# deer_3p_soft_diag.m

Complete set of simulations related to three-pulse DEER. Runs pulse diagnostics, which is followed by echo diagnostics, which is followed by DEER simulation.

## Syntax

    deer_3p_soft_diag(spin_system,parameters)


## Arguments

     parameters.pulse_frq  - frequencies for the three
pulses, Hz

parameters.pulse_pwr  - power levels for the three
pulses, Hz

parameters.pulse_dur  - durations for the three
pulses, seconds

parameters.pulse_phi  - initial phases for the three

parameters.pulse_rnk  - Fokker-Planck ranks for the
three pulses

parameters.offset     - receiver offset for the time
domain detection, Hz

parameters.sweep      - sweep width for time domain
detection, Hz

parameters.npoints    - number of points in the free
induction decay

parameters.rho0       - initial state

parameters.coil       - detection state

parameters.p1_p3_gap  - time between the first and the
third pulses, seconds

parameters.p2_nsteps  - number of second pulse posi-
tions in the interval between
the first and the third pulse

parameters.echo_time  - time to sample around the ex-
pected echo position

parameters.echo_npts  - number of points in the echo
discretization

parameters.method     - soft puse propagation method,
'expv' for Krylov propagation,
'expm' for exponential propa-
gation, 'evolution' for Spin-
ach evolution function

parameters.assumptions - Hamiltonian generation assump-
tions, use 'deer' to keep two-
electron flip-flop terms and
'deer-zz' to drop them


## Outputs

  Figure 1: pulse diagnostics
Figure 2: DEER echo stack
Figure 3: principal components of the stack, echo
Figure 4: principal components of the stack, DEER


## Examples

A number of complete examples for two- and three-electron systems are given in examples/esr_solids folder. A good way to proceed (soft_3_pulse_deer_2e.m example file) is to look at how the pulses affect the system:

then to inspect the echo stack as a function of the pump pulse position:

and finally to inspect the principal components of the echo stack. The most prominent component is the DEER trace, the other components come from the finite size of the spherical integration grid.

## Notes

1. For the method, start with 'expm', change to 'expv' if the calculation runs out of memory, and use 'evolution' as the last resort.
2. Simulated echoes tend to be sharp and hard to catch because simulation does not have distributions in experimental parameters. Fourier transforming the echo prior to integration is recommended.
3. The time in the DEER trace refers to the second pulse insertion point, after end of first pulse.