13 research outputs found
Complete population transfer in a degenerate 3-level atom
We find conditions required to achieve complete population transfer, via
coherent population trapping, from an initial state to a designated final state
at a designated time in a degenerate 3-level atom, where transitions are caused
by an external interaction. Complete population transfer from an initially
occupied state 1 to a designated state 2 occurs under two conditions. First,
there is a constraint on the ratios of the transition matrix elements of the
external interaction. Second, there is a constraint on the action integral over
the interaction, or "area", corresponding to the phase shift induced by the
external interaction. Both conditions may be expressed in terms of simple odd
integers.Comment: 22 pages, 4 figure
Population control of 2s-2p transitions in hydrogen
We consider the time evolution of the occupation probabilities for the 2s-2p
transition in a hydrogen atom interacting with an external field, V(t). A
two-state model and a dipole approximation are used. In the case of degenerate
energy levels an analytical solution of the time-dependent Shroedinger equation
for the probability amplitudes exists. The form of the solution allows one to
choose the ratio of the field amplitude to its frequency that leads to temporal
trapping of electrons in specific states. The analytic solution is valid when
the separation of the energy levels is small compared to the energy of the
interacting radiation.Comment: 6 pages, 3 figure
Time Ordering in Kicked Qubits
We examine time ordering effects in strongly, suddenly perturbed two-state
quantum systems (kicked qubits) by comparing results with time ordering to
results without time ordering. Simple analytic expressions are given for state
occupation amplitudes and probabilities for singly and multiply kicked qubits.
We investigate the limit of no time ordering, which can differ in different
representations.Comment: 26 pages, 5 figure
Sudden switching in qubits
Analytic solutions are developed for two-state systems (e.g. qubits) strongly
perturbed by a series of rapidly changing pulses, called `kicks'. The evolution
matrix may be expressed as a time ordered product of evolution matrices for
single kicks. Single, double, and triple kicks are explicitly considered, and
the onset of observability of time ordering is examined. The effects of
different order of kicks on the dynamics of the system are studied and compared
with effects of time ordering in general. To determine the range of validity of
this approach, the effect of using pulses of finite widths for 2s-2p
transitions in atomic hydrogen is examined numerically.Comment: 22 pages, 7 figure