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




     parameters.pulse_frq  - frequencies for the three 
                             pulses, Hz

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

     parameters.pulse_dur  - durations for the three
                             pulses, seconds

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

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

     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

     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 p2_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_3_pulse_deer_2e.m example file) is to look at how the pulses affect the system:

Pulse effect.png

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

Deer echo stack.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.png Deer trace.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_deer.m, deer_4p_soft_hole.m, deer_4p_soft_diag.m, deer_3p_soft_hole.m, deer_3p_soft_diag.m

Version 2.4, authors: Ilya Kuprov