Using angle-resolved photoemission spectroscopy, we show that the recently discovered surface state on SrTiO(3) consists of nondegenerate t(2g) states with different dimensional characters. While the d(xy) bands have quasi-2D dispersions with weak k(z) dependence, the lifted d(xz)/d(yz) bands show 3D dispersions that differ significantly from bulk expectations and signal that electrons associated with those orbitals permeate the near-surface region. Like their more 2D counterparts, the size and character of the d(xz)/d(yz) Fermi surface components are essentially the same for different sample preparations. Irradiating SrTiO(3) in ultrahigh vacuum is one method observed so far to induce the "universal" surface metallic state. We reveal that during this process, changes in the oxygen valence band spectral weight that coincide with the emergence of surface conductivity are disproportionate to any change in the total intensity of the O 1s core level spectrum. This signifies that the formation of the metallic surface goes beyond a straightforward chemical doping scenario and occurs in conjunction with profound changes in the initial states and/or spatial distribution of near-E(F) electrons in the surface region.

The quantum noise of the vacuum limits the achievable sensitivity of quantum sensors. In non-classical measurement schemes the noise can be reduced to overcome this limitation. However, schemes based on squeezed or Schrödinger cat states require alignment of the relative phase between the measured interaction and the non-classical quantum state. Here we present two measurement schemes on a trapped ion prepared in a motional Fock state for displacement and frequency metrology that are insensitive to this phase. The achieved statistical uncertainty is below the standard quantum limit set by quantum vacuum fluctuations, enabling applications in spectroscopy and mass measurements.

Microwave trapped-ion quantum logic gates avoid spontaneous emission as a fundamental source of decoherence. However, microwave two-qubit gates are still slower than laser-induced gates and hence more sensitive to fluctuations and noise of the motional mode frequency. We propose and implement amplitude-shaped gate drives to obtain resilience to such frequency changes without increasing the pulse energy per gate operation. We demonstrate the resilience by noise injection during a two-qubit entangling gate with 9 Be + ion qubits. In absence of injected noise, amplitude modulation gives an operation infidelity in the 10 −3 range.Trapped ions are a leading platform for scalable quantum logic [1, 2] and quantum simulations [3]. Major challenges towards larger-scale devices include the integration of tasks and components that have been so far only demonstrated individually, as well as single and multiqubit gates with the highest possible fidelity to reduce the overhead in quantum error correction. Microwave control of trapped-ion qubits has the potential to address both challenges [4,5] as it allows the gate mechanism, potentially including control electronics, to be integrated into scalable trap arrays. Because spontaneous emission as a fundamental source of decoherence is absent and microwave fields are potentially easier to control than the laser beams that are usually employed, microwaves are a promising approach for high fidelity quantum operations. In fact, microwave two-qubit gate fidelities seem to improve more rapidly than laser-based gates. However, observed two-qubit gate speeds of laser-based gates [6,7] are still about an order of magnitude faster than for microwave gates [8][9][10]. This makes gates more susceptible to uncontrolled motional mode frequency changes, as transient entanglement with the motional degrees of freedom is the key ingredient in multi-qubit gates for trapped ions. As other error sources have been addressed recently, this is of growing importance. Merely increasing Rabi frequencies may not be the most resource-efficient approach, as it will increase energy dissipation in the device. A more efficient use of available resources could be obtained using pulse shaping or modulation techniques. In fact, a number of recent advances in achieving highfidelity operations or long qubit memory times have been proposed or obtained by tailored control fields. Examples include pulsed dynamic decoupling [11], Walsh modulation [12], additional dressing fields to increase coherence times [13], phase [14], amplitude [15][16][17][18][19][20] and fre-quency modulation [21] as well multi-tone fields [22][23][24]. In many cases, these techniques lead to significant advantages. For multi-qubit gates, one mechanism is to optimize the trajectory of the motional mode in phase space for minimal residual spin-motional entanglement in case of experimental imperfections. This effectively reduces the distance between the origin and the point in phase space at which the gate terminates in case of errors.Here we propo...