OneFManifold

class OneFManifold(atom, n, l, j, f)

Bases: AtomManifold

OneFManifold single-\(F\) hyperfine manifold (\(M_F\)).

Examples:

% Example1: Construct a specific F-manifold and get Zeeman Hamiltonian
alk = Alkali("Rubidium87");
Fg  = totalAngularMomentum(1/2, alk.I);
mani = OneFManifold(alk, alk.groundStateN, 0, 1/2, max(Fg));
B   = MagneticField(bias=[0;0;1e-4]);
Ha  = mani.HamiltonianAtom();

Constructor Summary

OneFManifold(atom, n, l, j, f)

Construct a OneFManifold.

Parameters:

• atom (Atom) – Atom context

• n (int32) – Principal quantum number

• l (int32) – Orbital angular momentum \(L\)

• j (double) – Total electronic angular momentum \(J\)

• f (double) – Hyperfine \(F\)

Property Summary

Energy double

Hyperfine energy shift [Hz]

F double

Total hyperfine angular momentum \(F\)

FOperator

Spin operators \(F_{x,y,z}\) (cell)

J double

Total electronic angular momentum \(J\)

L int32

Orbital angular momentum \(L\)

LandegF double

Landé \(g_F\)

LandegJ double

Landé \(g_J\)

MF double

Magnetic sublevel \(M_F\)

N int32

Principal quantum number

StateList table

Table of basis states and properties

Method Summary

HamiltonianAtom(fRot)

Diagonal Hamiltonian including rotating-frame shift for excited states.

Parameters:

fRot (double optional) – Rotation-frame frequency [Hz]

Returns:

Hamiltonian matrix [Hz]

Return type:

double

\[H_a = \operatorname{diag}\big(E - f_\mathrm{rot}\,\chi_\mathrm{exc}\big)\]

where \(\chi_\mathrm{exc}\) is 1 on excited states and 0 on ground states.