Ion Strings Research Articles

Individual Addressing and State Readout of Trapped Ions Utilizing Radio-Frequency Micromotion.

Excess "micromotion" of trapped ions due to the residual radio-frequency (rf) trapping field at their location is often undesirable and is usually carefully minimized. Here, we induce precise amounts of excess micromotion on individual ions by adjusting the local static electric field they experience. Micromotion modulates the coupling of an ion to laser fields, ideally tuning it from its maximum value to zero as the ion is moved away from the trap's rf null. We use tunable micromotion to vary the Rabi frequency of stimulated Raman transitions over two orders of magnitude, and to individually control the rates of resonant fluorescence from three ions under global laser illumination without any changes to the driving light fields. The technique is amenable to situations where addressing individual ions with focused laser beams is challenging, such as tightly packed linear ion strings or two-dimensional ion arrays illuminated from the side.

Design, fabrication and characterization of a micro-fabricated stacked-wafer segmented ion trap with two X-junctions

We describe the implementation of a three-dimensional Paul ion trap fabricated from a stack of precision-machined silica glass wafers, which incorporates a pair of junctions for two-dimensional ion transport. The trap has 142 dedicated electrodes which can be used to define multiple potential wells in which strings of ions can be held. By supplying time-varying potentials, this also allows for transport and re-configuration of ion strings. We describe the design, simulation, fabrication and packaging of the trap, including explorations of different parameter regimes and possible optimizations and design choices. We give results of initial testing of the trap, including measurements of heating rates and junction transport.

Creation of double-well potentials in a surface-electrode trap towards a nanofriction model emulator

We demonstrate a microfabricated surface-electrode ion trap that is applicable as a nanofriction emulator and studies of many-body dynamics of interacting systems. The trap enables both single-well and double-well trapping potentials in the radial direction, where the distance between the two potential wells can be adjusted by the applied RF voltage. In the double-well configuration, parallel ion strings can be formed, which is a suitable system for the emulation of the Frenkel–Kontorova (FK) model. We derive the condition under which the trap functions as an FK model emulator. The trap is designed so that the Coulomb interaction between two ion strings becomes significant. We report on the microfabrication process for such downsized trap electrodes and experimental results of single-well and double-well operation with calcium ions. With the trap demonstrated in this work we can create atomically accessible, self-assembled Coulomb systems with a wide tuning range of the corrugation parameter in the FK model. This makes it a promising system for quantum simulations, but also for the study of nanofriction in one and higher dimensional systems.

Scalable and Parallel Tweezer Gates for Quantum Computing with Long Ion Strings

Trapped-ion quantum computers have demonstrated high-performance gate operations in registers of about ten qubits. However, scaling up and parallelizing quantum computations with long one-dimensional (1D) ion strings is an outstanding challenge due to the global nature of the motional modes of the ions which mediate qubit-qubit couplings. Here, we devise methods to implement scalable and parallel entangling gates by using engineered localized phonon modes. We propose to tailor such localized modes by tuning the local potential of individual ions with programmable optical tweezers. Localized modes of small subsets of qubits form the basis to perform entangling gates on these subsets in parallel. We demonstrate the inherent scalability of this approach by presenting analytical and numerical results for long 1D ion chains and even for infinite chains of uniformly spaced ions. Furthermore, we show that combining our methods with optimal coherent control techniques allows to realize maximally dense universal parallelized quantum circuits.

Surface trap with dc-tunable ion-electrode distance.

We describe the design, fabrication, and operation of a novel surface-electrode Paul trap that produces a radio-frequency-null along the axis perpendicular to the trap surface. This arrangement enables control of the vertical trapping potential and consequentially the ion-electrode distance via dc-electrodes only. We demonstrate the confinement of single 40Ca+ ions at heights between 50 μm and 300 μm above planar copper-coated aluminum electrodes. Laser-cooling and coherent operations are performed on both the planar and vertical motional modes. This architecture provides a platform for precision electric-field noise detection and trapping of vertical ion strings without excess micromotion and may have applications for scalable quantum computers with surface ion traps.

Creating equally spaced linear ion string in a surface-electrode trap by feedback control

A feedback control method for producing an equidistant ion string in a surface-electrode ion trap has been experimentally demonstrated. This method features three advantages: (i) The optimal voltage can be constrained within the specified reachable range. (ii) The height of trapped ions from the trap surface can be maintained at the same value when strings with different number of ions or with different ion spacings are to be trapped. (iii) This method is resistant to a stray electric field near the trap. By this method, the asymmetry of the ion string caused by a stray field is minimized. The robustness of trapping a variable number of ions at the same potential and the dependency of the axial frequency on the number of ions are also investigated experimentally. This work would be a practical method to create a linear ion string with a large number of ions and may find applications in large-scale quantum computing, quantum simulation, and phase transition studies utilizing homogeneous ion strings.

Electromagnetically-induced-transparency ground-state cooling of long ion strings

Electromagnetically-induced-transparency (EIT) cooling is a ground-state cooling technique for trapped particles. EIT offers a broader cooling range in frequency space compared to more established methods. In this work, we experimentally investigate EIT cooling in strings of trapped atomic ions. In strings of up to 18 ions, we demonstrate simultaneous ground state cooling of all radial modes in under 1 ms. This is a particularly important capability in view of emerging quantum simulation experiments with large numbers of trapped ions. Our analysis of the EIT cooling dynamics is based on a novel technique enabling single-shot measurements of phonon numbers, by rapid adiabatic passage on a vibrational sideband of a narrow transition.

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 is accurate over a large dynamic range, applied to single ions and small ion crystals. Laser induced fluorescence is detected over a time of only , allowing for rapid determination of the ion temperature. In the measurement range of 10−1– mK we reach better than accuracy. Tuning the cooling laser to selected resonance features allows us to control the ion temperatures between mK and more than mK. Experimental work is supported by a solution of the eight-level optical Bloch equations when including the ions’ classical motion. This technique paves the way for many experiments, including heat transport in ion strings, heat engines, non-equilibrium thermodynamics or thermometry of large ion crystals.

Fast transport of mixed-species ion chains within a Paul trap

We investigate the dynamics of mixed-species ion crystals during transport between spatially distinct locations in a linear Paul trap in the diabatic regime. In a general mixed-species crystal, all degrees of freedom along the direction of transport are excited by an accelerating well, so unlike the case of same-species ions, where only the center-of-mass mode is excited, several degrees of freedom have to be simultaneously controlled by the transport protocol. We design protocols that lead to low final excitations in the diabatic regime using invariant-based inverse engineering for two different-species ions and also show how to extend this approach to longer mixed-species ion strings. Fast transport of mixed-species ion strings can significantly reduce the operation time in certain architectures for scalable quantum-information processing with trapped ions.

Isotope shifts of naturalSr+measured by laser fluorescence in a sympathetically cooled Coulomb crystal

We measured by laser spectroscopy the isotope shifts between naturally occurring even isotopes of strontium ions for both the $5s\phantom{\rule{0.16em}{0ex}}{\phantom{\rule{0.16em}{0ex}}}^{2}{S}_{1/2}\ensuremath{\rightarrow}5p\phantom{\rule{0.16em}{0ex}}{\phantom{\rule{0.16em}{0ex}}}^{2}{P}_{1/2}$ (violet) and the $4d\phantom{\rule{0.16em}{0ex}}{\phantom{\rule{0.16em}{0ex}}}^{2}{D}_{3/2}\ensuremath{\rightarrow}5p\phantom{\rule{0.16em}{0ex}}{\phantom{\rule{0.16em}{0ex}}}^{2}{P}_{1/2}$ (infrared) dipole-allowed optical transitions. Fluorescence spectra were taken by simultaneous measurements on a two-component Coulomb crystal in a linear Paul trap containing ${10}^{3}$--${10}^{4}$ laser-cooled ${\mathrm{Sr}}^{+}$ ions. The isotope shifts are extracted from the experimental spectra by fitting the data with the analytical solution of the optical Bloch equations describing a three-level atom interacting with two laser beams. This technique allowed us to increase the precision with respect to previously reported data obtained by optogalvanic spectroscopy or fast atomic-beam techniques. The results for the $5s\phantom{\rule{0.16em}{0ex}}{\phantom{\rule{0.16em}{0ex}}}^{2}{S}_{1/2}\ensuremath{\rightarrow}5p\phantom{\rule{0.16em}{0ex}}{\phantom{\rule{0.16em}{0ex}}}^{2}{P}_{1/2}$ transition are ${\ensuremath{\nu}}_{88}\ensuremath{-}{\ensuremath{\nu}}_{84}=+378(4)$ MHz and ${\ensuremath{\nu}}_{88}\ensuremath{-}{\ensuremath{\nu}}_{86}=+170(3)$ MHz, in agreement with previously reported measurements. In the case of the previously unexplored $4d\phantom{\rule{0.16em}{0ex}}{\phantom{\rule{0.16em}{0ex}}}^{2}{D}_{3/2}\ensuremath{\rightarrow}5p\phantom{\rule{0.16em}{0ex}}{\phantom{\rule{0.16em}{0ex}}}^{2}{P}_{1/2}$ transition we find ${\ensuremath{\nu}}_{88}\ensuremath{-}{\ensuremath{\nu}}_{84}=\ensuremath{-}828(4)$ MHz and ${\ensuremath{\nu}}_{88}\ensuremath{-}{\ensuremath{\nu}}_{86}=\ensuremath{-}402(2)$ MHz. These results provide more data for stringent tests of theoretical calculations of the isotope shifts of alkali-metal-like atoms. Moreover, they simplify the identification and the addressing of ${\mathrm{Sr}}^{+}$ isotopes for ion frequency standards or quantum-information-processing applications in the case of multi-isotope ion strings.

Design of a surface electrode trap for parallel ion strings

We report a linear surface-electrode trap that can be used to form parallel ion strings. By adjusting the balance of the radio-frequency (RF) voltages applied to central and RF electrodes, the RF pseudopotential can be varied from single-well to double-well in the radial direction. Ions located on two parallel lines of the RF potential null are in principle free from excess micromotion if appropriate static voltages are applied. Calcium ions were trapped for the evaluation of the designed electrode. An ion string in the single-well potential and two ion strings in the double-well potential were observed by changing the RF voltages. Such traps could be used for quantum simulation of coupled spin systems.

Manipulating the singlet–triplet transition in ion strings by nonresonant dynamic Stark effect

Using strong laser pulses, we show that it is possible to control the spin state in a model system based on a two-electron extension with spin couplings of the Shin–Metiu Hamiltonian, truncated to account for the lowest electronic energy states. We consider two different models depending on the number of electronic states included in the calculation. The initial electronic state determines when the spin state is stable or not in the absence of an external field. In the latter case, by nonresonant dynamic Stark effect, we show that it is possible to avoid spin transitions with strong fields, using different pulse frequencies. This effective spin locking requires minimizing absorption to excited singlets as well as decoupling the singlet and triplet electronic states. In the first case, we show that it is possible to force the spin transition by a combination of two pulses, a chirped pulse and a transform limited pulse, where the time-delay must be chosen to maximize spin switching on a different electronic state. Our results show that forcing the spin switching is a more difficult goal than avoiding it and that this goal becomes highly restricted when many electronic pathways or multi-photon processes are available.

Structural Transitions of Ion Strings in Quantum Potentials

We analyze the stability and dynamics of an ion chain confined inside a high-finesse optical resonator. When the dipolar transition of the ions strongly couples to one cavity mode, the mechanical effects of light modify the chain properties close to a structural transition. We focus on the linear chain close to the zigzag instability and show that linear and zigzag arrays are bistable for certain strengths of the laser pumping the cavity. For these regimes the chain is cooled into one of the configurations by cavity-enhanced photon scattering. The excitations of these structures mix photonic and vibrational fluctuations, which can be entangled at steady state. These features are signaled by Fano-like resonances in the spectrum of light at the cavity output.

Quantum superpositions of crystalline structures

A procedure is discussed for creating coherent superpositions of motional states of ion strings. The motional states are across the structural transition linear-zigzag, and their coherent superposition is achieved by means of spin-dependent forces, such that a coherent superposition of the electronic states of one ion evolves into an entangled state between the chain's internal and external degrees of freedom. It is shown that the creation of such an entangled state can be revealed by performing Ramsey interferometry with one ion of the chain.

Deterministic reordering of 40Ca+ ions in a linear segmented Paul trap

In the endeavour to scale up the number of qubits in an ion-based quantum computer several groups have started to develop miniaturized ion traps for extended spatial control and manipulation of the ions. Shuttling and separation of ion strings have been the foremost issues in linear-trap arrangements and some prototypes of junctions have been demonstrated for the extension of ion motion to two dimensions (2D). While junctions require complex trap structures, small extensions to the 1D motion can be accomplished in simple linear trap arrangements. Here, control of the extended field in a planar, linear chip trap is used to shuttle ions in 2D. With this approach, the order of ions in a string is deterministically reversed. Optimized potentials are theoretically derived and simulations show that the reordering can be carried out adiabatically. The control over individual ion positions in a linear trap presents a new tool for ion-trap quantum computing. The method is also expected to work with mixed crystals of different ion species and as such could have applications for sympathetic cooling of an ion string.

Quantum Computing With Ions

The article reports on research into the development of quantum computers, which store and process data using atom or photon level micro-structures. These machines may be able to perform previously impossible computations. The manipulation of trapped ions is discussed. There are believed to be no fundamental, theoretical obstacles to the development of trapped-ion computers. INSETS: SPOOKY ACTION AT A DISTANCE;TRUTH TABLE;ION STRINGS;THE SMALL FRONTIER

Simultaneous cooling of axial vibrational modes in a linear ion trap

In order to use a collection of trapped ions for experiments where a well defined preparation of vibrational states is necessary, all vibrational modes have to be cooled to ensure precise and repeatable manipulation of the ions' quantum states. A method for simultaneous sideband cooling of all axial vibrational modes is proposed. By application of a magnetic field gradient the absorption spectrum of each ion is modified such that sideband resonances of different vibrational modes coincide. The ion string is then irradiated with monochromatic electromagnetic radiation, in the optical or microwave regime, for sideband excitation. This cooling scheme is investigated in detailed numerical studies. Its application for initializing ion strings for quantum information processing is extensively discussed.

Laser cooling with electromagnetically induced transparency: application to trapped samples of ions or neutral atoms

A novel method of ground state laser cooling of trapped atoms utilizes the absorption profile of a three (or multi-) level system which is tailored by a quantum interference. With cooling rates comparable to conventional sideband cooling, lower final temperatures may be achieved. The method was experimentally implemented to cool a single Ca$^+$ ion to its vibrational ground state. Since a broad band of vibrational frequencies can be cooled simultaneously, the technique will be particularly useful for the cooling of larger ion strings, thereby being of great practical importance for initializing a quantum register based on trapped ions. We also discuss its application to different level schemes and for ground state cooling of neutral atoms trapped by a far detuned standing wave laser field.

Addressing and Cooling of Single Ions in Paul Traps

The use of cold trapped ions for quantum information processing requires the preparation of linear strings of ions at low temperatures and the coherent manipulation by laser light of the quantum state of individual ions in the string. In our experiment, 40Ca+ ions are trapped in a linear Paul trap, forming crystallized linear strings when laser cooled. These strings are observed by fluorescence detection on the S1/2-P1/2 dipole transition at 397 nm using a photomultiplier and a CCD camera. The narrow S1/2-D5/2 quadrupole transition at 729 nm is used to investigate and manipulate the vibrational motion of the ion in the trap. The spectral resolution obtained up to now on this transition is 2 · 10—12, proving long coherence time of the two-level system. Addressing of individual ions in the string is achieved, using a tightly focused laser beam at 729 nm, and detected by the observation of quantum jumps from the S1/2 to the D5/2 level. These experimental techniques make ions in a superposition of their S1/2 and D5/2 states suitable as qubits for quantum information processing. The realization of a two-ion quantum gate furthermore requires ground-state cooling of the string. The status of current experiments is reviewed and techniques to achieve ground-state cooling of ion strings are discussed.

Addressing and Cooling of Single Ions in Paul Traps

The use of cold trapped ions for quantum information processing requires the preparation of linear strings of ions at low temperatures and the coherent manipulation by laser light of the quantum state of individual ions in the string. In our experiment, 40Ca+ ions are trapped in a linear Paul trap, forming crystallized linear strings when laser cooled. These strings are observed by fluorescence detection on the S1/2-P1/2 dipole transition at 397 nm using a photomultiplier and a CCD camera. The narrow S1/2-D5/2 quadrupole transition at 729 nm is used to investigate and manipulate the vibrational motion of the ion in the trap. The spectral resolution obtained up to now on this transition is 2 · 10—12, proving long coherence time of the two-level system. Addressing of individual ions in the string is achieved, using a tightly focused laser beam at 729 nm, and detected by the observation of quantum jumps from the S1/2 to the D5/2 level. These experimental techniques make ions in a superposition of their S1/2 and D5/2 states suitable as qubits for quantum information processing. The realization of a two-ion quantum gate furthermore requires ground-state cooling of the string. The status of current experiments is reviewed and techniques to achieve ground-state cooling of ion strings are discussed.