Fast quantum control in dissipative systems using dissipationless solutions

We report on a systematic geometric procedure, built up on solutions designed in the absence of dissipation, to mitigate the effects of dissipation in the control of open quantum systems. Our method addresses a standard class of open quantum systems modeled by non-Hermitian Hamiltonians. It provides the analytical expression of the extra magnetic field to be superimposed to the driving field in order to compensate the geometric distortion induced by dissipation, and produces an exact geometric optimization of fast population transfer. Interestingly, it also preserves the robustness properties of protocols originally optimized against noise. Its extension to two interacting spins restores a fidelity close to unity for the fast generation of Bell state in the presence of dissipation

Standard and nonstandard polynomial approximation

AbstractAs foundation of polynomial approximation, uniform convergence is replaced with basic nonstandard notions like S-continuity and standard part. In the real case, Weierstrass' approximation theorem is generalized to Gδ-sets. In the complex case the standard compactness requirements also disappear. Standard applications include a direct proof of a generalized Bernstein theorem on analyticity of C∞ and of continuous functions

Space-time sensors using multiple-wave atom levitation

The best clocks to date control the atomic motion by trapping the sample in an optical lattice and then interrogate the atomic transition by shining on these atoms a distinct laser of controlled frequency. In order to perform both tasks simultaneously and with the same laser field, we propose to use instead the levitation of a Bose-Einstein condensate through multiple-wave atomic interferences. The levitating condensate experiences a coherent localization in momentum and a controlled diffusion in altitude. The sample levitation is bound to resonance conditions used either for frequency or for acceleration measurements. The chosen vertical geometry solves the limitations imposed by the sample free fall in previous optical clocks using also atomic interferences. This configuration yields multiple-wave interferences enabling levitation and enhancing the measurement sensitivity. This setup, analogous to an atomic resonator in momentum space, constitutes an attractive alternative to existing atomic clocks and gravimeters.Comment: 5 pages, 4 figures.Final versio