Kenton R. Brown

Microwave quantum logic gates for trapped ions

Control over physical systems at the quantum level is important in fields as diverse as metrology, information processing, simulation and chemistry. For trapped atomic ions, the quantized motional and internal degrees of freedom can be coherently manipulated with laser light. Similar control is difficult to achieve with radio-frequency or microwave radiation: the essential coupling between internal degrees of freedom and motion requires significant field changes over the extent of the atoms’ motion, but such changes are negligible at these frequencies for freely propagating fields. An exception is in the near field of microwave currents in structures smaller than the free-space wavelength, where stronger gradients can be generated. Here we first manipulate coherently (on timescales of 20 nanoseconds) the internal quantum states of ions held in a microfabricated trap. The controlling magnetic fields are generated by microwave currents in electrodes that are integrated into the trap structure. We also generate entanglement between the internal degrees of freedom of two atoms with a gate operation suitable for general quantum computation; the entangled state has a fidelity of 0.76(3), where the uncertainty denotes standard error of the mean. Our approach, which involves integrating the quantum control mechanism into the trapping device in a scalable manner, could be applied to quantum information processing, simulation and spectroscopy.

Coupled quantized mechanical oscillators

The harmonic oscillator is one of the simplest physical systems but also one of the most fundamental. It is ubiquitous in nature, often serving as an approximation for a more complicated system or as a building block in larger models. Realizations of harmonic oscillators in the quantum regime include electromagnetic fields in a cavity and the mechanical modes of a trapped atom or macroscopic solid. Quantized interaction between two motional modes of an individual trapped ion has been achieved by coupling through optical fields, and entangled motion of two ions in separate locations has been accomplished indirectly through their internal states. However, direct controllable coupling between quantized mechanical oscillators held in separate locations has not been realized previously. Here we implement such coupling through the mutual Coulomb interaction of two ions held in trapping potentials separated by 40 μm (similar work is reported in a related paper). By tuning the confining wells into resonance, energy is exchanged between the ions at the quantum level, establishing that direct coherent motional coupling is possible for separately trapped ions. The system demonstrates a building block for quantum information processing and quantum simulation. More broadly, this work is a natural precursor to experiments in hybrid quantum systems, such as coupling a trapped ion to a quantized macroscopic mechanical or electrical oscillator.

Trapped-ion quantum logic gates based on oscillating magnetic fields.

Oscillating magnetic fields and field gradients can be used to implement single-qubit rotations and entangling multiqubit quantum gates for trapped-ion quantum information processing (QIP). With fields generated by currents in microfabricated surface-electrode traps, it should be possible to achieve gate speeds that are comparable to those of optically induced gates for realistic distances between the ion crystal and the electrode surface. Magnetic-field-mediated gates have the potential to significantly reduce the overhead in laser-beam control and motional-state initialization compared to current QIP experiments with trapped ions and will eliminate spontaneous scattering, a fundamental source of decoherence in laser-mediated gates.

100-fold reduction of electric-field noise in an ion trap cleaned with in situ argon-ion-beam bombardment.

Anomalous heating of trapped atomic ions is a major obstacle to their use as quantum bits in a scalable quantum computer. The physical origin of this heating is not fully understood, but experimental evidence suggests that it is caused by electric-field noise emanating from the surface of the trap electrodes. In this study, we have investigated the role that adsorbates on the electrodes play by identifying contaminant overlayers, developing an in situ argon-ion beam cleaning procedure, and measuring ion heating rates before and after cleaning the trap electrodes’ surfaces. We find a reduction of two orders of magnitude in heating rate after cleaning.

Single-qubit-gate error below10−4in a trapped ion

With a {sup 9}Be{sup +} trapped-ion hyperfine-state qubit, we demonstrate an error probability per randomized single-qubit gate of 2.0(2)x10{sup -5}, below the threshold estimate of 10{sup -4} commonly considered sufficient for fault-tolerant quantum computing. The {sup 9}Be{sup +} ion is trapped above a microfabricated surface-electrode ion trap and is manipulated with microwaves applied to a trap electrode. The achievement of low single-qubit-gate errors is an essential step toward the construction of a scalable quantum computer.

A 750-mW, continuous-wave, solid-state laser source at 313 nm for cooling and manipulating trapped 9Be+ ions

We present a solid-state laser system that generates 750 mW of continuous-wave, single-frequency output at 313 nm. Sum-frequency generation with fiber lasers at 1550 and 1051 nm produces up to 2 W at 626 nm. This visible light is then converted to ultraviolet by cavity-enhanced second-harmonic generation. The laser output can be tuned over a 495-GHz range, which includes the 9Be+ laser cooling and repumping transitions. This is the first report of a narrow-linewidth laser system with sufficient power to perform fault-tolerant quantum-gate operations with trapped 9Be+ ions by use of stimulated Raman transitions.

Passive Cooling of a Micromechanical Oscillator with a Resonant Electric Circuit

We cool the fundamental mode of a miniature cantilever by capacitively coupling it to a driven rf resonant circuit. Cooling results from the rf capacitive force, which is phase shifted relative to the cantilever motion. We demonstrate the technique by cooling a 7 kHz cantilever from room temperature to 45 K, obtaining reasonable agreement with a model for the cooling, damping, and frequency shift. Extending the method to higher frequencies in a cryogenic system could enable ground state cooling and may prove simpler than related optical experiments in a low temperature apparatus.

Tunable spin–spin interactions and entanglement of ions in separate potential wells

Quantum simulation—the use of one quantum system to simulate a less controllable one—may provide an understanding of the many quantum systems which cannot be modelled using classical computers. Considerable progress in control and manipulation has been achieved for various quantum systems, but one of the remaining challenges is the implementation of scalable devices. In this regard, individual ions trapped in separate tunable potential wells are promising. Here we implement the basic features of this approach and demonstrate deterministic tuning of the Coulomb interaction between two ions, independently controlling their local wells. The scheme is suitable for emulating a range of spin–spin interactions, but to characterize the performance of our set-up we select one that entangles the internal states of the two ions with a fidelity of 0.82(1) (the digit in parentheses shows the standard error of the mean). Extension of this building block to a two-dimensional network, which is possible using ion-trap microfabrication processes, may provide a new quantum simulator architecture with broad flexibility in designing and scaling the arrangement of ions and their mutual interactions. To perform useful quantum simulations, including those of condensed-matter phenomena such as the fractional quantum Hall effect, an array of tens of ions might be sufficient.

Techniques for microwave near-field quantum control of trapped ions

Abstract : Microwave near-field quantum control of spin and motional degrees of freedom of 25Mg+ ions can be used to generate two-ion entanglement, as recently demonstrated in Ospelkaus et al. [Nature 476, 181 (2011)]. Here, we describe additional details of the setup and calibration procedures for these experiments. We discuss the design and characteristics of the surface-electrode trap and the microwave system and compare experimental measurements of the microwave near fields with numerical simulations. Additionally, we present a method that utilizes oscillatingmagnetic-field gradients to detect micromotion induced by the ponderomotive radio-frequency potential in linear traps. Finally, we discuss the present limitations of microwave-driven two-ion entangling gates in our system.

In-vacuum active electronics for microfabricated ion traps

The advent of microfabricated ion traps for the quantum information community has allowed research groups to build traps that incorporate an unprecedented number of trapping zones. However, as device complexity has grown, the number of digital-to-analog converter (DAC) channels needed to control these devices has grown as well, with some of the largest trap assemblies now requiring nearly one hundred DAC channels. Providing electrical connections for these channels into a vacuum chamber can be bulky and difficult to scale beyond the current numbers of trap electrodes. This paper reports on the development and testing of an in-vacuum DAC system that uses only 9 vacuum feedthrough connections to control a 78-electrode microfabricated ion trap. The system is characterized by trapping single and multiple (40)Ca(+) ions. The measured axial mode stability, ion heating rates, and transport fidelities for a trapped ion are comparable to systems with external (air-side) commercial DACs.