Notions of controllability for quantum mechanical systems

In this paper, we define four different notions of controllability of physical interest for multilevel quantum mechanical systems. These notions involve the possibility of driving the evolution operator as well as the state of the system. We establish the connections among these different notions as well as methods to verify controllability. The paper also contains results on the relation between the controllability in arbitrary small time of a system varying on a compact transformation Lie group and the corresponding system on the associated homogeneous space. As an application, we prove that, for the system of two interacting spin 1/2 particles, not every state transfer can be obtained in arbitrary small time.Comment: Replaced by a new version which contains the proof

Quantum Control Theory for State Transformations: Dark States and their Enlightenment

For many quantum information protocols such as state transfer, entanglement transfer and entanglement generation, standard notions of controllability for quantum systems are too strong. We introduce the weaker notion of accessible pairs, and prove an upper bound on the achievable fidelity of a transformation between a pair of states based on the symmetries of the system. A large class of spin networks is presented for which this bound can be saturated. In this context, we show how the inaccessible dark states for a given excitation-preserving evolution can be calculated, and illustrate how some of these can be accessed using extra catalytic excitations. This emphasises that it is not sufficient for analyses of state transfer in spin networks to restrict to the single excitation subspace. One class of symmetries in these spin networks is exactly characterised in terms of the underlying graph properties.Comment: 14 pages, 3 figures v3: rewritten for increased clarit

Parallelism for Quantum Computation with Qudits

Robust quantum computation with d-level quantum systems (qudits) poses two requirements: fast, parallel quantum gates and high fidelity two-qudit gates. We first describe how to implement parallel single qudit operations. It is by now well known that any single-qudit unitary can be decomposed into a sequence of Givens rotations on two-dimensional subspaces of the qudit state space. Using a coupling graph to represent physically allowed couplings between pairs of qudit states, we then show that the logical depth of the parallel gate sequence is equal to the height of an associated tree. The implementation of a given unitary can then optimize the tradeoff between gate time and resources used. These ideas are illustrated for qudits encoded in the ground hyperfine states of the atomic alkalies $^{87}$Rb and $^{133}$Cs. Second, we provide a protocol for implementing parallelized non-local two-qudit gates using the assistance of entangled qubit pairs. Because the entangled qubits can be prepared non-deterministically, this offers the possibility of high fidelity two-qudit gates.Comment: 9 pages, 3 figure

Spin configurations in hard-soft coupled bilayer systems: from rigid magnet to exchange spring transitions

We investigate equilibrium properties of an exchange-spring magnetic system constituted of a soft layer (e.g. Fe) of a given thickness on top of a hard magnetic layer (e.g. FePt). The magnetization profile M(z) as a function of the atomic position ranging from the bottom of the hard layer to the top of the soft layer is obtained in two cases with regard to the hard layer: i) in the case of a rigid interface (the FePt layer is a single layer), the profile is obtained analytically as the exact solution of a sine-Gordon equation with Cauchy's boundary conditions. Additional numerical simulations also confirm this result. Asymptotic expressions of M(z) show a linear behavior near the bottom and the top of the soft layer. In addition, a critical value of the number of atomic planes in the soft layer, that is necessary for the onset of spin deviations, is obtained in terms of the anisotropy and exchange coupling between the adjacent plane in the soft layer. ii) in the case of a relaxed interface (the FePt layer is a multilayer), the magnetization profile is obtained numerically for various Fe and FePt films thicknesses and applied field.Comment: 10 pages, 9 figures, PRB submitted (12-07-2010

Degrees of controllability for quantum systems and applications to atomic systems

Precise definitions for different degrees of controllability for quantum systems are given, and necessary and sufficient conditions are discussed. The results are applied to determine the degree of controllability for various atomic systems with degenerate energy levels and transition frequencies.Comment: 20 pages, IoP LaTeX, revised and expanded versio

Owner and animal factors predict the incidence of, and owner reaction towards, problem behaviors in companion dogs

Unwelcome behaviors in pet dogs may have serious implications for the quality of life of both the animals and their owners. We investigated owners\u2019 perceptions about their dogs\u2019 behavioral issues as well as other factors that might be predictive of potential canine problem behaviors. We distinguished between \u201cundesirable behaviors\u201d (behaviors that were unpleasant to the owners) and \u201cproblematic behaviors\u201d (behaviors that the owners found difficult to overcome). We designed an on-line survey eliciting information about owners, their dogs, their relationship with their dogs and whether the animals exhibited any of 15 potentially problematic behaviors. The largest proportion of respondents (65%) reported that their dogs exhibited undesirable, but not problematic, behaviors and were not interested in their modification. Only 32% of the respondents considered the behavior to be both undesirable and problematic and wished to change it. The owners\u2019 perception of a problem was associated with reports of fear- and anxiety-related behaviors. The owner\u2019s gender, marital status and attitude towards the dog as his/her child as well as the dog\u2019s age, size, age at acquisition and breed emerged as robust predictors. Compared to all other behavioral categories, reported aggressive canine behaviors were three times more likely to elicit an owner\u2019s wish to address them. This study revealed that the behaviors of dogs may be perceived differently by their owners and the type of perception may influence the owner\u2019s actual willingness to change those behaviors. Moreover, we identified the most robust set of factors that, either individually or combined, would help predict a dog\u2019s potential problem behaviors and an owner\u2019s attitude towards them, which will be useful in improving rational prevention and treatment strategies

Electrophoretic deposition of bilayer composite films based on CoFe2O4 and Nb-doped PZT

The magnetoelectric (ME) composites with piezoelectric and magnetostrictive material are of interest in the smart manufacturing and mechatronics fields as actuators/transducers, sensors, antennas, filters, non-volatile memories, etc. Spinel cobalt ferrite (CFO), a highly magnetostrictive material and niobium-doped lead zirconate titanate (PZTN), a piezoelectric perovskite phase are chosen as constituent phases for ME composite. The production process is designed in order to avoid the chemical reaction between the piezoelectric and magnetostrictive materials, to prevent the formation of percolation chains of the magnetostrictive phase, and to maximize the mechanical coupling at the interface between the two phases. In this view, the electrophoretic deposition (EPD) is a low cost and flexible technique to shape nanoparticles into multilayered heterostructures. The combination of different materials by EPD, showing promising ME coupling, can be regarded as a useful, preliminary approach in the search of novel ME materials for many applications, potentially with great industrial and technological benefits. In this work, composite bilayer CFO/PZTN thick films were deposited on platinum coated alumina by EPD from ethanol-based colloidal suspensions. Good adhesion and compaction of the green film were achieved by optimization of deposition voltage and time, and high density of the film and minimized interphase reactions occurred after sintering. The chemical activity between the two layers was controlled through the batches composition and it could lead to the synthesis of complex engineered structures. The deposited volume, the mixing of dielectric and magnetic phases and the density and ordering of the films have been verified by electron scanning microscopy after heat treatment. The ferroelectric, piezoelectric and magnetic properties were tested on the sintered films

A comparative investigation of the efficacy of CO2 and high power diode lasers for the forming of EN3 mild steel sheets

A comparative investigation of the effectiveness of a high power diode laser (HPDL) and a CO2 laser for the forming of thin section EN3 mild steel sheet has been conducted. The buckling mechanism was identified as the laser forming mechanism responsible for the induced bending. For both lasers it was found that the induced bending angles increased with an increasing number of irradiations and high laser powers, whilst decreasing as the traverse speed was increased. Also, it was apparent from the experimental results that the laser bending angle was only linearly proportional to the number of irradiations when the latter was small due to local material thickening along the bend edge with a high number of irradiations. Owing to the mild steel’s greater beam absorption at the HPDL wavelength, larger bending angles were induced when using the HPDL. However, under certain conditions the performance of the CO2 laser in terms of induced bending angle was seen to approach that of the HPDL. Nevertheless, similar results between the two lasers were only achieved with increasing irradiations, thus it was concluded that the efficacy of the HPDL was higher than that of the CO2 laser insofar as it was more efficient. From graphical results and the employment of an analytical procedure, the laser line energy range in which accurate control of the HPDL bending of the mild steel sheets could be exercised efficiently was found to be 53 J mm-1 < P/v < 78 J mm-1, whilst for the CO2 laser the range was 61 J mm-1 < P/v < 85 J mm-1