qspec.simulate. Interaction.schroedinger  (  t ,  delta = None ,  m = 0 ,  v = None ,  y0 = None  )[source]

Solver for the Schrödinger equation $$\begin{aligned} \frac{\partial\vec{\psi}}{\partial t} &= -\mathrm{i}H\vec{\psi}, \end{aligned}$$ where the Hamiltonian $H$ (2π MHz) is time-independent whenever possible, see qspec.simulate.Interaction.hamiltonian. Solutions for n samples can be calculated in parallel for nt times.

Parameters:

tarray_like

The times $t$ when to compute the solution. Any array is cast to the shape (nt, ), where nt is the size of the array t (μs).

deltaarray_like

An array of laser frequency shifts $\vec{\Delta}$. delta must be a scalar, a 1d- or 2d-array with shapes (n, ) or (n, nl), respectively, where nl is the number of lasers of the Interaction (MHz).

mOptional[int]

The index of the shifted laser. If delta is a 2d-array, m ist omitted.

varray_like

Atom velocities $\vec{v}$. Must be a scalar or have shape (n, ) or (n, 3). In the first two cases, the velocity vector(s) are assumed to be aligned with the $x$-axis (m/s).

y0array_like

The initial state of the Atom. This must be None or have shape (Atom.size, ) or (n, Atom.size). If None, all states with the same label as the first State in atom.states are populated equally.

Returns:

psi_tndarray

The integrated Schrödinger equation as a complex-valued array of shape (n, Atom.size, nt).