John J. Bollinger

Microfabricated surface-electrode ion trap for scalable quantum information processing.

Individual laser-cooled 24Mg+ ions are confined in a linear Paul trap with a novel geometry where gold electrodes are located in a single plane and the ions are trapped 40 microm above this plane. The relatively simple trap design and fabrication procedure are important for large-scale quantum information processing (QIP) using ions. Measured ion motional frequencies are compared to simulations. Measurements of ion recooling after cooling is temporarily suspended yield a heating rate of approximately 5 motional quanta per millisecond for a trap frequency of 2.83 MHz, sufficiently low to be useful for QIP.

Engineered two-dimensional Ising interactions in a trapped-ion quantum simulator with hundreds of spins.

The presence of long-range quantum spin correlations underlies a variety of physical phenomena in condensed-matter systems, potentially including high-temperature superconductivity. However, many properties of exotic, strongly correlated spin systems, such as spin liquids, have proved difficult to study, in part because calculations involving N-body entanglement become intractable for as few as N ≈ 30 particles. Feynman predicted that a quantum simulator—a special-purpose ‘analogue’ processor built using quantum bits (qubits)—would be inherently suited to solving such problems. In the context of quantum magnetism, a number of experiments have demonstrated the feasibility of this approach, but simulations allowing controlled, tunable interactions between spins localized on two- or three-dimensional lattices of more than a few tens of qubits have yet to be demonstrated, in part because of the technical challenge of realizing large-scale qubit arrays. Here we demonstrate a variable-range Ising-type spin–spin interaction, Ji,j, on a naturally occurring, two-dimensional triangular crystal lattice of hundreds of spin-half particles (beryllium ions stored in a Penning trap). This is a computationally relevant scale more than an order of magnitude larger than previous experiments. We show that a spin-dependent optical dipole force can produce an antiferromagnetic interaction , where 0 ≤ a ≤ 3 and di,j is the distance between spin pairs. These power laws correspond physically to infinite-range (a = 0), Coulomb–like (a = 1), monopole–dipole (a = 2) and dipole–dipole (a = 3) couplings. Experimentally, we demonstrate excellent agreement with a theory for 0.05 ≲ a ≲ 1.4. This demonstration, coupled with the high spin count, excellent quantum control and low technical complexity of the Penning trap, brings within reach the simulation of otherwise computationally intractable problems in quantum magnetism.

Optimized dynamical decoupling in a model quantum memory

Any quantum system, such as those used in quantum information or magnetic resonance, is subject to random phase errors that can dramatically affect the fidelity of a desired quantum operation or measurement. In the context of quantum information, quantum error correction techniques have been developed to correct these errors, but resource requirements are extraordinary. The realization of a physically tractable quantum information system will therefore be facilitated if qubit (quantum bit) error rates are far below the so-called fault-tolerance error threshold, predicted to be of the order of 10-3–10-6. The need to realize such low error rates motivates a search for alternative strategies to suppress dephasing in quantum systems. Here we experimentally demonstrate massive suppression of qubit error rates by the application of optimized dynamical decoupling pulse sequences, using a model quantum system capable of simulating a variety of qubit technologies. We demonstrate an analytically derived pulse sequence, UDD, and find novel sequences through active, real-time experimental feedback. The latter sequences are tailored to maximize error suppression without the need for a priori knowledge of the ambient noise environment, and are capable of suppressing errors by orders of magnitude compared to other existing sequences (including the benchmark multi-pulse spin echo). Our work includes the extension of a treatment to predict qubit decoherence under realistic conditions, yielding strong agreement between experimental data and theory for arbitrary pulse sequences incorporating nonidealized control pulses. These results demonstrate the robustness of qubit memory error suppression through dynamical decoupling techniques across a variety of qubit technologies.

Quantum spin dynamics and entanglement generation with hundreds of trapped ions

Hundreds of ions simulate magnetism Strongly interacting quantum systems present a challenge to computational methods even at a relatively low particle number of a few dozen. Researchers are looking to tackle such problems by simulating them in a well-understood and controllable system. A linear array of ions is one such system; however, assembling a large enough number of ions is tricky. Bohnet et al. show that a two-dimensional “crystal” of around 200 9Be+ ions held together by magnetic and electric fields in a so-called Penning trap can simulate quantum magnetism. The work sets the stage for simulations with more complicated forms of interaction that classical computers would find intractable. Science, this issue p. 1297 A two-dimensional array of around 200 beryllium ions in a Penning trap simulates the quantum dynamics of the homogeneous Ising model. Quantum simulation of spin models can provide insight into problems that are difficult or impossible to study with classical computers. Trapped ions are an established platform for quantum simulation, but only systems with fewer than 20 ions have demonstrated quantum correlations. We studied quantum spin dynamics arising from an engineered, homogeneous Ising interaction in a two-dimensional array of 9Be+ ions in a Penning trap. We verified entanglement in spin-squeezed states of up to 219 ions, directly observing 4.0 ± 0.9 decibels of spectroscopic enhancement, and observed states with non-Gaussian statistics consistent with oversqueezed states. The good agreement with ab initio theory that includes interactions and decoherence lays the groundwork for simulations of the transverse-field Ising model with variable-range interactions, which are generally intractable with classical methods.

Entangled mechanical oscillators

Hallmarks of quantum mechanics include superposition and entanglement. In the context of large complex systems, these features should lead to situations as envisaged in the ‘Schrödinger’s cat’ thought experiment (where the cat exists in a superposition of alive and dead states entangled with a radioactive nucleus). Such situations are not observed in nature. This may be simply due to our inability to sufficiently isolate the system of interest from the surrounding environment—a technical limitation. Another possibility is some as-yet-undiscovered mechanism that prevents the formation of macroscopic entangled states. Such a limitation might depend on the number of elementary constituents in the system or on the types of degrees of freedom that are entangled. Tests of the latter possibility have been made with photons, atoms and condensed matter devices. One system ubiquitous to nature where entanglement has not been previously demonstrated consists of distinct mechanical oscillators. Here we demonstrate deterministic entanglement of separated mechanical oscillators, consisting of the vibrational states of two pairs of atomic ions held in different locations. We also demonstrate entanglement of the internal states of an atomic ion with a distant mechanical oscillator. These results show quantum entanglement in a degree of freedom that pervades the classical world. Such experiments may lead to the generation of entangled states of larger-scale mechanical oscillators, and offer possibilities for testing non-locality with mesoscopic systems. In addition, the control developed here is an important ingredient for scaling-up quantum information processing with trapped atomic ions.

Non-neutral ion plasmas and crystals, laser cooling, and atomic clocks

Experimental work which uses Penning and Paul traps to confine non‐neutral ion plasmas is discussed. Penning traps use a static uniform magnetic field and a static electric field to confine ions. The Paul trap uses the ponderomotive force from inhomogeneous radio‐frequency fields to confine ions to a region of minimum field strength. In many atomic physics experiments, these traps are designed to produce a harmonic restoring force for small numbers of stored ions (<104). Under these conditions and at low temperatures, both traps produce plasmas with simple shapes whose mode properties can be calculated exactly. Laser cooling has been used to reduce the temperature of trapped ions to less than 10 mK with ion spacings less than 20 μm. At such temperatures and interion spacings, the Coulomb potential energy between nearest neighbor ions is greater than the ion thermal energy and the ions exhibit spatial correlations characteristic of a liquid or crystal. Laser beams also apply a torque which, by changing the...

A 303-MHz frequency standard based on trapped Be/sup +/ ions

A 303-MHz hyperfine transition in the ground state of Be/sup +/ ions stored in a Penning trap was used as the basis for a frequency standard. Linewidths as narrow as 900 mu Hz were obtained. The inaccuracy in the second-order Doppler shift was reduced to 5 parts in 10/sup 15/ by laser cooling.<<ETX>>

Measuring out-of-time-order correlations and multiple quantum spectra in a trapped-ion quantum magnet

Characterizing the correlations of quantum many-body systems is known to be hard, but there are ways around: for example, a new method for measuring out-of-time correlations demonstrated in a Penning trap quantum simulator with over 100 ions.

Simplified motional heating rate measurements of trapped ions

We have measured motional heating rates of trapped atomic ions, a factor that can influence multi-ion quantum logic gate fidelities. Two simplified techniques were developed for this purpose: one relies on Raman sideband detection implemented with a single laser source, while the second is even simpler and is based on time-resolved fluorescence detection during Doppler recooling. We applied these methods to determine heating rates in a microfrabricated surface-electrode trap made of gold on fused quartz, which traps ions 40 {mu}m above its surface. Heating rates obtained from the two techniques were found to be in reasonable agreement. In addition, the trap gives rise to a heating rate of 300{+-}30 s{sup -1} for a motional frequency of 5.25 MHz, substantially below the trend observed in other traps.

Ultrasensitive detection of force and displacement using trapped ions

The ability to detect extremely small forces and nanoscale displacements is vital for disciplines such as precision spin-resonance imaging, microscopy, and tests of fundamental physical phenomena. Current force-detection sensitivity limits have surpassed 1 aN Hz(-1/2) (refs 6,7) through coupling of nanomechanical resonators to a variety of physical readout systems. Here, we demonstrate that crystals of trapped atomic ions behave as nanoscale mechanical oscillators and may form the core of exquisitely sensitive force and displacement detectors. We report the detection of forces with a sensitivity of 390 +/- 150 yN Hz(-1/2), which is more than three orders of magnitude better than existing reports using nanofabricated devices(7), and discriminate ion displacements of approximately 18 nm. Our technique is based on the excitation of tunable normal motional modes in an ion trap and detection through phase-coherent Doppler velocimetry, and should ultimately allow force detection with a sensitivity better than 1 yN Hz(-1/2) (ref. 16). Trapped-ion-based sensors could enable scientists to explore new regimes in materials science where augmented force, field and displacement sensitivity may be traded against reduced spatial resolution.