arc.alkali_atom_data.Hydrogen#

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

Properties of hydrogen 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)	Vapour pressure (in Pa) 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
`stateQuantumDefect`(n, l, j)
`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 fitted from experimental observations for different l (electron angular momentum)
`a2`	Model potential parameters fitted from experimental observations for different l (electron angular momentum)
`a3`	Model potential parameters fitted from experimental observations for different l (electron angular momentum)
`a4`	Model potential parameters fitted from experimental observations for different l (electron angular momentum)
`abundance`	relative isotope abundance
`alpha`
`alphaC`	Core polarizability
`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 principal quantum number (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`	file cotaining data on hyperfine structure (magnetic dipole A and magnetic quadrupole B constnats).
`ionisationEnergy`	(eV), 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`	melting point of the element at standard conditions
`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`	Contains list of modified Rydberg-Ritz coefficients for calculating quantum defects for [[ \(S_{1/2},P_{1/2},D_{3/2},F_{5/2}\)], [ \(S_{1/2},P_{3/2},D_{5/2},F_{7/2}\)]]."""
`rc`	Model potential parameters fitted from experimental observations for different l (electron angular momentum)
`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`