cchandre / OCDM

Optical Centrifuge for Diatomic Molecules

OCDM

Optical Centrifuge for Diatomic Molecules (OCDM) - codes for the chlorine molecule Cl₂

• ocdm_dict.py: to be edited to change the parameters of the OCDM computation (see below for a dictionary of parameters)

• ocdm.py: contains the DiaMol class and main functions defining the OCDM dynamics (for Cl₂)

• ocdm_modules.py: contains the methods to integrate the OCDM dynamics

• read_DiaMol_dissocation.m: MATLAB script to produce the dissociation probability figure from the output files DiaMol_dissociation.txt

• read_DiaMol_trajectories.m: MATLAB script to plot the trajectories from the output files DiaMol.mat

• read_DiaMol_pphi.m: MATLAB script to plot the distributions of p_φ values from the output files DiaMol.mat

Once ocdm_dict.py has been edited with the relevant parameters, run the file as

python3 ocdm.py

or

nohup python3 -u ocdm.py &>ocdm.out < /dev/null &

The list of Python packages and their version are specified in requirements.txt. The code is using NumPy, SciPy, SymPy and Matplotlib.

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Parameter dictionary

• Method: string
  • 'plot_potentials': plot the potential ε(r) and polarizabilities α(r)
  • 'plot_ZVS': plot zero velocity functions
  • 'dissociation': computes the dissociation probability as a function of the amplitude F₀ of the electric field
  • 'trajectories': computes and displays the trajectories according to type_traj
  • 'poincaré'; Poincaré section is φ=0 (mod 2 π) with φ'<0 in the plane (r,p_r) if EventPS='phi', and p_r =0 with p_r'<0 in the plane (φ,p_φ) if EventPS='phi'
• dimension: 2 or 3; dimension of the computation
• F0: float or array of floats; amplitude(s) F₀ of the electric field, E(t) = F₀ f(t) [e_x cosΦ(t) + e_y sinΦ(t)] cosωt, considered in the computation (atomic units)
• Omega: lambda function; values of the frequency of rotation of the polarisation axis, Ω=Φ'(t), as a function of time (atomic units)
• envelope: string ('const', 'sinus', 'trapez'); envelope function f(t) of the laser field
• te: array of 3 or 4 floats; duration of ramp-up, plateau, ramp-down and (optional) after pulse (in picoseconds)
• Ntraj: integer; number of trajectories to be integrated
• r: array of two floats; minimum and maximum values of r for the display of potentials, and range of r (atomic units) for the selection of initial conditions
• initial_conditions: string or array of floats;
  • ['microcanonical', E₀] for a microcanonical distribution with energy E₀
  • ['microcanonical_J', n, J] for a microcanonical distribution with initial energy E₀ = ω_e (n+1/2) + B_e J(J+1)-D_e
  • array of shape (Ntraj, 2dimension) containing the initial conditions to be integrated
• spread3D: float; between 0 and 1; spread in angle theta for the initial conditions (only in the 3D case)
• TimePS: float; time (in picoseconds) at which the Poincaré section is computed (adiabatic approximation)
• EnergyPS: float; initial value of the energy (in atomic units) used in Method='poincaré'
• EventPS: string; 'phi' or 'pr'; choice of Poincaré section; Poincaré section is φ=0 (mod 2 π) with φ'<0 in the plane (r,p_r) if EventPS='phi', and p_r =0 with p_r'<0 in the plane (φ,p_φ) if EventPS='phi'
• ode_solver: string; 'RK45', 'RK23', 'DOP853', 'Radau', 'BDF', 'LSODA', 'Verlet', 'BM4'; method for the integration of trajectories
  • 'RK45', 'RK23', 'DOP853', 'Radau', 'BDF', 'LSODA': (non-symplectic, variable time step); see ivp_solve for more details
  • 'Verlet': Strang splitting or symplectic leap-frog integrator (symplectic, fixed time step, order 2); see Wikipedia for more details
  • 'BM4' or 'BM6': BM₆4 or BM₁₀6 (symplectic, fixed time step, order 4 or 6) from Blanes, Moan, J. Comput. Appl. Math. 142, 313 (2002)
  • NB: For Poincaré sections, ode_solver = 'RK45' by default
• ode_tol: array of two floats; absolute and relative tolerances [atol, rtol] for variable time-step integrators; see ivp_solve for more details
• ode_step: float; time step (in picoseconds) for the symplectic integrators 'Verlet' and 'BM4'
• r_thresh: float; threshold for the integration of trajectories; the integration is stopped whenever the distance r is larger than r_thresh
• frame: string; 'fixed' or 'rotating'; specifies in which frame the numerical integration is performed
• type_traj: array of 3 strings; ['all' or 'dissociated' or 'bounded', 'cartesian' or 'spherical', 'fixed' or 'rotating'] for the type of trajectories to be plotted and/or saved
• dpi: integer; dpi value for the figures

• SaveData: boolean; if True, the results are saved in a .mat file (with the type specified in 'type_traj'); if Method='dissociation', the trajectories are saved at t=0, t=t_u, t=t_u+t_p and t=t_u+t_p+t_d; if Method='trajectories', the trajectories are saved with 'dpi' equispaced times from t=0 to t=t_u+t_p+t_d; NB: the dissociation probabilities are saved in a .txt file regardless of the value of SaveData
• PlotResults: boolean; if True, the results (for 'plot_potentials', 'plot_ZVS' and 'trajectories') are plotted right after the computation (with the type specified in 'type_traj' for 'trajectories')
• Parallelization: int or string; int is the number of cores to be used, 'all' for all of the cores
• darkmode: boolean; if True, plots are done in dark mode

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Reference:

• C. Chandre, J. Pablo Salas, Nonlinear dynamics of molecular super-rotors, Physical Review A 107, 063105 (2023); arXiv:2303.05090

@article{PhysRevA.107.063105,
  title = {Nonlinear dynamics of molecular superrotors},
  author = {Chandre, C. and Salas, J. Pablo},
  journal = {Phys. Rev. A},
  volume = {107},
  issue = {6},
  pages = {063105},
  numpages = {12},
  year = {2023},
  month = {Jun},
  publisher = {American Physical Society},
  doi = {10.1103/PhysRevA.107.063105},
  url = {https://link.aps.org/doi/10.1103/PhysRevA.107.063105}
}

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