qspec.simulate.lambda_states  (  t ,  delta_1 ,  delta_2 ,  a_ge ,  a_me ,  s_1 ,  s_2 ,  lw_1 = 0.0 ,  lw_2 = 0.0 ,  p0 = None ,  time_resolved = False ,  show = False  )[source]

Computes the evolution of Lambda-systems such as the alkali metals or the singly-charged alkaline-earth metals. The state vector is defined as (g, m, e), where g is the first end of the Lambda, m the second end and e the intermediate state.

Parameters:

tarray_like

The time after which the probability is returned. If all times from 0 to 't' are required, use 'time_resolved'=True (us).

delta_1scalar

The detuning of the first laser relative to the g->e transition.

delta_2scalar

The detuning of the second laser relative to the m->e transition.

a_gescalar

The Einstein coefficient of the e->g transition.

a_mescalar

The Einstein coefficient of the e->m transition.

s_1scalar

The saturation parameter of the g->e transition.

s_2scalar

The saturation parameter of the m->e transition.

lw_1scalar

The frequency width of the first laser.

lw_2scalar

The frequency width of the second laser.

p0array_like | None

The initial density matrix. Must have shape (6, ), containing the elements [gg, mm, ee, gm, eg, em]. If None, initially all population is in the g state.

time_resolvedbool

Whether to return the complete history of the result.

showbool

Whether to plot the result.

Returns:

outndarray | tuple[ndarray, ndarray]

The density matrix elements after the time 't'. If time_resolved is True, a 2-tuple similar to (time, density matrix) is returned, were the density matrix has shape (time.size, 6). time will be an array of equally spaced times, such that numerical integrations can be performed easily.