Hermann Uys

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.

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.

Experimental Uhrig dynamical decoupling using trapped ions

We present a detailed experimental study of the Uhrig dynamical decoupling UDD sequence in a variety of noise environments. Our qubit system consists of a crystalline array of 9 Be + ions confined in a Penning trap. We use an electron-spin-flip transition as our qubit manifold and drive qubit rotations using a 124 GHz microwave system. We study the effect of the UDD sequence in mitigating phase errors and compare against the well known Carr-Purcell-Meiboom-Gill-style multipulse spin echo as a function of pulse number, rotation axis, noise spectrum, and noise strength. Our results agree well with theoretical predictions for qubit decoherence in the presence of classical phase noise, accounting for the effect of finite-duration pulses. Finally, we demonstrate that the Uhrig sequence is more robust against systematic over- or under-rotation and detuning errors than is multipulse spin echo, despite the precise prescription for pulse timing in UDD.

Optomechanical trapping and cooling of partially reflective mirrors

We consider the radiative trapping and cooling of a partially reflecting mirror suspended inside an optical cavity, generalizing the case of a perfectly reflecting mirror previously considered [M. Bhattacharya and P. Meystre, Phys. Rev. Lett. 99, 073601 (2007)]. This configuration was recently used in an experiment to cool a nanometers-thick dielectric membrane [J. D. Thompson et al., e-print arXiv:0707.1724v2]. The self-consistent cavity field modes of this system depend strongly on the position of the middle mirror, leading to important qualitative differences in the radiation pressure effects: in one case, the situation is similar to that of a perfectly reflecting middle mirror, with only minor quantitative modifications. In addition, we also identify a range of mirror positions for which the radiation-mirror-coupling becomes purely dispersive and the back-action effects that usually lead to cooling are absent, although the mirror can still be optically trapped. The existence of these two regimes leads us to propose a bichromatic scheme that optimizes the cooling and trapping of partially reflective mirrors.

Arbitrary quantum control of qubits in the presence of universal noise

We address the problem of deriving analytic expressions for calculating universal decoherence-induced errors in qubits undergoing arbitrary, unitary, time-dependent quantum control protocols. We show that the fidelity of a control operation may be expressed in terms of experimentally relevant spectral characteristics of the noise and of the control, over all Cartesian directions. We formulate control matrices in the time domain to capture the effects of piecewise-constant control, and convert them to generalized Fourier-domain filter functions. These generalized filter functions may be derived for complex temporally modulated control protocols, accounting for susceptibility to rotations of the qubit state vector in three dimensions. Taken together, we show that this framework provides a computationally efficient means to calculate the effects of universal noise on arbitrary quantum control protocols, producing results comparable with those obtained via time-consuming simulations of Bloch vector evolution. As a concrete example, we apply our method to treating the problem of dynamical decoupling incorporating realistic control pulses of arbitrary duration or form, including the replacement of simple π-pulses with complex dynamically corrected gates.

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.

Foundations of Nonextensive Statistical Mechanics and Its Cosmological Applications

The q-generalized quantum distributions, arising within the context of q-nonextensive thermostatistics, have recently found interesting applications to cosmology. These applications rest upon an approximated form of the q-distributions whose properties are not yet completely known. In order to shed some new light on this subject we consider here a maximum entropy principle leading to the q-generalized Fermi–Dirac distribution. This variational principle is formulated entirely in terms of the mean occupation numbers. It constitutes a natural generalization to the nonextensive regime of the well-known prescription leading, in the standard q= 1 case, to the usual distribution for fermions. We analyze some important properties of this variational approach. In particular, we discuss 1) the invariance of the associated solutions under uniform shifts of the energy spectrum; 2) the role played by different kinds of constraints (i.e. linear or q-generalized constraints); and 3) the probabilistic interpretation of the variational procedure. The possibility of extending the present approach to bosons is also considered.

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.

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.