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




     parameters.pulse_frq  - frequencies for the four 
                             pulses, Hz

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

     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.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.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


  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


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_deer.m, deer_4p_soft_hole.m, deer_3p_soft_deer.m, deer_3p_soft_hole.m, deer_3p_soft_diag.m

Version 2.4, authors: Ilya Kuprov