tanerture / floquet_dynamics

Implementation of Floquet Dynamics for open and closed systems

Floquet Dynamics

This repository contains code that uses recently derived Magnus Expansion propagators for the time evolution of a lambda system. Because the time evolution is periodic, the dynamics can be sped up exponentially similar to the average Hamiltonian theory or Floquet-Magnus expansion. However, our method has the additional benefit of including the intraperiod motion. For theory and general description of the system, see the corresponding submitted paper.

File Structure

Producing Data

The three .py files beginning with data (data_dynamics.py, data_wp.py, data_parallel_3D.py) are scripts to run the dynamics and store either steady state values or the dynamical data. Files can be run by using python data_dynamics.py or python3 data_dynamics.py. The data is stored as binary files in the Data folder. These binary files are required to produce the plots, as described in the next section.

The most time consuming calculations are in data_parallel_3D.py; to reduce the computational time, the code is written to perform calculations in parallel.

Making Plots

Plots are made using the corresponding .py file that begin with plotting: (plotting_dynamics.py, plotting_wp.py, data_parallel_3D.py). Any of these can be run by using python plotting_dynamics.py or python3 data_dynamics.py

Helper Files

The code concerning the Magnus Expansion propagators can be found in Magnus_Expansion.py. The system parameters are defined in ME_params.py. Other commonly used functions for the dynamics (such as taking advantage of the Floquet time evolution, or transformation to the rotating frame) are defined in dynamics_functions.py. Helper functions for making the plots can be found in plotting_functions.py.

Code Convention

The density operator in the code has the convention $|1\rangle$ as the excited state, $|2\rangle$ as the state coupled by the control pulse $\omega_c$, and $|3\rangle$ as the state coupled by the probe pulse $\omega_p$. This is a less used convention, and different from the main paper. These differences are summarized in the following table.

Code	Paper
$|1\rangle$	$|2\rangle$
$|2\rangle$	$|3\rangle$
$|3\rangle$	$|1\rangle$