Controllability of spin 1 systems and realization of ternary SWAP gate in two spin 1 systems coupled with Ising interaction

In this paper,we investigate the controllability of spin 1 systems and the realization of ternary gates.Using dipole and quadrupole operators as the orthogonal basis of su(3) algebra,we discuss the controllability of one spin 1 systems and offer the concept of a complete set of control operators first.Then we present the controllability of two spin 1 systems coupled with Ising interaction and the transforming relations of the drift process of the system.Finally the specific realization of the ternary SWAP gate in these systems is discussed.It takes 9 drift processes and 25 basic control processes.     

Deterministic implementations of fermionic quantum SWAP and Fredkin gates for spin qubits based on charge detection

We propose a scheme to implement fermionic quantum SWAP and Fredkin gates for spin qubits with the aid of charge detection. The scheme is deterministic without the need of qubit–qubit interaction, and the proposed setups consist of simple polarizing beam splitters, single-spin rotations, and charge detectors. Compared with linear optics quantum computation, this charge-measurement-based qubit scheme greatly enhances the success probability for im- plementing quantum SWAP and Fredkin gates and greatly simplifies the experimental realization of scalable quantum computers with noninteracting electrons.     

Universal set of quantum gates for double-dot spin qubits with fixed interdot coupling

We propose a set of universal gate operations for the singlet-triplet qubit realized by two-electron spins in a double quantum dot, in the presence of a fixed inhomogeneous magnetic field. All gate operations are achieved by switching the potential offset between the two dots with an electrical bias, and do not require time-dependent control of the tunnel coupling between the dots. We analyze the two-electron dynamics and calculate the effective qubit rotation angle as a function of the applied electric bias. We present explicit gate sequences for single-qubit rotations about two orthogonal axes, and a CNOT gate sequence, completing the universal gate set.     

Broadband pulses for excitation and inversion in I = 1 systems

New composite pulses for exciting and inverting three-level systems are presented. The π/2 pulse is designed for use in quadrupole echo spectroscopy and has a bandwidth comparable to existing sequences and is slightly shorter. Two new broadband π pulses are presented which have bandwidths larger than other existing I = 1 inverting pulses without being significantly longer. Numerical calculations and experimental examples demonstrate the usefulness of the new sequences.     

Derivation of effective spin models from a three band model for CuO-planes

The derivation of effective spin models describing the low energy magnetic properties of undoped CuO₂-planes is reinvestigated. Our study aims at a quantitative determination of the parameters of effective spin models from those of a multi-band model and is supposed to be relevant to the analysis of recent improved experimental data on the spin wave spectrum of La₂CuO₄. Starting from a conventional three-band model we determine the exchange couplings for the nearest and next-nearest neighbor Heisenberg exchange as well as for 4- and 6-spin exchange terms via a direct perturbation expansion up to 12th (14th for the 4-spin term) order with respect to the copper-oxygen hopping t_pd. Our results demonstrate that this perturbation expansion does not converge for hopping parameters of the relevant size. Well behaved extrapolations of the couplings are derived, however, in terms of Padé approximants. In order to check the significance of these results from the direct perturbation expansion we employ the Zhang-Rice reformulation of the three band model in terms of hybridizing oxygen Wannier orbitals centered at copper ion sites. In the Wannier notation the perturbation expansion is reorganized by an exact treatment of the strong site-diagonal hybridization. The perturbation expansion with respect to the weak intersite hybridizations is calculated up to 4th order for the Heisenberg coupling and up to 6th order for the 4-spin coupling. It shows excellent convergence and the results are in agreement with the Padé approximants of the direct expansion. The relevance of the 4-spin coupling as the leading correction to the nearest neighbor Heisenberg model is emphasized. Received 8 June 2001 / Received in final form 28 May 2002 Published online 19 July 2002     

Oxoferryl porphyrin cation radicals in model systems: Evidence for variable metal-radical spin coupling

Magnetic properties of frozen solutions of highly oxidized iron porphyrin complexes were investigated by EPR and Mössbauer spectroscopy. The Mössbauer spectra, recorded at low temperatures in various magnetic fields, were analyzed on the basis of spin Hamiltonian simulations. Spin coupling between ferryl iron (Fe^IV) and porphyrin cation radical was taken into account explicitly. Hyperfine and spin-coupling parameters are given for several complexes, together with zero-field parameters. One of the complexes exhibits weak spin coupling, it is the first model system exhibiting properties comparable to those of the oxoferryl cation radical enzyme Horse Radish Peroxidase I.     

Nonthermal fixed points: effective weak coupling for strongly correlated systems far from equilibrium

Strongly correlated systems far from equilibrium can exhibit scaling solutions with a dynamically generated weak coupling. We show this by investigating isolated systems described by relativistic quantum field theories for initial conditions leading to nonequilibrium instabilities, such as parametric resonance or spinodal decomposition. The nonthermal fixed points prevent fast thermalization if classical-statistical fluctuations dominate over quantum fluctuations. We comment on the possible significance of these results for the heating of the early Universe after inflation and the question of fast thermalization in heavy-ion collision experiments.     

Nonlinear surface acoustic waves: realization of solitary pulses and fracture

A laser-based technique for the contact-free generation and detection of strongly nonlinear surface acoustic wave (SAW) pulses with amplitudes limited by the materials strength has been developed. The effects of nonlinear propagation of short elastic surface pulses with finite strength in isotropic solids, such as fused quartz, anisotropic solids, such as silicon, and dispersive media were investigated. Solitary surface wave propagation was observed in layered structures for normal and anomalous dispersion. In addition, a SAW-based method for evaluating the critical fracture stress of anisotropic brittle solids, such as single crystal silicon, is introduced.     

Light scattering from bulk and surface spin waves in opaque ferromagnets; The influence of quadratic coupling terms

We calculate the light scattering spectrum from spin waves, for backscattering from an opaque ferromagnet with magnetization parallel to the surface. The spectra contain features arising from both bulk and surface magnons. Including the quadratic terms in the spin density in the fluctuating part of the dielectric tensor leads to an asymmetry in the Stokes/anti-Stokes ratio for scattering for both bulk and surface waves. Our calculations give a good account of the data reported by Grunberg and Metawe, for scattering from EuO.     

Analytical treatment for synchronizing chaos through unidirectional coupling and implementation of logic gates

The idea of synchronization can be explicitly demonstrated by both numerical and analytical means on a nonlinear electronic circuit. Also, we introduce a scheme to obtain various logic gate structures, using synchronization of chaotic systems. By a small change in the response parameter of unidirectionally coupled nonlinear systems, one is able to construct various logic behaviours by both numerical and analytical methods.     

Two-dimensional atom-phonon coupling model for spin conversion: role of metastable states

Spin conversion, (SC), compounds are composed of molecules organized around a transition metal ion. The ion spin value is smaller for the ion fundamental level than for its first excited one. So, increasing the temperature changes the spin mean value. This spin conversion can be continuous or can display a first order phase transition called spin transition. The atom phonon coupling model, introduced recently, allows to describe at least qualitatively different experimental results. Up to now, this model has been applied on a linear chain of atoms. In this paper we apply it on a square lattice. We study the thermal variations of different thermodynamic parameters and the metastable states which are present around the transition. In this study, it is expected that the critical point of some (SC) compounds can be reached by applying on them a small hydrostatic pressure; it is also expected that ultrasound pulses can induce, at a very low temperature, a conversion between the stable low spin state and the metastable high spin state and it is also predicted that the crystal sound velocity can display a discontinuity at the first order phase transition.     

Spin-dependent forces on trapped ions for phase-stable quantum gates and entangled states of spin and motion

Favored schemes for trapped-ion quantum logic gates use bichromatic laser fields to couple internal qubit states with external motion through a "spin-dependent force." We introduce a new degree of freedom in this coupling that reduces its sensitivity to phase decoherence. We demonstrate bichromatic spin-dependent forces on a single trapped 111Cd+ ion, and show that phase coherence of the resulting entangled states of spin and motion depends critically upon the spectral arrangement of the optical fields. This applies directly to the operation of entangling gates on multiple ions.     

Tomograms for open quantum systems: In(finite) dimensional optical and spin systems

Tomograms are obtained as probability distributions and are used to reconstruct a quantum state from experimentally measured values. We study the evolution of tomograms for different quantum systems, both finite and infinite dimensional. In realistic experimental conditions, quantum states are exposed to the ambient environment and hence subject to effects like decoherence and dissipation, which are dealt with here, consistently, using the formalism of open quantum systems. This is extremely relevant from the perspective of experimental implementation and issues related to state reconstruction in quantum computation and communication. These considerations are also expected to affect the quasiprobability distribution obtained from experimentally generated tomograms and nonclassicality observed from them.     

Design and interpretation of laser pulses for the control of quantum systems

An extended theory of optimal control strategies for the design of feasible laser pulses is presented. The theoretical framework includes the control of population-transfer and expectation values. Selected studies for two-dimensional model systems providing aspects of uni- and bimolecular reactions are presented. Subsequent analysis of the obtained laser fields is performed to gain insight into the underlying reaction mechanisms. The effect of non-uniform spatial laser profiles and the orientation of the molecules versus the laser beam on controlling quantum dynamics is investigated with the main interest focussed on the achievable quantum yield and information on variable pathways stored in the laser field. Received: 10 November 1999 / Published online: 5 July 2000     

Existence and uniqueness of equilibrium states for some spin and continuum systems

The one to one correspondence between the existence of a unique equilibrium state and the differentiability of the free energy density with respect to the external field previously shown for Ising ferromagnetis is extendend to higher valued spin systems as well as to continuum systems satisfying the Fortuin, Kasteleyn and Ginibre inequalities. In particular this is shown to hold for a mixture ofA –B particles in which there is no interaction between like particles and a repulsion between unlike particles. Where the derivative of the free energy is discontinuous there are at least two equilibrium states.Supported in part by Air Force Grant n. 732430.