# deer_3p_hard_deer.m

Three-pulse DEER pulse sequence. Idealized hard pulses are used, each pulse only affects its specific electron or transition, depending on the pulse operators supplied.

## Syntax

    deer=deer_3p_hard_deer(spin_system,parameters,H,R,K)


## Arguments

  parameters.rho0            initial state

parameters.coil_prob       detection state on probe spin

parameters.stepsize        increment time for the pump pulse
sandwich

parameters.nsteps          number of steps for the pump pulse
sandwich

parameters.ex_prob         excitation operators to be used for
parameters.ex_pump         the probe and pump electron respec-
tively.

parameters.output          'brief' returns just the DEER trace,
'detailed' also returns excitation
profiles and the EPR spectrum.

H  - Hamiltonian matrix, received from context function

R  - relaxation superoperator, received from context function

K  - kinetics superoperator, received from context function


If 'detailed' is selected as the output option, the following parameters are also required:

  parameters.ex_hard          hard pulse excitation operator

parameters.spectrum_sweep   sweep width of the EPR spectrum, Hz

parameters.spectrum_nsteps  number of time steps in the FID

parameters.coil_pump        detection state on pump spin


## Outputs

  deer.hard_pulse_fid  - ('detailed') free induction decay
after a non-selective ideal pulse

deer.prob_pulse_fid  - ('detailed') free induction decay
after just the the probe pulse

deer.pump_pulse_fid  - ('detailed') free induction decay
after just the pump pulse

deer.deer_trace      - DEER signal


## Examples

A simulation of a system with two Gd(III) ions, probe transition at the edge of the spectrum and pump transition at the centre of the spectrum (examples/esr_solids/hard_3_pulse_deer_gd_2.m), is shown below.

The "noise" comes from incomplete spherical averaging.

## Notes

Hard pulses are only appropriate for spin-1/2 systems; for higher spin systems transition selective pulse operators must be supplied - see the example set.