Quantum systems engineering

Abstract:

We consider the case of a cubic nonlinear Schrödinger equation with an additional chaotic potential, in the sense that such a potential produces chaotic dynamics in classical mechanics. We derive and describe an appropriate semiclassical limit to such a nonlinear Schrödinger equation, using a semiclassical interpretation of the Wigner function, and relate this to the hydrodynamic limit of the Gross-Pitaevskii equation used in the context of Bose-Einstein condensation. We investigate a specific example of a Gross-Pitaevskii equation with such a chaotic potential, the one-dimensional δ-kicked harmonic oscillator, and its semiclassical limit, discovering in the process an interesting interference effect, where increasing the strength of the repulsive nonlinearity promotes localization of the wave function. We explore the feasibility of an experimental realization of such a system in a Bose-Einstein condensate experiment, giving a concrete proposal of how to implement such a configuration, and considering the problem of condensate depletion. ©2000 The American Physical Society.

Abstract:

We propose several schemes for implementing a fast two-qubit quantum gate for neutral atoms with the gate operation time much faster than the time scales associated with the external motion of the atoms in the trapping potential. In our example, the large interaction energy required to perform fast gate operations is provided by the dipole-dipole interaction of atoms excited to low-lying Rydberg states in constant electric fields. A detailed analysis of imperfections of the gate operation is given.

Abstract:

An appropriate semiclassical limit for a general cubic nonlinear Schrodinger equation, or Gross-Pitaevskii equation was derived. The derivation was shown to be a Liouville-type equation. Using this derivation, it was demonstrated how an eccentric wave function φ (x) can produce large deviations from the semiclassical limit.

Abstract:

We review recent proposals for performing entanglement manipulation via cold collisions between neutral atoms. State-dependent, time-varying trapping potentials allow one to control the interaction between atoms, so that conditional phase shifts realizing a universal quantum gate can be obtained with high fidelity. We discuss possible physical implementations with existing experimental techniques, for example optical lattices and magnetic micro-traps. © 2000 Taylor & Francis Group, LLC.

Abstract:

Quantum optical systems that implement quantum computing tasks concentrating on two-qubit gates are presented. Two schemes, one based on dipole moments of Rydberg atoms and the other base on conditional Coulomb interactions between ions in arrays of micro-traps, are analyzed. These schemes are combined with the features of quantum optics, in particular quantum control and long decoherence times.