sqtom - Squeezed state tomography in Python

This repository implements the mode tomography ideas presented in

"Full statistical mode reconstruction of a light field via a photon-number-resolved measurement" by Burenkov. et al. Phys. Rev. A 95, 053806 (2017) and in Burenkov et al. in J. Res. Natl. Inst. Stan. 122, 30 (2017).

for twin beam light and extends it to degenerate squeezed light. By leveraging lmfit we can also give a number of uncertainty estimates, and moreover provide routines for thresholding photon-number measurements and useful heuristics for initial guesses for the solutions of the problem.

Contents

The main physical ideal used by Burenkov et al. is to model the joint photon distribution of the variables associated to the photon numbers in signal and idler beams as resulting from one or several lossy two-mode squeezed distributions hitting the detectors. To model dark counts they also allow for modes prepared in states with Poisson statistics to hit the detectors.

To obtain the joint probability distribution of the photon numbers in the signal and idlers one needs to convolve the probability distributions of the modes entering in the problem.

Requirements

• SciPy to calculate probability distributions of Poisson, Geometric or Negative Binomial random variables.

• NumPy to perform 2D convolutions and matrix manipulations.

• The Walrus to calculate loss matrices and squeezed states probability distributions.

With the tools described so far we can solve the forward problem, i.e., given a set of physical parameters what is the probability distribution.

• If we augment our tools with lmfit we can solve the inverse problem: to find the best set of parameters that explain a given observed frequency distribution of photon numbers.

Finally, we use pytest for testing.

All of these prerequisites can be installed via pip:

pip install sqtom

Author

Nicolas Quesada

License

This source code is free and open source, released under the Apache License, Version 2.0.