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




   parameters.pulse_frq  - frequencies for the four 
                           pulses, Hz

   parameters.pulse_pwr  - power levels for the four
                           pulses, rad/s

   parameters.pulse_dur  - durations for the four
                           pulses, seconds

   parameters.pulse_phi  - initial phases for the four 
                           pulses, radians

   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

   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


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


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:

Pulse effect 4p.png

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

Deer echo stack 4p.png

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.

Deer echo 4p.png Deer trace 4p.png


  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.

See also

deer_3p_hard_echo.m, deer_3p_hard_deer.m, deer_analyt.m, eseem.m, oopeseem.m, deer_4p_soft_hole.m, deer_4p_soft_diag.m, deer_3p_soft_deer.m, deer_3p_soft_hole.m, deer_3p_soft_diag.m

Version 2.4, authors: Ilya Kuprov