 140 \micro m, which can be extended to the mm range, still with sub \micro m resolution. A fast experimental sequence is presented…

Trapped Rydberg ions: A new platform for quantum information processing

Abstract In this chapter, we present an overview of experiments with trapped Rydberg ions and outline the advantages and challenges of developing applications of this new platform for quantum computing, sensing, and simulation. Trapped Rydberg ions feature several important properties, unique in their combination: they are tightly bound in a harmonic potential of a Paul trap, in which their internal and external degrees of freedom can be controlled in a precise fashion. High fidelity state preparation of both internal and motional states of the ions has been demonstrated, and the internal states have been employed to store and manipulate qubit information. Furthermore, strong dipolar intera…

Shot-noise-limited monitoring and phase locking of the motion of a single trapped ion.

We perform a high-resolution real-time readout of the motion of a single trapped and laser-cooled ${\mathrm{Ba}}^{+}$ ion. By using an interferometric setup, we demonstrate a shot-noise-limited measurement of thermal oscillations with a resolution of 4 times the standard quantum limit. We apply the real-time monitoring for phase control of the ion motion through a feedback loop, suppressing the photon recoil-induced phase diffusion. Because of the spectral narrowing in the phase-locked mode, the coherent ion oscillation is measured with a resolution of about 0.3 times the standard quantum limit.

Shuttling-Based Trapped-Ion Quantum Information Processing

Moving trapped-ion qubits in a microstructured array of radiofrequency traps offers a route toward realizing scalable quantum processing nodes. Establishing such nodes, providing sufficient functionality to represent a building block for emerging quantum technologies, e.g., a quantum computer or quantum repeater, remains a formidable technological challenge. In this review, the authors present a holistic view on such an architecture, including the relevant components, their characterization, and their impact on the overall system performance. The authors present a hardware architecture based on a uniform linear segmented multilayer trap, controlled by a custom-made fast multichannel arbitra…

Fast shuttling of a trapped ion in the presence of noise

We theoretically investigate the motional excitation of a single ion caused by spring-constant and position fluctuations of a harmonic trap during trap shuttling processes. A detailed study of the sensitivity on noise for several transport protocols and noise spectra is provided. The effect of slow spring-constant drifts is also analyzed. Trap trajectories that minimize the excitation are designed combining invariant-based inverse engineering, perturbation theory, and optimal control.