Ferromagnetic resonance of a two-dimensional array of nanomagnets: Effects of surface anisotropy and dipolar interactions

We develop an analytical approach for studying the FMR frequency shift due to dipolar interactions and surface effects in two-dimensional arrays of nanomagnets with (effective) uniaxial anisotropy along the magnetic field. For this we build a general formalism on the basis of perturbation theory that applies to dilute assemblies but which goes beyond the point-dipole approximation as it takes account of the size and shape of the nano-elements, in addition to their separation and spatial arrangement. The contribution to the frequency shift due to the shape and size of the nano-elements has been obtained in terms of their aspect ratio, their separation and the lattice geometry. We have also varied the size of the array itself and compared the results with a semi-analytical model and reached an agreement that improves as the size of the array increases. We find that the red-shift of the ferromagnetic resonance due to dipolar interactions decreases for smaller arrays. Surface effects may induce either a blue-shift or a red-shift of the FMR frequency, depending on the crystal and magnetic properties of the nano-elements themselves. In particular, some configurations of the nano-elements assemblies may lead to a full compensation between surface effects and dipole interactions.Comment: 14 pages, 5 figure

Dynamics of a magnetic dimer with exchange, dipolar and Dzyalozhinski-Moriya interaction

We investigate the dynamics of a magnetic system consisting of two magnetic moments coupled by either exchange, dipole-dipole, or Dzyalozhinski-Moriya interaction. We compare the switching mechanisms and switching rates as induced by the three couplings. For each coupling and each configuration of the two anisotropy axes, we describe the switching modes and, using the kinetic theory of Langer, we provide (semi-)analytical expressions for the switching rate. We then compare the three interactions with regard to their efficiency in the reversal of the net magnetic moment of the dimer. We also investigate how the energy barriers vary with the coupling. For the dipole-dipole interaction we find that the energy barrier may either increase or decrease with the coupling depending on whether the latter is weak or strong. Finally, upon comparing the various switching rates, we find that the dipole-dipole coupling leads to the slowest magnetic dimer, as far as the switching of its net magnetic moment is concerned.Comment: 20 pages, 18 Figures, 2 table

Enhancing the conductance of a two-electron nanomechanical oscillator

We consider electron transport through a mobile island (i.e., a nanomechanical oscillator) which can accommodate one or two excess electrons and show that, in contrast to immobile islands, the Coulomb blockade peaks, associated with the first and second electrons entering the island, have different functional dependences on the nano-oscillator parameters when the island coupling to its leads is asymmetric. In particular, the conductance for the second electron (i.e., when the island is already charged) is greatly enhanced in comparison to the conductance of the first electron in the presence of an external electric field. We also analyze the temperature dependence of the two conduction peaks and show that these exhibit different functional behaviors.Comment: 16 pages, 5 figure

AFM pulling and the folding of donor-acceptor oligorotaxanes: phenomenology and interpretation

The thermodynamic driving force in the self-assembly of the secondary structure of a class of donor-acceptor oligorotaxanes is elucidated by means of molecular dynamics simulations of equilibrium isometric single-molecule force spectroscopy AFM experiments. The oligorotaxanes consist of cyclobis(paraquat-\emph{p}-phenylene) rings threaded onto an oligomer of 1,5-dioxynaphthalenes linked by polyethers. The simulations are performed in a high dielectric medium using MM3 as the force field. The resulting force vs. extension isotherms show a mechanically unstable region in which the molecule unfolds and, for selected extensions, blinks in the force measurements between a high-force and a low-force regime. From the force vs. extension data the molecular potential of mean force is reconstructed using the weighted histogram analysis method and decomposed into energetic and entropic contributions. The simulations indicate that the folding of the oligorotaxanes is energetically favored but entropically penalized, with the energetic contributions overcoming the entropy penalty and effectively driving the self-assembly. In addition, an analogy between the single-molecule folding/unfolding events driven by the AFM tip and the thermodynamic theory of first-order phase transitions is discussed and general conditions, on the molecule and the cantilever, for the emergence of mechanical instabilities and blinks in the force measurements in equilibrium isometric pulling experiments are presented. In particular, it is shown that the mechanical stability properties observed during the extension are intimately related to the fluctuations in the force measurements.Comment: 42 pages, 17 figures, accepted to the Journal of Chemical Physic

Controllable coherent population transfers in superconducting qubits for quantum computing

We propose an approach to coherently transfer populations between selected quantum states in one- and two-qubit systems by using controllable Stark-chirped rapid adiabatic passages (SCRAPs). These {\it evolution-time insensitive} transfers, assisted by easily implementable single-qubit phase-shift operations, could serve as elementary logic gates for quantum computing. Specifically, this proposal could be conveniently demonstrated with existing Josephson phase qubits. Our proposal can find an immediate application in the readout of these qubits. Indeed, the broken parity symmetries of the bound states in these artificial "atoms" provide an efficient approach to design the required adiabatic pulses.Comment: 4 pages, 6 figures. to appear in Physical Review Letter

Doorway States and Billiards

Whenever a distinct state is immersed in a sea of complicated and dense states, the strength of the distinct state, which we refer to as a doorway, is distributed in their neighboring states. We analyze this mechanism for 2-D billiards with different geometries. One of them is symmetric and integrable, another is symmetric but chaotic, and the third has a capricious form. The fact that the doorway-state mechanism is valid for such highly diverse cases, proves that it is robust.Comment: 7 pages, 6 figures, Accepted in Proceedings of "Symmetries in Nature", Symposium in Memoriam Marcos Moshinsk

Effects of dynamical phases in Shor's factoring algorithm with operational delays

Ideal quantum algorithms usually assume that quantum computing is performed continuously by a sequence of unitary transformations. However, there always exist idle finite time intervals between consecutive operations in a realistic quantum computing process. During these delays, coherent "errors" will accumulate from the dynamical phases of the superposed wave functions. Here we explore the sensitivity of Shor's quantum factoring algorithm to such errors. Our results clearly show a severe sensitivity of Shor's factorization algorithm to the presence of delay times between successive unitary transformations. Specifically, in the presence of these {\it coherent "errors"}, the probability of obtaining the correct answer decreases exponentially with the number of qubits of the work register. A particularly simple phase-matching approach is proposed in this paper to {\it avoid} or suppress these {\it coherent errors} when using Shor's algorithm to factorize integers. The robustness of this phase-matching condition is evaluated analytically or numerically for the factorization of several integers: $4, 15, 21$, and 33.Comment: 8 pages with 5 figure