zftrip.m

Projection of the zero-field triplet state with user-specified populations of Cartesian ZFS eigenstates onto the higher-field ZFS + Zeeman eigenstates. This is commonly seen in triplet DNP with photo-generated two-electron triplets.

Syntax

   rho=zftrip(spin_system,ZFS,pops,Z,B,idx)

Parameters

   spin_system - Spinach spin system object

   ZFS         - 3x3 ZFS tensor (Hz) in the laboratory frame of reference;
                 use zfs2mat() to get it from D, E, and molecular Euler angles

   pops        - populations of X, Y, and Z eigenstates of the ZFS tensor at zero field [pX pY pZ]

   Z           - 3x3 Zeeman interaction tensor (Hz/Tesla) in the laboratory
                 frame of reference; use functions like axrh2mat() to get it
                 from eigenvalues and molecular Euler angles

   B           - magnetic field along the laboratory Z axis, Tesla

   idx         - index of the electron triplet, using 'E3', in the sys.isotopes list

Outputs

   rho         - spin density matrix (Hilbert space) or state vector (Liouville space)

Notes

X, Y, and Z in pops are labelled using the organic triplet convention |Dzz|>|Dxx|>|Dyy|, under which D and E have opposite signs, -1/3<E/D<0 (C.P. Poole, H.A. Farach, W.K. Jackson, J. Chem. Phys. 61, 2220 (1974), DOI: 10.1063/1.1682294). Populations quoted in the transition metal convention |Dzz|>|Dyy|>|Dxx| with 0<E/D<1/3 must have their X and Y entries swapped before the call. At E=0 the X and Y states are degenerate (all three when D=0 as well) and the labelling within the degenerate set is undefined. At E/D=-1/3 the X and Z energies are opposite in sign, not degenerate, but equal in magnitude, so the sort by |energy| cannot tell X from Z. In both cases the affected populations must be equal for the result to be meaningful.

See also

deut_pair.m, equilibrium.m, four_spin_states.m, partner_state.m, singlet.m, state.m, triplet.m, Kernel_functions

Version 2.11, authors: Guinevere Mathies, Ilya Kuprov