arc.alkali_atom_data.Rubidium87#
- class Rubidium87(preferQuantumDefects=True, cpp_numerov=True)[source]#
Properites of rubidium 87 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 \(\vert F,m_f\rangle\) in the \(\ell,j\) manifold via exact diagonalisation of the Zeeman interaction \(\mathcal{H}_z\) and the hyperfine interaction \(\mathcal{H}_\mathrm{hfs}\) given by equations
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 \(\vert j_e,f_e,m_{f_e} \rangle \rightarrow \vert j_g,f_g,m_{f_g}\rangle\)
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, ...)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
INuclear spin
NISTdataLevelsZAtomic number
model potential parameters from [#c1]_
model potential parameters from [#c1]_
model potential parameters from [#c1]_
model potential parameters from [#c1]_
source NIST, Atomic Weights and Isotopic Compositions [#c14]_
alphamodel potential parameters from [#c1]_
cpp_numerovswich - should the wavefunction be calculated with Numerov algorithm implemented in C++
dataFolderdipoleMatrixElementFilelocation of hard-disk stored dipole matrix elements
elementNameHuman-readable element name
levels that are for smaller n than ground level, but are above in energy due to angular part
Nuclear g-factor [#Steck87Rb]_
Electron orbital g-factor [#Steck87Rb]_
gSgroundStateNprincipal quantum number for the ground state
source of HFS magnetic dipole and quadrupole constants
(eV) Ref.
levelDataFromNISTlocation of stored NIST values of measured energy levels in eV
literatureDMEfilenameFilename of the additional literature source values of dipole matrix elements.
source NIST, Atomic Weights and Isotopic Compositions [#c14]_
in K
minQuantumDefectNminimal quantum number for which quantum defects can be used; uses measured energy levels otherwise
precalculatedDBpreferQuantumDefectsquadrupoleMatrixElementFilelocation of hard-disk stored dipole matrix elements
quantum defects for \(nF\) states are from [#c5]_.
model potential parameters from [#c1]_
sEnergystate 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
in eV (M_ion core = m_atomic - m_electron)