This is proof-of-concept code for the paper, which can be obtained at https://arxiv.org/pdf/1907.07734.pdf.
The algorithm is entirely located in NLSolve.jl. Starting with the
matrix mu
for the transition dipole moments in the eigenbasis, the vector of
eigenenergies e0
and the initial density matrix rho0
, you can compute a
nonlinear response using,
include("NLSolve.jl")
include("GaussianField.jl")
# initialize state
y0 = NLSolve.steady_state(rho0 , T)
# make an evaluator for the Green's function
ħ = 0.6582119514
G! = NLSolve.make_G!(e0, ħ=ħ)
# make a pump field
w0 = wpump
sigma = fwhm2sigma(FWHMpump)
et, ew = make_gaussian_field(1.0, w0, sigma)
wmin = w0-4*sigma
wmax = w0+4*sigma
pump = NLSolve.Interaction([wmin], [wmax], [ew], [false])
cpump = NLSolve.compile_interaction(pump + conj(pump), y0)
# Compute first order
y1 = NLSolve.V!(y0, mu, ħ=ħ)
y1 = NLSolve.E(y1, cpump)
y1 = G!(y1)
# Compute second order
y2 = NLSolve.V!(y1, mu, ħ=ħ)
y2 = NLSolve.E(y2, cpump)
y2 = G!(y2)
# Save the density matrix at time times[i] in output[:,:,i]
NLSolve.at_t!(output[:,:,i], y2, times[i])
The code in this repo is extremely rough, as is often the case when produced by a finishing PhD student… It should be taken more as a guide on how to implement the method than as a working program.
To run the scaling analysis shown in Figs. 1-3, execute the script lambda_system.jl using
julia lambda_system.jl
This will produce the data required to make the graphs, which can be processed as described below. You’ll need a bunch of RAM (24 Gb or so) to run the final scaling analysis.
To produce the pyrazine spectroscopic experiments shown in Figs. 4-6, you need to first build the requisite Hamiltonian using
julia pyr2_build.jl
Then, compute the spectroscopic experiments using
julia pyrazine_spectra.jl
This code will compute linear, TA and CARS spectra.
To reproduce the plots of the paper from these results, use
julia process_outputs.jl
which will compile the data from the .jld
files into HDF5 for plotting with
python. The python plots can be generated using
python graphs.py
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