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, J(i,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 J(i,j) proportional variant d(-a)(i,j), where 0 ≤ a ≤ 3 and d(i,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.

High-order noise filtering in nontrivial quantum logic gates.

Treating the effects of a time-dependent classical dephasing environment during quantum logic operations poses a theoretical challenge, as the application of noncommuting control operations gives rise to both dephasing and depolarization errors that must be accounted for in order to understand total average error rates. We develop a treatment based on effective Hamiltonian theory that allows us to efficiently model the effect of classical noise on nontrivial single-bit quantum logic operations composed of arbitrary control sequences. We present a general method to calculate the ensemble-averaged entanglement fidelity to arbitrary order in terms of noise filter functions, and provide explicit expressions to fourth order in the noise strength. In the weak noise limit we derive explicit filter functions for a broad class of piecewise-constant control sequences, and use them to study the performance of dynamically corrected gates, yielding good agreement with brute-force numerics.

Spectroscopy and thermometry of drumhead modes in a mesoscopic trapped-ion crystal using entanglement.

We demonstrate spectroscopy and thermometry of individual motional modes in a mesoscopic 2D ion array using entanglement-induced decoherence as a method of transduction. Our system is a ~400 µm-diameter planar crystal of several hundred 9Be(+) ions exhibiting complex drumhead modes in the confining potential of a Penning trap. Exploiting precise control over the 9Be(+) valence electron spins, we apply a homogeneous spin-dependent optical dipole force to excite arbitrary transverse modes with an effective wavelength approaching the interparticle spacing (~20 µm). Center-of-mass displacements below 1 nm are detected via the entanglement of spin and motional degrees of freedom.

Laser induced and controlled chemical reaction of carbon monoxide and hydrogen.

Bimolecular chemical reaction control of gaseous CO and H(2) at room temperature and atmospheric pressure, without any catalyst, using shaped femtosecond laser pulses is presented. High intensity laser radiation applied to a reaction cell facilitates non-resonant bond breakage and the formation of a range of ions, which can then react to form new products. Stable reaction products are measured after irradiation of a reaction cell, using time of flight mass spectroscopy. Bond formation of C-O, C-C, and C-H bonds is demonstrated as CO(2)(+), C(2)H(2)(+), CH(+), and CH(3)(+) were observed in the time of flight mass spectrum of the product gas, analyzed after irradiation. The formation of CO(2) is shown to be dependent on laser intensity, irradiation time, and on the presence of H(2) in the reaction cell. Using negatively chirped laser pulses more C-O bond formation takes place as compared to more C-C bond formation for unchirped pulses.

Generating Greenberger-Horne-Zeilinger states with squeezing and postselection.

Many quantum state preparation methods rely on a combination of dissipative quantum state initialization followed by unitary evolution to a desired target state. Here we demonstrate the usefulness of quantum measurement as an additional tool for quantum state preparation. Starting from a pure separable multipartite state, a control sequence, which includes rotation, spin squeezing via one-axis twisting, quantum measurement, and postselection, generates highly entangled multipartite states, which we refer to as projected squeezed (PS) states. Through an optimization method, we then identify parameters required to maximize the overlap fidelity of the PS states with the maximally entangled Greenberger-Horne-Zeilinger (GHZ) states. The method leads to an appreciable decrease in the state preparation time of GHZ states for successfully postselected outcomes when compared to preparation through unitary evolution with one-axis twisting only.

Precessive sand ripples in intense steady shear flows.

We describe experimental observations of fully developed, large-amplitude bars under the action of a shearing fluid. The experiments were performed in an annular tank filled with water and sheared above by a steady motor source. The same steady shearing flow can produce a variety of different erodible bed manifestations: advective or precessive bars, which refer to bar structures with global regularity and a near-steady precession velocity; interactive bars, the structure of which depends on local rearrangements, which are in turn a response to complex background topography; and dispersive bars, which are created when an initially isolated mound of sand evolves into a train of sand ripples. Of these, the most amenable to analysis are the precessive bars. For precession bars, we find that the skin depth, which is the nondimensionalized mean-field transport rate, grows exponentially as a function of the shear velocity. From this, we arrive at an analytical expression that approximates the precession speed of the bars as a function of shear velocity. We use this to obtain a formula for sediment transport rate. However, in intense flows, the bars can get large engendering boundary layer separation, leading to a different dynamic for bar formation and evolution. Numerical flow calculations over an experimentally obtained set of precessive bars are presented and show that classical parametrizations of mass flux in terms of bottom gradients have shortcomings. Within the range of shear rates considered, a quantity that does not change appreciably in time is the aspect ratio, which is defined as the ratio of the average bar amplitude, with respect to a mean depth, to the average bar length.

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.

Optimized noise filtration through dynamical decoupling.

Recent studies have shown that applying a sequence of Hahn spin-echo pulses to a qubit system at judiciously chosen intervals can, in certain noise environments, greatly improve the suppression of phase errors compared to traditional dynamical decoupling approaches. By enforcing a simple analytical condition, we obtain sets of dynamical decoupling sequences that are designed for optimized noise filtration, but are independent of the noise spectrum up to a single scaling factor set by the coherence time of the system. These sequences are tested in a model qubit system, ;{9}Be;{+} ions in a Penning trap. Our combined theoretical and experimental studies show that in high-frequency-dominated noise environments with sharp high-frequency cutoffs this approach may suppress phase errors orders of magnitude more efficiently than comparable techniques can.

Matter-wave decoherence due to a gas environment in an atom interferometer.

Decoherence due to scattering from background gas particles is observed for the first time in a Mach-Zehnder atom interferometer, and compared with decoherence due to scattering photons. A single theory is shown to describe decoherence due to scattering either atoms or photons. Predictions from this theory are tested by experiments with different species of background gas, and also by experiments with different collimation restrictions on an atom beam interferometer.