qspec.simulate.lambda_ge_rec  (  t ,  n ,  delta ,  a_ge ,  a_me ,  s ,  f ,  m ,  p0 = None ,  dt = 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, taking into account photon recoils. The system is driven by a single laser. The state vector is defined as (g0, m0, e0, g1, m1, e1, ..., gn, mn, en), where g is the first end of the Lambda, m the second end and e the intermediate state. The photon recoils are modeled using a discrete subspace and not the continuous momentum space. The number of photon recoils increases by one when the system is excited from the g state to the e state. Vice-versa, the number of photon recoils decreases by one when the system is deexcited from the e state to the g state via the process of stimulated emission. When the system decays into the g state via the dissipative mechanism described by the Einstein coefficient 'a_ge', the number of photon recoils does not change.

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).

narray_like

The maximum number of photon recoils to consider.

deltaarray_like

The detuning of the laser relative to the g->e transition (MHz).

a_gearray_like

The Einstein coefficient of the e->g transition (MHz).

a_mearray_like

The Einstein coefficient of the e->m transition (MHz).

sarray_like

The saturation parameter of the g->e transition.

farray_like

The transition frequency of the g->e transition (MHz).

marray_like

The mass number of the element (u).

p0array_like

The initial density matrix. Must have shape (6, ), containing the elements [gg, mm, ee, gm, eg, em](0) or be the full density matrix with all the recoil information.

dtfloat

The width of the time steps.

time_resolvedbool

Whether to return the complete history of the result.

showbool

Whether to plot the result.

Returns:

outNone

The diagonal 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, 3(n+1)). time will be an array of equally spaced times, such that numerical integrations can be performed easily.