Search

Quantum computers, much like their classical counterparts, will likely benefit from flexible qubit encodings that can be matched to different tasks. For trapped ion quantum processors, a common way to access multiple encodings is to use multiple, co-trapped atomic species. Here, we outline an alternative approach that allows flexible encoding capabilities in single-species systems through the use of long-lived metastable states as an effective, programmable second species. We describe the set of additional trapped ion primitives needed to enable this protocol and show that they are compatible with large-scale systems that are already in operation.

Over the last decade, optical atomic clocks have surpassed their microwave counterparts and now offer the ability to measure time with an increase in precision of two orders of magnitude or more. This performance increase is compelling not only for enabling new science, such as geodetic measurements of the earth, searches for dark matter, and investigations into possible long-term variations of fundamental physics constants but also for revolutionizing existing technology, such as the global positioning system (GPS). A significant remaining challenge is to transition these optical clocks to non-laboratory environments, which requires the ruggedization and miniaturization of the atomic reference and clock laser along with their supporting lasers and electronics. Here, using a compact stimulated Brillouin scattering (SBS) laser to interrogate a $^8$$^8$Sr$^+$ ion, we demonstrate a promising component of a portable optical atomic clock architecture. In order to bring the stability of the SBS laser to a level suitable for clock operation, we utilize a self-referencing technique to compensate for temperature drift of the laser to within $170$ nK. Our SBS optical clock achieves a short-term stability of $3.9 \times 10^{-14}$ at $1$ s---an order of magnitude improvement over state-of-the-art microwave clocks. Based on this technology, a future GPS employing portable SBS clocks offers the potential for distance measurements with a 100-fold increase in resolution.

Monolithic integration of control technologies for atomic systems is a promising route to the development of quantum computers and portable quantum sensors. Trapped atomic ions form the basis of high-fidelity quantum information processors and high-accuracy optical clocks. However, current implementations rely on free-space optics for ion control, which limits their portability and scalability. Here we demonstrate a surface-electrode ion-trap chip using integrated waveguides and grating couplers, which delivers all the wavelengths of light required for ionization, cooling, coherent operations, and quantum-state preparation and detection of Sr+ qubits. Laser light from violet to infrared is coupled onto the chip via an optical-fiber array, creating an inherently stable optical path, which we use to demonstrate qubit coherence that is resilient to platform vibrations. This demonstration of CMOS-compatible integrated-photonic surface-trap fabrication, robust packaging, and enhanced qubit coherence is a key advance in the development of portable trapped-ion quantum sensors and clocks, providing a way toward the complete, individual control of larger numbers of ions in quantum information processing systems., Comment: Updated to be consistent with published version

We demonstrate key multi-qubit quantum logic primitives in a dual-species trapped-ion system based on $^{40}$Ca+ and $^{88}$Sr+ ions, using two optical qubits with quantum-logic-control frequencies in the red to near-infrared range. With all ionization, cooling, and control wavelengths in a wavelength band similar for the two species and centered in the visible, and with a favorable mass ratio for sympathetic cooling, this pair is a promising candidate for scalable quantum information processing. Same-species and dual-species two-qubit gates, based on the Moelmer-Soerensen interaction and performed in a cryogenic surface-electrode trap, are characterized via the fidelity of generated entangled states; we achieve fidelities of 98.8(2)% and 97.5(2)% in Ca+ - Ca+ and Sr+ - Sr+ gates, respectively. For a similar Ca+ - Sr+ gate, we achieve a fidelity of 94.3(3)%, and carrying out a Sr+ - Sr+ gate performed with a Ca+ sympathetic cooling ion in a Sr+ - Ca+ - Sr+ crystal configuration, we achieve a fidelity of 95.7(3)%. These primitives form a set of trapped-ion capabilities for logic with sympathetic cooling and ancilla readout or state transfer for general quantum computing and communication applications., Comment: 12 pages, 4 figures, 2 tables

Trapped ions are among the most promising systems for practical quantum computing (QC). The basic requirements for universal QC have all been demonstrated with ions and quantum algorithms using few-ion-qubit systems have been implemented. We review the state of the field, covering the basics of how trapped ions are used for QC and their strengths and limitations as qubits. In addition, we discuss what is being done, and what may be required, to increase the scale of trapped ion quantum computers while mitigating decoherence and control errors. Finally, we explore the outlook for trapped-ion QC. In particular, we discuss near-term applications, considerations impacting the design of future systems of trapped ions, and experiments and demonstrations that may further inform these considerations., Comment: The following article has been submitted to Applied Physics Reviews

Trapped-ion quantum information processors offer many advantages for achieving high-fidelity operations on a large number of qubits, but current experiments require bulky external equipment for classical and quantum control of many ions. We demonstrate the cryogenic operation of an ion-trap that incorporates monolithically-integrated high-voltage CMOS electronics ($\pm 8\mathrm{V}$ full swing) to generate surface-electrode control potentials without the need for external, analog voltage sources. A serial bus programs an array of 16 digital-to-analog converters (DACs) within a single chip that apply voltages to segmented electrodes on the chip to control ion motion. Additionally, we present the incorporation of an integrated circuit that uses an analog switch to reduce voltage noise on trap electrodes due to the integrated amplifiers by over $50\mathrm{dB}$. We verify the function of our integrated electronics by performing diagnostics with trapped ions and find noise and speed performance similar to those we observe using external control elements., Comment: 7 pages, 3 figures

Electric-field noise from ion-trap electrode surfaces can limit the fidelity of multiqubit entangling operations in trapped-ion quantum information processors and can give rise to systematic errors in trapped-ion optical clocks. The underlying mechanism for this noise is unknown, but it has been shown that the noise amplitude can be reduced by energetic ion bombardment, or "ion milling," of the trap electrode surfaces. Using a single trapped $^{88}$Sr$^{+}$ ion as a sensor, we investigate the temperature dependence of this noise both before and after ex situ ion milling of the trap electrodes. Making measurements over a trap electrode temperature range of 4 K to 295 K in both sputtered niobium and electroplated gold traps, we see a marked change in the temperature scaling of the electric-field noise after ion milling: power-law behavior in untreated surfaces is transformed to Arrhenius behavior after treatment. The temperature scaling becomes material-dependent after treatment as well, strongly suggesting that different noise mechanisms are at work before and after ion milling. To constrain potential noise mechanisms, we measure the frequency dependence of the electric-field noise, as well as its dependence on ion-electrode distance, for niobium traps at room temperature both before and after ion milling. These scalings are unchanged by ion milling., Comment: 9 pages, 5 figures, 2 tables. v2: Added note on comparison of results with predictions of thermally activated fluctuator model. General updates made to text and figures to address reviewer comments. Consistent with published version

Microfabricated Paul ion traps show tremendous promise for large-scale quantum information processing. However, motional heating of ions can have a detrimental effect on the fidelity of quantum logic operations in miniaturized, scalable designs. In many experiments, contributions to ion heating due to technical voltage noise present on the static (DC) and radio frequency (RF) electrodes can be overlooked. We present a reliable method for determining the extent to which motional heating is dominated by residual voltage noise on the DC or RF electrodes. Also, we demonstrate that stray DC electric fields can shift the ion position such that technical noise on the RF electrode can significantly contribute to the motional heating rate. After minimizing the pseudopotential gradient experienced by the ion induced by stray DC electric fields, the motional heating due to RF technical noise can be significantly reduced., Comment: 8 pages, 4 figures

We investigate anomalous ion-motional heating, a limitation to multi-qubit quantum-logic gate fidelity in trapped-ion systems, as a function of ion-electrode separation. Using a multi-zone surface-electrode trap in which ions can be held at five discrete distances from the metal electrodes, we measure power-law dependencies of the electric-field noise experienced by the ion on the ion-electrode distance $d$. We find a scaling of approximately $d^{-4}$ regardless of whether the electrodes are at room temperature or cryogenic temperature, despite the fact that the heating rates are approximately two orders of magnitude smaller in the latter case. Through auxiliary measurements using application of noise to the electrodes, we rule out technical limitations to the measured heating rates and scalings. We also measure frequency scaling of the inherent electric-field noise close to $1/f$ at both temperatures. These measurements eliminate from consideration anomalous-heating models which do not have a $d^{-4}$ distance dependence, including several microscopic models of current interest., Comment: 6 pages (incl. references), 4 figures

Classical imaging works by scattering photons from an object to be imaged, and achieves resolution scaling as $1/\sqrt{t}$, with $t$ the imaging time. By contrast, the laws of quantum mechanics allow one to utilize quantum coherence to obtain imaging resolution that can scale as quickly as $1/t$ -- the so-called "Heisenberg limit." However, ambiguities in the obtained signal often preclude taking full advantage of this quantum enhancement, while imaging techniques designed to be unambiguous often lose this optimal Heisenberg scaling. Here, we demonstrate an imaging technique which combines unambiguous detection of the target with Heisenberg scaling of the resolution. We also demonstrate a binary search algorithm which can efficiently locate a coherent target using the technique, resolving a target trapped ion to within 0.3% of the $1/e^2$ diameter of the excitation beam., Comment: 8 pages, 5 figures

We describe rapid, random-access loading of a two-dimensional (2D) surface-electrode ion-trap array based on two crossed photo-ionization laser beams. With the use of a continuous flux of pre-cooled neutral atoms from a remotely-located source, we achieve loading of a single ion per site while maintaining long trap lifetimes and without disturbing the coherence of an ion quantum bit in an adjacent site. This demonstration satisfies all major criteria necessary for loading and reloading extensive 2D arrays, as will be required for large-scale quantum information processing. Moreover, the already high loading rate can be increased by loading ions in parallel with only a concomitant increase in photo-ionization laser power and no need for additional atomic flux., Comment: 5 pages, 4 figures, 1 table

The long coherence times and strong Coulomb interactions afforded by trapped ion qubits have enabled realizations of the necessary primitives for quantum information processing (QIP), and indeed the highest-fidelity quantum operations in any qubit to date. But while light delivery to each individual ion in a system is essential for general quantum manipulations and readout, experiments so far have employed optical systems cumbersome to scale to even a few tens of qubits. Here we demonstrate lithographically defined nanophotonic waveguide devices for light routing and ion addressing fully integrated within a surface-electrode ion trap chip. Ion qubits are addressed at multiple locations via focusing grating couplers emitting through openings in the trap electrodes to ions trapped 50 $\mu$m above the chip; using this light we perform quantum coherent operations on the optical qubit transition in individual $^{88}$Sr$^+$ ions. The grating focuses the beam to a diffraction-limited spot near the ion position with a 2 $\mu$m 1/$e^2$-radius along the trap axis, and we measure crosstalk errors between $10^{-2}$ and $4\times10^{-4}$ at distances 7.5-15 $\mu$m from the beam center. Owing to the scalability of the planar fabrication employed, together with the tight focusing and stable alignment afforded by optics integration within the trap chip, this approach presents a path to creating the optical systems required for large-scale trapped-ion QIP.

We present measurements of the motional heating rate of a trapped ion at different trap frequencies and temperatures between $\sim$0.6 and 1.5 MHz and $\sim$4 and 295 K. Additionally, we examine the possible effect of adsorbed surface contaminants with boiling points below $\sim$105$^{\circ}$C by measuring the ion heating rate before and after locally baking our ion trap chip under ultrahigh vacuum conditions. We compare the heating rates presented here to those calculated from available electric-field noise models. We can tightly constrain a subset of these models based on their expected frequency and temperature scaling interdependence. Discrepancies between the measured results and predicted values point to the need for refinement of theoretical noise models in order to more fully understand the mechanisms behind motional trapped-ion heating., Comment: 6 pages, 3 figures, 2 tables

We demonstrate trapping in a surface-electrode ion trap fabricated in a 90-nm CMOS (complementary metal-oxide-semiconductor) foundry process utilizing the top metal layer of the process for the trap electrodes. The process includes doped active regions and metal interconnect layers, allowing for co-fabrication of standard CMOS circuitry as well as devices for optical control and measurement. With one of the interconnect layers defining a ground plane between the trap electrode layer and the p-type doped silicon substrate, ion loading is robust and trapping is stable. We measure a motional heating rate comparable to those seen in surface-electrode traps of similar size. This is the first demonstration of scalable quantum computing hardware, in any modality, utilizing a commercial CMOS process, and it opens the door to integration and co-fabrication of electronics and photonics for large-scale quantum processing in trapped-ion arrays., Comment: 4 pages, 3 figures

We present measurements of trapped-ion motional-state heating rates in niobium and gold surface-electrode ion traps over a range of trap-electrode temperatures from approximately 4 K to room temperature (295 K) in a single apparatus. Using the sideband-ratio technique after resolved-sideband cooling of single ions to the motional ground state, we find low-temperature heating rates more than two orders of magnitude below the room-temperature values and approximately equal to the lowest measured heating rates in similarly-sized cryogenic traps. We find similar behavior in the two very different electrode materials, suggesting that the anomalous heating process is dominated by non-material-specific surface contaminants. Through precise control of the temperature of cryopumping surfaces, we also identify conditions under which elastic collisions with the background gas can lead to an apparent steady heating rate, despite rare collisions., Comment: v1: 6 pages, 3 figures; v2: 7 pages, 3 figures, analysis of temperature dependence and calculation of effects of collisions expanded and improved, minor errors corrected in discussions of Johnson noise and collisions and in appendix B

We demonstrate loading of ions into a surface-electrode trap (SET) from a remote, laser-cooled source of neutral atoms. We first cool and load $\sim$ $10^6$ neutral $^{88}$Sr atoms into a magneto-optical trap from an oven that has no line of sight with the SET. The cold atoms are then pushed with a resonant laser into the trap region where they are subsequently photoionized and trapped in an SET operated at a cryogenic temperature of 4.6 K. We present studies of the loading process and show that our technique achieves ion loading into a shallow (15 meV depth) trap at rates as high as 125 ions/s while drastically reducing the amount of metal deposition on the trap surface as compared with direct loading from a hot vapor. Furthermore, we note that due to multiple stages of isotopic filtering in our loading process, this technique has the potential for enhanced isotopic selectivity over other loading methods. Rapid loading from a clean, isotopically pure, and precooled source may enable scalable quantum information processing with trapped ions in large, low-depth surface trap arrays that are not amenable to loading from a hot atomic beam.

Superconducting coplanar waveguide (SCPW) resonators have a wide range of applications due to the combination of their planar geometry and high quality factors relative to normal metals. However, their performance is sensitive to both the details of their geometry and the materials and processes that are used in their fabrication. In this paper, we study the dependence of SCPW resonator performance on materials and geometry as a function of temperature and excitation power. We measure quality factors greater than $2\times10^6$ at high excitation power and $6\times10^5$ at a power comparable to that generated by a single microwave photon circulating in the resonator. We examine the limits to the high excitation power performance of the resonators and find it to be consistent with a model of radiation loss. We further observe that while in all cases the quality factors are degraded as the temperature and power are reduced due to dielectric loss, the size of this effect is dependent on resonator materials and geometry. Finally, we demonstrate that the dielectric loss can be controlled in principle using a separate excitation near the resonance frequencies of the resonator., Comment: Replacing original version. Changes made based on referee comments. Fixed typo in equation (3) and added appendix

Ultra-cold RbCs molecules in high-lying vibrational levels of the a$^3\Sigma^+$ ground electronic state are confined in an optical trap. Inelastic collision rates of these molecules with both Rb and Cs atoms are determined for individual vibrational levels, across an order of magnitude of binding energies. A simple model for the collision process is shown to accurately reproduce the observed scattering rates.

This paper describes and examines the experiences of eight learners and two teachers in an online distance education graduate course taught using an asynchronous program and a problem-based learning (PBL) pedagogy. The course, "Integrating the Internet across the Curriculum," was offered by Indiana University Bloomington as a 6-week summer course in 1999. As a World Wide Web-based course, it was available to a worldwide audience of K-12 educators in graduate or certification programs. The focus of the paper is on the general learning experience, particularly during the PBL portion of the course. The course was observed online, and additional information was obtained from students through e-mail questions and telephone interviews, and from the instructors through telephone interviews. Results are presented related to: the constructivist learning environment; individual learning and experience; group learning experiences; assessment and grading; developing an atmosphere of trust and collaboration; problem-solving student issues online; and design and implementation of PBL. Technology interface considerations related to these learning and teaching issues are outlined. A decision-making model for online PBL courses is presented that addresses student, teacher, curriculum, technology, and structural contextual issues. Contains 20 references. (MES)

We demonstrate the production of ultracold polar RbCs molecules in their vibronic ground state, via photoassociation of laser-cooled atoms followed by a laser-stimulated state transfer process. The resulting sample of $X ^1\Sigma^+ (v=0)$ molecules has a translational temperature of $\sim100 \mu$K and a narrow distribution of rotational states. With the method described here it should be possible to produce samples even colder in all degrees of freedom, as well as other bi-alkali species.

Using resonance-enhanced two-photon ionization, we detect ultracold, ground-state RbCs molecules formed via photoassociation in a laser-cooled mixture of 85Rb and 133Cs atoms. We obtain extensive bound-bound excitation spectra of these molecules, which provide detailed information about their vibrational distribution, as well as spectroscopic data on the RbCs ground a^3\Sigma^+ and excited (2)^3\Sigma^+, (1)^1\Pi states. Analysis of this data allows us to predict strong transitions from observed excited levels to the absolute vibronic ground state of RbCs, potentially allowing the production of stable, ultracold polar molecules at rates as large as 10^7 s^{-1}.

We have produced ultracold, polar RbCs* molecules via photoassociation in a laser-cooled mixture of Rb and Cs atoms. Using a model of the RbCs* molecular interaction which reproduces the observed rovibrational structure, we infer decay rates in our experiments into deeply bound singlet ground state RbCs vibrational levels as high as 5 x 10^5 s^-1 per level. Population in such deeply bound levels could be efficiently transferred to the vibrational ground state using a single stimulated Raman transition, opening the possibility to create large samples of stable, ultracold polar molecules., Comment: 4 pages, 4 figures. accepted to prl

Problem-based learning (PBL), often used in medical education, is an educational approach that organizes curriculum and instruction around carefully crafted "ill-structured" problems, to which students apply knowledge from multiple disciplines and critical thinking. PBL is being investigated as a teaching approach for elementary and middle schools. Its use was evaluated in three classrooms in two schools, at combined first and second grade levels, combined third and fourth grade levels, and eighth grade levels. Preliminary qualitative data have been gathered through classroom observation, semistructured interviews, and review of student-generated and classroom records. Brief case studies from each of the classrooms illustrate PBL in action at the K-8 level. Preliminary ideas for the further study of PBL are emerging, beginning with the question of whether ill-structured problems are appropriate for young students, and if so, how should they be developed? The implementation of PBL in the elementary and middle school classroom is, of necessity, very different from its implementation in medical school, and its success may rest on the careful identification of the outcomes to be desired or expected. Appendix A is an instructional template for a PBL unit, and Appendix B is a list of resource persons and organizations. (Contains 3 unnumbered tables and 23 references.) (SLD)