StarkMap#

class StarkMap(atom)[source]#

Calculates Stark maps for single atom in a field

This initializes calculation for the atom of a given type. For details of calculation see Zimmerman 1. For a quick working example see Stark map example snippet.

Parameters: atom (arc.alkali_atom_functions.AlkaliAtom or arc.divalent_atom_functions.DivalentAtom) – ={ arc.alkali_atom_data.Lithium6, arc.alkali_atom_data.Lithium7, arc.alkali_atom_data.Sodium, arc.alkali_atom_data.Potassium39, arc.alkali_atom_data.Potassium40, arc.alkali_atom_data.Potassium41, arc.alkali_atom_data.Rubidium85, arc.alkali_atom_data.Rubidium87, arc.alkali_atom_data.Caesium, arc.divalent_atom_data.Strontium88, arc.divalent_atom_data.Calcium40 arc.divalent_atom_data.Ytterbium174 } Select the alkali metal for energy level diagram calculation

Examples

State \(28~S_{1/2}~|m_j|=0.5\) polarizability calculation

>>> from arc import *
>>> calc = StarkMap(Caesium())
>>> calc.defineBasis(28, 0, 0.5, 0.5, 23, 32, 20)
>>> calc.diagonalise(np.linspace(00.,6000,600))
>>> print("%.5f MHz cm^2 / V^2 " % calc.getPolarizability())
0.76705 MHz cm^2 / V^2

Stark map calculation

>>> from arc import *
>>> calc = StarkMap(Caesium())
>>> calc.defineBasis(28, 0, 0.5, 0.5, 23, 32, 20)
>>> calc.diagonalise(np.linspace(00.,60000,600))
>>> calc.plotLevelDiagram()
>>> calc.showPlot()
<< matplotlib plot will open containing a Stark map >>

Examples

Advanced interfacing of Stark map calculations (StarkMap class) Here we show one easy way to obtain the Stark matrix (from diagonal mat1 and off-diagonal part mat2 ) and basis states (stored in basisStates ), if this middle-product of the calculation is needed for some code build on top of the existing ARC package.

>>> from arc import *
>>> calc = StarkMap(Caesium())
>>> calc.defineBasis(28, 0, 0.5, 0.5, 23, 32, 20)
>>> # Now we have matrix and basis states, that we can used in our own code
>>> # Let's say we want Stark map at electric field of 0.2 V/m
>>> eField = 0.2 # V/m
>>> # We can easily extract Stark matrix
>>> # as diagonal matrix (state detunings)
>>> #  + off-diagonal matrix (propotional to electric field)
>>> matrix = calc.mat1+calc.mat2*eField
>>> # and the basis states as array [ [n,l,j,mj] , ...]
>>> basisStates = calc.basisStates
>>> # you can do your own calculation now...

References

1: M. L. Zimmerman et.al, PRA 20:2251 (1979) https://doi.org/10.1103/PhysRevA.20.2251

Calculate#

`defineBasis`(n, l, j, mj, nMin, nMax, maxL[, ...])	Initializes basis of states around state of interest
`diagonalise`(eFieldList[, drivingFromState, ...])	Finds atom eigenstates in a given electric field

Analyse#

`getPolarizability`([maxField, showPlot, ...])	Returns the polarizability of the state (set during the initalization process).
`getState`(state, electricField, minN, maxN, maxL)	Returns basis states and coefficients that make up for a given electric field the eigenstate with largest contribution of the original state.
`exportData`(fileBase[, exportFormat])	Exports StarkMap calculation data.

Visualise#

`plotLevelDiagram`([units, highlightState, ...])	Makes a plot of a stark map of energy levels
`showPlot`([interactive])	Shows plot made by `plotLevelDiagram`
`savePlot`([filename])	Saves plot made by `plotLevelDiagram`

Attributes#

Internal variables of the class. This is for low-level access to intermediate results (low level API).

`s`	spin manifold in which we are working default value of 0.5 is correct for Alkaline Atoms.
`y`	y[i] is an array of eigenValues corresponding to the energies of the atom states at the electric field eFieldList[i].
`ax`	pointer towards matplotlib figure axis after `plotLevelDiagram` is called to create figure
`fig`	pointer towards matplotlib figure after `plotLevelDiagram` is called to create figure
`mat1`	diagonal elements of Stark-matrix (detuning of states) calculated by `defineBasis` in the basis `basisStates`.
`mat2`	off-diagonal elements of Stark-matrix divided by electric field value. To get off diagonal elemements multiply this matrix with electric field value. Full Stark matrix is obtained as fullStarkMatrix = `mat1` + `mat2` *eField. Calculated by `defineBasis` in the basis `basisStates`.
`basisStates`	List of basis states for calculation in the form [ [n,l,j,mj], ...].
`eFieldList`	Saves electric field (in units of V/m) for which energy levels are calculated
`highlight`	highlight[i] is an array of values measuring highlighted feature in the eigenstates at electric field intensity eFieldList[i].
`indexOfCoupledState`	Index of coupled state (initial state passed to `defineBasis`) in `basisStates` list of basis states