TwoJManifoldDivalent

TwoJManifoldDivalent#

class TwoJManifoldDivalent(atom, nG, lG, jG, sG, nE, lE, jE, sE)#

Bases: AtomManifold

TwoJManifoldDivalent divalent transition manifolds (\(J_g\rightarrow J_e\), with \(S\)).

Provides transition frequency, natural linewidth, reduced dipole matrix element, reduced saturation intensity, and Doppler temperature for divalent-like transitions (with spin \(S\)).

Examples:

% Example1: Build a blue-line-like manifold (divalent)
at = Divalent("Strontium88");
M  = TwoJManifoldDivalent(at, nG=5, lG=0, jG=0, sG=0, ...
                             nE=5, lE=1, jE=1, sE=1);
Isat = M.ReducedSaturationIntensity;
Constructor Summary
TwoJManifoldDivalent(atom, nG, lG, jG, sG, nE, lE, jE, sE)#

Construct a TwoJManifoldDivalent.

Parameters:

  • atom (Atom) – Atom context

  • nG (int32) – Ground principal quantum number

  • lG (int32) – Ground \(L\)

  • jG (double) – Ground \(J\)

  • sG (double) – Ground spin \(S\)

  • nE (int32) – Excited principal quantum number

  • lE (int32) – Excited \(L\)

  • jE (double) – Excited \(J\)

  • sE (double) – Excited spin \(S\)

Property Summary
DopplerTemperature double#

Doppler temperature [K]

EnergyExcited double#

HFSCoefficientExcited %[A,B]

EnergyGround double#

HFSCoefficientGround %[A,B]

IOperator cell#

Nuclear spin operators

JExcited double#

Excited \(J\)

JGround double#

Ground \(J\)

JOperator cell#

Electronic spin operators

LExcited int32#

Excited \(L\)

LGround int32#

Ground \(L\)

LandegFExcited double#

Excited Landé \(g_F\) (if applicable)

LandegFGround double#

Ground Landé \(g_F\) (if applicable)

LandegJExcited double#

Excited Landé \(g_J\)

LandegJGround double#

Ground Landé \(g_J\)

LifetimeExcited double#

Excited-state lifetime [s]

MJExcited double#

FExcited double

MJGround double#

FGround double

NExcited int32#

Excited principal quantum number

NGround int32#

Ground principal quantum number

NaturalLinewidth double#

FOperator cell

ReducedDipoleMatrixElement double#

\(\langle J_g\Vert d\Vert J_e\rangle\) [C·m]

ReducedSaturationIntensity double#

Reduced Isat [W/m^2]

ReducedSaturationIntensityLu double#

Reduced Isat [mW/cm^2]

SExcited#

Excited spin \(S\)

SGround double#

Ground spin \(S\)

StateList table#

State table (if constructed)

Method Summary
BiasDressedStateList(B, isPlot, options)#

Compute dressed states versus bias field and assemble blocks.

Parameters:

  • B (MagneticField) – Magnetic field

  • isPlot (logical, optional) – Plot results

  • samplingSize (double, optional) – Number of bias samples

Returns:

Dressed state table, unitary U, and branch map

Return type:

table, double, cell

DipoleMatrixElement(fG, mfG, fE, mfE, q, U)#

Dipole matrix element \(\langle f_G,m_F^G| d_q | f_E,m_F^E\rangle\) [C·m].

Selection rule: \(m_F^E + q = m_F^G\). Sign of \(q\) follows Steck-like convention.

\[m_F^E = m_F^G + q\]
Parameters:

  • fG (double) – Ground \(F\)

  • mfG (double) – Ground \(M_F\)

  • fE (double) – Excited \(F'\)

  • mfE (double) – Excited \(M_F'\)

  • q (double) – Spherical component (\(-1,0,+1\))

  • U (double, optional) – Basis transform

Returns:

Dipole matrix element [C·m]

Return type:

double

DipoleMatrixElementNu(fG, mfG, fE, mfE, q, U)#

Dipole matrix element normalized by reduced DME.

\[d_\nu = \frac{\langle f_G m_F^G | d_q | f_E m_F^E \rangle}{\langle J_G \Vert d \Vert J_E \rangle}\]
Returns:

Dimensionless ratio

Return type:

double

HamiltonianAtom(fRot, U)#

Diagonal Hamiltonian with rotating-frame shift on excited states.

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

  • fRot (double, optional) – Rotating-frame frequency [Hz]

  • U (double, optional) – Basis transform

Returns:

Hamiltonian matrix [Hz]

Return type:

double

HamiltonianAtomBiasField(B, U)#

Zeeman Hamiltonian from OneJManifold blocks.

\[H_Z = U^\dagger \, \mathrm{blkdiag}\big(H_Z^{(e)}, H_Z^{(g)}\big) \, U\]

where each block uses \(H_Z = \mu_B ( g_J \mathbf{J} + g_I \mathbf{I} )\cdot\mathbf{B} / h\).

Parameters:

  • B (MagneticField) – Magnetic field object

  • U (double, optional) – Basis transform

Returns:

Hamiltonian matrix [Hz]

Return type:

double

HamiltonianAtomLaser(laser, fRot, U)#

Atom-light interaction Hamiltonian \(H_\mathrm{AL}(t)\).

\[H_{\mathrm{AL}}(t) = \sum_{q=-1}^{+1} \frac{\Omega^*}{2}\, e_q\, \Sigma_q\, e^{i\Delta t} + \mathrm{h.c.}\]
Parameters:

  • laser (Laser) – Driving field

  • fRot (double, optional) – Rotating-frame frequency [Hz]

  • U (double, optional) – Basis transform

Returns:

Function handle H(r,t) [Hz]

Return type:

function_handle

LoweringOperator(q, U)#

Spherical lowering operator (Steck Eq. 7.407 analogue).

\[\Sigma_q = \sum_{g,e} |g\rangle\langle e|\, d_\nu(g\leftarrow e;q)\]
ReducedRabiFrequency(laser)#

Reduced Rabi frequency for linearly polarized light.

\[\Omega = -\sqrt{\frac{I}{2 I_{\mathrm{sat}}^{(\mathrm{red})}}}\, \Gamma\]
Parameters:

laser (Laser) – Driving field

Returns:

\(\Omega\) [Hz]

Return type:

double

SaturationIntensity(fG, mfG, fE, mfE, U)#

Saturation intensity for specified sublevels.

\[I_{\mathrm{sat}} = \frac{I_{\mathrm{sat}}^{(\mathrm{red})}}{|d_\nu|^2}\]
Returns:

\(I_{sat}\) [W/m^2]

Return type:

double

getMIMJ()#

Compute \((M_I,M_J)\) labels by adiabatic mapping.

Returns:

Table of MI, MJ per basis state

Return type:

table