# deer_4p_soft_deer.m

Four-pulse DEER/PELDOR pulse sequence. The sequence uses soft pulses computed with the Fokker-Planck formalism.

## Syntax

    echo_stack=deer_4p_soft_deer(spin_system,parameters,H,R,K)


## Arguments

   parameters.pulse_frq  - frequencies for the four
pulses, Hz

parameters.pulse_pwr  - power levels for the four

parameters.pulse_dur  - durations for the four
pulses, seconds

parameters.pulse_phi  - initial phases for the four

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

parameters.p1_p2_gap  - time between the end of the
first and the start of the
second pulse, seconds

parameters.p2_p4_gap  - time between the end of the
second the start of the third
pulse, seconds

parameters.p3_nsteps  - number of third pulse posi-
tions in the interval between
the first echo and the fourth
pulse

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

parameters.echo_npts  - number of points in the second
echo discretization

parameters.rho0       - initial state

parameters.coil       - detection state

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

H  - Hamiltonian matrix, received from context function

R  - relaxation superoperator, received from context function

K  - kinetics superoperator, received from context function


## Outputs

   echo_stack  - DEER echo stack, a matrix with p3_nsteps echoes
with echo_npts points each


## 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_4_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.