Sequential modular position and momentum measurements of a trapped ion mechanical oscillator

The non-commutativity of position and momentum observables is a hallmark feature of quantum physics. However this incompatibility does not extend to observables which are periodic in these base variables. Such modular-variable observables have been suggested as tools for fault-tolerant quantum computing and enhanced quantum sensing. Here we implement sequential measurements of modular variables in the oscillatory motion of a single trapped ion, using state-dependent displacements and a heralded non-destructive readout. We investigate the commutative nature of modular variable observables by demonstrating no-signaling-in-time between successive measurements, using a variety of input states. In the presence of quantum interference, which we enhance using squeezed input states, measurements of different periodicity show signaling-in-time. The sequential measurements allow us to extract two-time correlators for modular variables, which we use to violate a Leggett-Garg inequality. The experiments involve control and coherence of multi-component superpositions of up to 8 coherent, squeezed or Fock state wave-packets. Signaling-in-time as well as Leggett-Garg inequalities serve as efficient quantum witnesses which we probe here with a mechanical oscillator, a system which has a natural crossover from the quantum to the classical regime.Comment: 6 pages, 3 figures and supplemental informatio

Scalable arrays of micro-Penning traps for quantum computing and simulation

We propose the use of 2-dimensional Penning trap arrays as a scalable platform for quantum simulation and quantum computing with trapped atomic ions. This approach involves placing arrays of micro-structured electrodes defining static electric quadrupole sites in a magnetic field, with single ions trapped at each site and coupled to neighbors via the Coulomb interaction. We solve for the normal modes of ion motion in such arrays, and derive a generalized multi-ion invariance theorem for stable motion even in the presence of trap imperfections. We use these techniques to investigate the feasibility of quantum simulation and quantum computation in fixed ion lattices. In homogeneous arrays, we show that sufficiently dense arrays are achievable, with axial, magnetron and cyclotron motions exhibiting inter-ion dipolar coupling with rates significantly higher than expected decoherence. With the addition of laser fields these can realize tunable-range interacting spin Hamiltonians. We also show how local control of potentials allows isolation of small numbers of ions in a fixed array and can be used to implement high fidelity gates. The use of static trapping fields means that our approach is not limited by power requirements as system size increases, removing a major challenge for scaling which is present in standard radio-frequency traps. Thus the architecture and methods provided here appear to open a path for trapped-ion quantum computing to reach fault-tolerant scale devices.Comment: 21 pages, 10 figures Changes include adding section IX (Implementation Example) and substantially rewriting section X (Scaling

Pulsed force sequences for fast phase-insensitive quantum gates in trapped ions

We show how to create quantum gates of arbitrary speed between trapped ions, using a laser walking wave, with complete insensitivity to drift of the optical phase, and requiring cooling only to the Lamb-Dicke regime. We present pulse sequences that satisfy the requirements and are easy to produce in the laboratory.Comment: 11 pages, 3 figure

A review of knowledge: inter-row hoeing & its associated agronomy in organic cereal & pulse crops

The aim of this project was to establish the “state of the art” for inter-row hoeing and its associated agronomic practices in organic cereal and pulse crops. To achieve this a detailed review of literature was undertaken. • To facilitate inter-row cultivation in cereal and pulse crops, some adjustment of row spacing may be required. For cereals, drilling crops in 25 cm rows can reduce yield compared with normal drilling practice, primarily due to greater intra-specific competition amongst the crop (i.e. competition between crop plants). • The yield penalty resulting from widely spaced crop rows can be minimised using a number of approaches, depending on the drill: 1. Reducing the seed rate in widely spaced crop rows can help to minimise excessive intra-specific competition. 2. Band sowing the crop in wide rows can also help to minimise intra-specific competition as the seed is distributed over a greater area. 3. Using a twin-row arrangement can completely overcome the yield penalty. • The recommended row spacing for peas (up to 20 cm) and beans (up to 35 cm) does not require any further adjustment for inter-row hoeing. • Recent developments in automated guidance of inter-row hoeing equipment mean that weeding operations can now be conducted a much higher speeds (10 km h-1). This has highlighted the limitations of some of the cultivators currently used (e.g. ‘A’ blades), as excessive soil throw can occur at this high speed. Rolling cultivators may prove to be the most suitable at high forward speeds. For manually guided hoes working at slower speeds (5 km h-1), ‘A’ and ‘L’ blades offer an effective low cost solution. • In terms of the timing of inter-row hoeing, it is suggested that weeding operations should be conducted at an early stage in the growing season, as the weeds that emerge with or shortly after the crop are the ones that pose the most significant threat for crop yield. Weeding on two occasions can provide better levels of weed control than weeding once, but weeding more frequently offered little additional benefit. Reductions of weed biomass of up to 99 % have been reported as a result of inter-row hoeing, although this has not always resulted in a positive crop yield response. This is probably due to crop damage resulting from inaccurate hoeing, a problem that can be overcome with automated guidance. • There is some evidence to suggest that mechanical weeding operations can mineralise soil bound nitrogen. • The impact of inter-row hoeing on ground nesting birds is uncertain. Early indications suggest that skylarks prefer to nest directly adjacent to or in the crop row rather than between rows. The information contained within this review should enable farmers to make best use of inter-row hoeing in their arable crops. There are a number of areas that require further research and development: • The interaction of seed rate and row spacing needs to be confirmed in organic systems. • Relatively little is known about the mechanisms of weed kill and the detailed interaction between the cultivator blade, the weed and the soil. This is particularly important with the new automated guidance equipment that allows weeding at high forward speeds. • The timing and frequency of inter-row hoeing has received very little attention. The optimum weed control timings are based on small-plot crop:weed competition studies and need to be verified under field scale management with inter-row hoeing equipment. • Finally, the impact of inter-row hoeing and widely spaced crop rows on ground-nesting birds has not been looked at directly, but is of importance. Please see the main report for a more detailed summary before the full text

Quantum control of the motional states of trapped ions through fast switching of trapping potentials

We propose a new scheme for supplying voltages to the electrodes of microfabricated ion traps, enabling access to a regime in which changes to the trapping potential are made on timescales much shorter than the period of the secular oscillation frequencies of the trapped ions. This opens up possibilities for speeding up the transport of ions in segmented ion traps and also provides access to control of multiple ions in a string faster than the Coulomb interaction between them. We perform a theoretical study of ion transport using these methods in a surface-electrode trap, characterizing the precision required for a number of important control parameters. We also consider the possibilities and limitations for generating motional state squeezing using these techniques, which could be used as a basis for investigations of Gaussian-state entanglement.Comment: Accepted by New Journal of Physic

Energy distribution of charged dilaton black holes

Chamorro and Virbhadra studied, using the energy-momentum complex of Einstein, the energy distribution associated with static spherically symmetric charged dilaton black holes for an arbitrary value of the coupling parameter $\gamma$ which controls the strength of the dilaton to the Maxwell field. We study the same in Tolman's prescription and get the same result as obtained by Chamorro and Virbhadra. The energy distribution of charged dilaton black holes depends on the value of $\gamma$ and the total energy is independent of this parameter.Comment: 8 pages, RevTex, no figure

A proposal for a scalable universal bosonic simulator using individually trapped ions

We describe a possible architecture to implement a universal bosonic simulator (UBS) using trapped ions. Single ions are confined in individual traps, and their motional states represent the bosonic modes. Single-mode linear operators, nonlinear phase-shifts, and linear beam splitters can be realized by precisely controlling the trapping potentials. All the processes in a bosonic simulation, except the initialization and the readout, can be conducted beyond the Lamb-Dicke regime. Aspects of our proposal can also be applied to split adiabatically a pair of ions in a single trap