Bounds to unitary evolution

Upper and lower bounds are established for the survival probability $||^{2}$ of a quantum state, in terms of the energy moments $$. Introducing a cut-off in the energy generally enables considerable improvement in these bounds and allows the method to be used where the exact energy moments do not exist.Comment: 5 pages, 8 figure

Intrinsic leakage of the Josephson flux qubit and breakdown of the two-level approximation for strong driving

Solid state devices for quantum bit computation (qubits) are not perfect isolated two-level systems, since additional higher energy levels always exist. One example is the Josephson flux qubit, which consists on a mesoscopic SQUID loop with three Josephson junctions operated at or near a magnetic flux of half quantum. We study intrinsic leakage effects, i.e., direct transitions from the allowed qubit states to higher excited states of the system during the application of pulses for quantum computation operations. The system is started in the ground state and rf- magnetic field pulses are applied at the qubit resonant frequency with pulse intensity $f_p$. A perturbative calculation of the average leakage for small $f_p$ is performed for this case, obtaining that the leakage is quadratic in $f_p$, and that it depends mainly on the matrix elements of the supercurrent. Numerical simulations of the time dependent Schr\"odinger equation corresponding to the full Hamiltonian of this device were also performed. From the simulations we obtain the value of $f_p$ above which the two-level approximation breaks down, and we estimate the maximum Rabi frequency that can be achieved. We study the leakage as a function of the ratio $\alpha$ among the Josephson energies of the junctions of the device, obtaining the best value for minimum leakage ($\alpha\approx0.85$). The effects of flux noise on the leakage are also discussed.Comment: Final improved version. Some figures have changed with new results added. To be published in Phys. Rev.

The quantum Gaussian well

Different features of a potential in the form of a Gaussian well have been discussed extensively. Although the details of the calculation are involved, the general approach uses a variational method and WKB approximation, techniques which should be familiar to advanced undergraduates. A numerical solution of the Schr\"odinger equation through diagonalization has been developed in a self-contained way, and physical applications of the potential are mentioned.Comment: 11 pages, 4 figures, To be published in American Journal of Physic

Quantum Langevin model for exoergic ion-molecule reactions and inelastic processes

We presents a fully quantal version of the Langevin model for the total rate of exoergic ion-molecule reactions or inelastic processes. The model, which is derived from a rigorous multichannel quantum-defect formulation of bimolecular processes, agrees with the classical Langevin model at sufficiently high temperatures. It also gives the first analytic description of ion-molecule reactions and inelastic processes in the ultracold regime where the quantum nature of the relative motion between the reactants becomes important.Comment: 5 pages, 3 figure

Singular solutions to the Seiberg-Witten and Freund equations on flat space from an iterative method

Although it is well known that the Seiberg-Witten equations do not admit nontrivial $L^2$ solutions in flat space, singular solutions to them have been previously exhibited -- either in $R^3$ or in the dimensionally reduced spaces $R^2$ and $R^1$ -- which have physical interest. In this work, we employ an extension of the Hopf fibration to obtain an iterative procedure to generate particular singular solutions to the Seiberg-Witten and Freund equations on flat space. Examples of solutions obtained by such method are presented and briefly discussed.Comment: 7 pages, minor changes. To appear in J. Math. Phy

Generating Schr\"{o}dinger-cat states in momentum and internal-state space from Bose-Einstein condensates with repulsive interactions

Resonant Raman coupling between internal levels induced by continuous illumination of non-collinear laser beams can create double-well momentum-space potentials for multi-level ``periodically-dressed'' atoms. We develop an approximate many-body formalism for a weakly interacting, trapped periodically-dressed Bose gas which illustrates how a tunable exchange interaction yields correlated many-body ground states. In contrast to the case of a position-space double well, the ground state of stable periodically-dressed Bose gases with repulsive interactions tends toward a Schr\"{o}dinger cat state in the regime where interactions dominate the momentum-space tunnelling induced by the external trapping potential. The dependence of the momentum-space tunnelling and exchange interaction on experimental parameters is derived. We discuss how real-time control of experimental parameters can be used to create Schr\"{o}dinger cat states either between momentum or internal states, and how these states could be dynamically controlled towards highly sensitive interferometry and frequency metrology.Comment: 7 pages, 3 figures. Submitted to PR

A fast and robust approach to long-distance quantum communication with atomic ensembles

Quantum repeaters create long-distance entanglement between quantum systems while overcoming difficulties such as the attenuation of single photons in a fiber. Recently, an implementation of a repeater protocol based on single qubits in atomic ensembles and linear optics has been proposed [Nature 414, 413 (2001)]. Motivated by rapid experimental progress towards implementing that protocol, here we develop a more efficient scheme compatible with active purification of arbitrary errors. Using similar resources as the earlier protocol, our approach intrinsically purifies leakage out of the logical subspace and all errors within the logical subspace, leading to greatly improved performance in the presence of experimental inefficiencies. Our analysis indicates that our scheme could generate approximately one pair per 3 minutes over 1280 km distance with fidelity (F>78%) sufficient to violate Bell's inequality.Comment: 10 pages, 4 figures, 5 tables (Two appendixes are added to justify two claims used in the maintext.

Gauge dependence of calculations in relativistic Coulomb excitation

Before a quantum-mechanical calculation involving electromagnetic interactions is performed, a choice must be made of the gauge to be used in expressing the potentials. If the calculation is done exactly, the observable results it predicts will be independent of the choice of gauge. However, in most practical calculations approximations are made, which can destroy the gauge invariance of the predictions. We compare here the results of coupled-channel time-dependent relativistic Coulomb excitation calculations, as performed in either Lorentz or Coulomb gauges. We find significant differences when the bombarding energy per nucleon is $\geq$ 2 GeV, which indicates that the common practice of relying completely on the Lorentz gauge can be dangerous.Comment: 23 pages, 3 figure

Loss of purity by wave packet scattering at low energies

We study the quantum entanglement produced by a head-on collision between two gaussian wave packets in three-dimensional space. By deriving the two-particle wave function modified by s-wave scattering amplitudes, we obtain an approximate analytic expression of the purity of an individual particle. The loss of purity provides an indicator of the degree of entanglement. In the case the wave packets are narrow in momentum space, we show that the loss of purity is solely controlled by the ratio of the scattering cross section to the transverse area of the wave packets.Comment: 7 pages, 1 figur

Barrier transmission for the Nonlinear Schr\"odinger Equation: Surprises of nonlinear transport

In this communication we report on a peculiar property of barrier transmission that systems governed by the nonlinear Schroedinger equation share with the linear one: For unit transmission the potential can be divided at an arbitrary point into two sub-potentials, a left and a right one, which have exactly the same transmission. This is a rare case of an exact property of a nonlinear wave function which will be of interest, e.g., for studies of coherent transport of Bose-Einstein condensates through mesoscopic waveguideComment: 7 pages, 2 figure