Four-level systems and a universal quantum gate

We discuss the possibility of implementing a universal quantum XOR gate by using two coupled quantum dots subject to external magnetic fields that are parallel and slightly different. We consider this system in two different field configurations. In the first case, parallel external fields with the intensity difference at each spin being proportional to the time-dependent interaction between the spins. A general exact solution describing this system is presented and analyzed to adjust field parameters. Then we consider parallel fields with intensity difference at each spin being constant and the interaction between the spins switching on and off adiabatically. In both cases we adjust characteristics of the external fields (their intensities and duration) in order to have the parallel pulse adequate for constructing the XOR gate. In order to provide a complete theoretical description of all the cases, we derive relations between the spin interaction, the inter-dot distance, and the external field. (C) 2008 WILEYNCH Verlag GmbH & Co. KGaA. Weinheim.

Spontaneous recoherence of quantum states after decoherence

In this work, we identify the set of time-dependent pure states building the statistical mixture to which a system, initially in a pure state, is driven by the reservoir. This set of time-dependent pure states, composing what we term a pure basis, are those that diagonalize the reduced density operator of the system. Next, we show that the evolution of the pure-basis states reveals an interesting phenomenon as the system, after decoherence, evolves toward the equilibrium: the spontaneous recoherence of quantum states. Around our defined recoherence time, the statistical mixture associated with a special kind of initial states termed even-symmetric, spontaneously undergoes a recoherence process, by which the initial state of the system emerges from the mixture except for its reduced excitation drained into the reservoir. This phenomenon reveals that the reservoir only shuffle the original information carried out by the initial state of the system instead of erasing it. Moreover, as the spontaneously recohered state occurs only for asymptotic time, we also present a protocol to extract it from the mixture through specific projective measurements. The password to retrieve the original information stems is the knowledge of both the initial state itself and the associated pure basis. A definition of the decoherence time of an N-state superposition is also presented.

Effects of a quantum measurement on the electric conductivity : Application to graphene

We generalize the standard linear-response (Kubo) theory to obtain the conductivity of a system that is subject to a quantum measurement of the current. Our approach can be used to specifically elucidate how back-action inherent to quantum measurements affects electronic transport. To illustrate the utility of our general formalism, we calculate the frequency-dependent conductivity of graphene and discuss the effect of measurement-induced decoherence on its value in the dc limit. We are able to resolve an ambiguity related to the parametric dependence of the minimal conductivity.

Position-dependent effective mass Dirac equations with PT-symmetric and non-PT-symmetric potentials

We present a new procedure to construct the one-dimensional non-Hermitian imaginary potential with a real energy spectrum in the context of the position-dependent effective mass Dirac equation with the vector-coupling scheme in 1 + 1 dimensions. In the first example, we consider a case for which the mass distribution combines linear and inversely linear forms, the Dirac problem with a PT-symmetric potential is mapped into the exactly solvable Schrodinger-like equation problem with the isotonic oscillator by using the local scaling of the wavefunction. In the second example, we take a mass distribution with smooth step shape, the Dirac problem with a non-PT-symmetric imaginary potential is mapped into the exactly solvable Schrodinger-like equation problem with the Rosen-Morse potential. The real relativistic energy levels and corresponding wavefunctions for the bound states are obtained in terms of the supersymmetric quantum mechanics approach and the function analysis method.

Two-dimensional position-dependent massive particles in the presence of magnetic fields

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Wigner distribution for a class of isospectral position-dependent mass systems

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

Parameter-dependent Lyapunov functions for state-derivative feedback control in polytopic linear systems

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Energy-dependent point interaction: Self-adjointness

Recently, we constructed an energy-dependent point interaction (EDPI) in its most general form in one-dimensional quantum mechanics. In this paper, we show that stationary solutions of the Schrodinger equation with the EDPI form a complete set. Then any nonstationary solution of the time-dependent Schrodinger equation can be expressed as a linear combination of stationary solutions. This, however, does not necessarily mean that the EDPI is self-adjoint and the time-development of the nonstationary state is unitary. The EDPI is self-adjoint provided that the stationary solutions are all orthogonal to one another. We illustrate situations in which this orthogonality condition is not satisfied.

Aspects of classical and quantum motion on a flux cone

Motion of a nonrelativistic particle on a cone with a magnetic flux running through the cone axis (a flux cone) is studied. It is expressed as the motion of a particle moving on the Euclidean plane under the action of a velocity-dependent force. The probability fluid (quantum flow) associated with a particular stationary state is studied close to the singularity, demonstrating nontrivial Aharonov-Bohm effects. For example, it is shown that, near the singularity, quantum flow departs from classical flow. In the context of the hydrodynamical approach to quantum mechanics, quantum potential due to the conical singularity is determined, and the way it affects quantum flow is analyzed. It is shown that the winding number of classical orbits plays a role in the description of the quantum Bow. The connectivity of the configuration space is also discussed.

Energy-dependent point interactions in one dimension

We consider a new type of point interaction in one-dimensional quantum mechanics. It is characterized by a boundary condition at the origin that involves the second and/or higher order derivatives of the wavefunction. The interaction is effectively energy dependent. It leads to a unitary S-matrix for the transmission-reflection problem. The energy dependence of the interaction can be chosen such that any given unitary S-matrix (or the transmission and reflection coefficients) can be reproduced at all energies. Generalization of the results to coupled-channel cases is discussed.

C programs for solving the time-dependent Gross-Pitaevskii equation in a fully anisotropic trap

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Quantum mechanics versus equivalence principle

We consider the scattering of a photon by a weak gravitational field, treated as an external field, up to second order of the perturbation expansion. The resulting cross section is energy dependent which indicates a violation of Galileo's equivalence principle (universality of free fall) and, consequently, of the classical equivalence principle. The deflection angle theta for a photon passing by the sun is evaluated afterward and the likelihood of detecting Delta theta/theta(E) theta-theta(E)/theta(E) (where theta(E) is the value predicted by Einstein's geometrical theory for the light bending) in the foreseeable future, is discussed.

Scalar quantum field theory in disordered media

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

Construction of time-dependent dynamical invariants: A new approach

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Renormalizability of generalized quantum electrodynamics

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)