In a recent publication [Phys. Rev. A 79, 065602 (2009)] it was shown that an avoided-crossing resonance can be defined in different ways, according to level-structural or dynamical aspects, which do not coincide in general. Here a simple $3$-level s
ystem in a $Lambda$ configuration is discussed, where the difference between both definitions of the resonance may be observed. We also discuss the details of a proposed experiment to observe this difference, using microwave fields coupling hyperfine magnetic sublevels in alkali atoms.
We examine structural and dynamical properties of quantum resonances associated with an avoided crossing and identify the parameter shifts where these properties attain maximal or extreme values, first at a general level, and then for a two-level sys
tem coupled to a harmonic oscillator, of the type commonly found in quantum optics. Finally the results obtained are exemplified and applied to optimize the fidelity and speed of quantum gates in trapped ions.
A relation is found between pulsed measurements of the excited state probability of a two-level atom illuminated by a driving laser, and a continuous measurement by a second laser coupling the excited state to a third state which decays rapidly and i
rreversibly. We find the time between pulses to achieve the same average detection time than a given continuous measurement in strong, weak, or intermediate coupling regimes, generalizing the results in L. S. Schulman, Phys. Rev. A 57, 1509 (1998).
When trapped atoms are illuminated by weak lasers, off-resonant transitions cause shifts in the frequencies of the vibrational-sideband resonances. These frequency shifts may be understood in terms of Stark-shifts of the individual levels or, as prop
osed here, as a vibrational Bloch-Siegert shift, an effect closely related to the usual (radio-frequency or optical) Bloch-Siegert shift and associated with rapidly oscillating terms when the Rotating Wave Approximation is not made. Explicit analytic expressions are derived and compared to numerical results, and the similarities and differences between the usual and the vibrational Bloch-Siegert shifts are also spelled out.
We study the effect of quantum motion in a Mach-Zehnder interferometer where ultracold, two-level atoms cross a $pi/2 $-$pi $-$pi/2$ configuration of separated, laser illuminated regions. Explicit and exact expressions are obtained for transmission a
mplitudes of monochromatic, incident atomic waves using recurrence relations which take into account all possible paths: the direct ones usually considered in the simple semiclassical treatment, but including quantum motion corrections, and the paths in which the atoms are repeatedly reflected at the fields.
