arc.alkali_atom_data.Potassium41#

class Potassium41(preferQuantumDefects=True, cpp_numerov=True)[source]#

Properties of potassium 41 atoms

__init__(preferQuantumDefects=True, cpp_numerov=True)#

Methods

__init__([preferQuantumDefects, cpp_numerov])

breitRabi(n, l, j, B)

Returns exact Zeeman energies math:E_z for states

corePotential(l, r)

core potential felt by valence electron

effectiveCharge(l, r)

effective charge of the core felt by valence electron

getAverageInteratomicSpacing(temperature)

Returns average interatomic spacing in atomic vapour

getAverageSpeed(temperature)

Average (mean) speed at a given temperature

getBranchingRatio(jg, fg, mfg, je, fe, mfe)

Branching ratio for decay from \(\vert j_e,f_e,m_{f_e} \rangle \rightarrow \vert j_g,f_g,m_{f_g}\rangle\)

getBranchingRatioFStoFS(jg, mjg, je, mje[, s])

Branching ratio for decay from \(\vert j_e, m_{j_e} \rangle \rightarrow \vert j_g,m_{j_g} \rangle\)

getBranchingRatioFStoHFS(jg, fg, mfg, je, mje)

Branching ratio for decay from \(\vert j_e, m_{j_e} \rangle \rightarrow \vert j_g,f_g,m_{f_g} \rangle\)

getBranchingRatioHFStoFS(jg, mjg, je, fe, mfe)

Branching ratio for decay from \(\vert j_e,f_e,m_{f_e} \rangle \rightarrow \vert j_g,m_{j_g} \rangle\)

getC3term(n, l, j, n1, l1, j1, n2, l2, j2[, s])

C3 interaction term for the given two pair-states

getC6term(n, l, j, n1, l1, j1, n2, l2, j2[, s])

C6 interaction term for the given two pair-states

getDipoleMatrixElement(n1, l1, j1, mj1, n2, ...)

Dipole matrix element \(\langle n_1 l_1 j_1 m_{j_1} |e\mathbf{r}|\ n_2 l_2 j_2 m_{j_2}\rangle\) in units of \(a_0 e\)

getDipoleMatrixElementHFS(n1, l1, j1, f1, ...)

Dipole matrix element for hyperfine structure resolved transitions \(\langle n_1 l_1 j_1 f_1 m_{f_1} |e\mathbf{r}|\ n_2 l_2 j_2 f_2 m_{f_2}\rangle\) in units of \(a_0 e\)

getDipoleMatrixElementHFStoFS(n1, l1, j1, ...)

Dipole matrix element for transition from hyperfine resolved state to unresolved fine-structure state \(\langle n_1 l_1 j_1 f_1 m_{f_1} |e\mathbf{r}|\ n_2 l_2 j_2 m_{j_2}\rangle\) in units of \(a_0 e\)

getEnergy(n, l, j[, s])

Energy of the level relative to the ionisation level (in eV)

getEnergyDefect(n, l, j, n1, l1, j1, n2, l2, j2)

Energy defect for the given two pair-states (one of the state has two atoms in the same state)

getEnergyDefect2(n, l, j, nn, ll, jj, n1, ...)

Energy defect for the given two pair-states

getHFSCoefficients(n, l, j[, s])

Returns hyperfine splitting coefficients for state \(n\), \(l\), \(j\).

getHFSEnergyShift(j, f, A[, B, s])

Energy shift of HFS from centre of mass \(\Delta E_\mathrm{hfs}\)

getLandegf(l, j, f[, s])

Lande g-factor \(g_F\simeq g_J\frac{f(f+1)-I(I+1)+j(j+1)}{2f(f+1)}\)

getLandegfExact(l, j, f[, s])

Lande g-factor \(g_F\) \(g_F=g_J\frac{f(f+1)-I(I+1)+j(j+1)}{2f(f+1)}+g_I\frac{f(f+1)+I(I+1)-j(j+1)}{2f(f+1)}\)

getLandegj(l, j[, s])

Lande g-factor \(g_J\simeq 1+\frac{j(j+1)+s(s+1)-l(l+1)}{2j(j+1)}\)

getLandegjExact(l, j[, s])

Lande g-factor \(g_J=g_L\frac{j(j+1)-s(s+1)+l(l+1)}{2j(j+1)}+g_S\frac{j(j+1)+s(s+1)-l(l+1)}{2j(j+1)}\)

getLiteratureDME(n1, l1, j1, n2, l2, j2[, s])

Returns literature information on requested transition.

getMagneticDipoleMatrixElementHFS(l, j, f1, ...)

Magnetic dipole matrix element \(\langle f_1,m_{f_1} \vert \mu_q \vert f_2,m_{f_2}\rangle\) for transitions from \(\vert f_1,m_{f_1}\rangle\rightarrow\vert f_2,m_{f_2}\rangle\) within the same \(n,\ell,j\) state in units of \(\mu_B B_q\).

getNumberDensity(temperature)

Atom number density at given temperature

getPressure(temperature)

Pressure of atomic vapour at given temperature.

getQuadrupoleMatrixElement(n1, l1, j1, n2, ...)

Radial part of the quadrupole matrix element

getQuantumDefect(n, l, j[, s])

Quantum defect of the level.

getRabiFrequency(n1, l1, j1, mj1, n2, l2, ...)

Returns a Rabi frequency for resonantly driven atom in a center of TEM00 mode of a driving field

getRabiFrequency2(n1, l1, j1, mj1, n2, l2, ...)

Returns a Rabi frequency for resonant excitation with a given electric field amplitude

getRadialCoupling(n, l, j, n1, l1, j1[, s])

Returns radial part of the coupling between two states (dipole and quadrupole interactions only)

getRadialMatrixElement(n1, l1, j1, n2, l2, j2)

Radial part of the dipole matrix element

getReducedMatrixElementJ(n1, l1, j1, n2, l2, j2)

Reduced matrix element in \(J\) basis (symmetric notation)

getReducedMatrixElementJ_asymmetric(n1, l1, ...)

Reduced matrix element in \(J\) basis, defined in asymmetric notation.

getReducedMatrixElementL(n1, l1, j1, n2, l2, j2)

Reduced matrix element in \(L\) basis (symmetric notation)

getSaturationIntensity(ng, lg, jg, fg, mfg, ...)

Saturation Intensity \(I_\mathrm{sat}\) for transition \(\vert j_g,f_g,m_{f_g}\rangle\rightarrow\vert j_e,f_e,m_{f_e}\rangle\) in units of \(\mathrm{W}/\mathrm{m}^2\).

getSaturationIntensityIsotropic(ng, lg, jg, ...)

Isotropic Saturation Intensity \(I_\mathrm{sat}\) for transition \(f_g\rightarrow f_e\) averaged over all polarisations in units of \(\mathrm{W}/\mathrm{m}^2\).

getSphericalDipoleMatrixElement(j1, mj1, j2, ...)

Spherical Component of Angular Matrix Element

getSphericalMatrixElementHFStoFS(j1, f1, ...)

Spherical matrix element for transition from hyperfine resolved state to unresolved fine-structure state \(\langle f,m_f \vert\mu_q\vert j',m_j'\rangle\) in units of \(\langle j\vert\vert\mu\vert\vert j'\rangle\)

getStateLifetime(n, l, j[, temperature, ...])

Returns the lifetime of the state (in s)

getTransitionFrequency(n1, l1, j1, n2, l2, j2)

Calculated transition frequency in Hz

getTransitionRate(n1, l1, j1, n2, l2, j2[, ...])

Transition rate due to coupling to vacuum modes (black body included)

getTransitionWavelength(n1, l1, j1, n2, l2, j2)

Calculated transition wavelength (in vacuum) in m.

getZeemanEnergyShift(l, j, mj, magneticFieldBz)

Retuns linear (paramagnetic) Zeeman shift.

groundStateRamanTransition(Pa, wa, qa, Pb, ...)

Returns two-photon Rabi frequency \(\Omega_R\), differential AC Stark shift \(\Delta_\mathrm{AC}\) and probability to scatter a photon during a \(\pi\)-pulse \(P_\mathrm{sc}\) for two-photon ground-state Raman transitions from \(\vert f_g,m_{f_g}\rangle\rightarrow\vert nL_{j_r} j_r,m_{j_r}\rangle\) via an intermediate excited state \(n_e,\ell_e,j_e\).

potential(l, s, j, r)

returns total potential that electron feels

radialWavefunction(l, s, j, stateEnergy, ...)

Radial part of electron wavefunction

twoPhotonRydbergExcitation(Pp, wp, qp, Pc, ...)

Returns two-photon Rabi frequency \(\Omega_R\), ground AC Stark shift \(\Delta_{\mathrm{AC}_g}\), Rydberg state AC Stark shift \(\Delta_{\mathrm{AC}_r}\) and probability to scatter a photon during a \(\pi\)-pulse \(P_\mathrm{sc}\) for two-photon excitation from \(\vert f_h,m_{f_g}\rangle\rightarrow \vert j_r,m_{j_r}\rangle\) via intermediate excited state

updateDipoleMatrixElementsFile()

Updates the file with pre-calculated dipole matrix elements.

Attributes

I

Nuclear spin

NISTdataLevels

Z

Atomic number

a1

model potential parameters from [#c1]_

a2

model potential parameters from [#c1]_

a3

model potential parameters from [#c1]_

a4

model potential parameters from [#c1]_

abundance

source NIST, Atomic Weights and Isotopic Compositions [#c14]_

alpha

alphaC

model potential parameters from [#c1]_

cpp_numerov

swich - should the wavefunction be calculated with Numerov algorithm implemented in C++

dataFolder

dipoleMatrixElementFile

location of hard-disk stored dipole matrix elements

elementName

Human-readable element name

extraLevels

levels that are for smaller n than ground level, but are above in energy due to angular part

gI

Nuclear g-factor

gL

Electron Orbital g-factor

gS

groundStateN

principal quantum number for the ground state

hyperfineStructureData

source of HFS magnetic dipole and quadrupole constants

ionisationEnergy

(eV), weighted average of values in Ref.

levelDataFromNIST

location of stored NIST values of measured energy levels in eV

literatureDMEfilename

Filename of the additional literature source values of dipole matrix elements.

mass

source NIST, Atomic Weights and Isotopic Compositions [#c14]_

meltingPoint

in K

minQuantumDefectN

minimal quantum number for which quantum defects can be used; uses measured energy levels otherwise

precalculatedDB

preferQuantumDefects

quadrupoleMatrixElementFile

location of hard-disk stored dipole matrix elements

quantumDefect

quantum defects from Ref.

rc

model potential parameters from [#c1]_

sEnergy

state energies from NIST values sEnergy [n,l] = state energy for n, l, j = l-1/2 sEnergy [l,n] = state energy for j = l+1/2

scaledRydbergConstant

in eV