Wigner Function in Quantum Optics

MATLAB scripts to calculate and plot Wigner quasiprobability and Q-Husimi distributions for any quantum state in Coherent or Fock basis.

https://github.com/Filippos-Dakis/Wigner-Function-Quantum-Optics

Version 1.2.4.1 (3 MB)
227 Downloads
(3)
11 Jun 2024

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Filippos Tzimkas-Dakis Virginia Tech February 2024
All the scripts were developed on MATLAB 2023a (compatible with MATLAB 2022b or later)
( Find the Python version here : https://github.com/Filippos-Dakis/Quantum-Optics-Lab )
This file contains two main scripts:
  • CoherentBasis.m
  • FockBasis.m
which define two types of classes. The first one, CoherentBasis.m , refers to Coherent states basis of Qunatum Harmonic Oscillator (QHO), while the second, FockBasis.m, refers to the number/Fock states of QHO.
The file also includes four examples
  • CoherentBasis_Example_1.m
  • FockBasis_Example_1.m
  • Q_function_CoherentBasis_Example.m
  • Q_function_FockBasis_Example.m
  • Example_Squeezed_states.m
that help the user explore the features of the two main classes.
The key feature of these two classes (CoherentBasis, and FockBasis) is the calculation of the Wigner Quasi-Probability distribution and the Q-Husimi Distributions for any given state! However, they also include other useful features such as quantum state addition, normalization, Displacement and Squeezing operations, annihilation and creation operators etc.
For instance, CoherentBasis_Example_1.m produces the following Wigner Quasi-Probability distributions
and FockBasis_Example_1.m produces these three Wigner Distributions
This is the very first version and I intend to incorporate more features. Some of them are
  • density matrix
  • quantum Zeno gate for Cat-qubits
  • switch between the two bases (connect the two classes somehow)
Suggested textbooks:
  • Exploring the Quantum Atoms, Cavities and Photons. Serge Haroche Jean-Michel Raimond
  • Introductory Quantum Optics. Christopher Gerry Peter Knight
I am open to other suggestion. Please feel free to contact me at dakisfilippos@vt.edu .
If you found my code useful, please cite is as https://github.com/Filippos-Dakis/Wigner-Function-Quantum-Optics
Any feedback and suggestions are much appreciated!
More features are comming... Stay tuned!!

Cite As

Filippos Dakis (2026). Wigner Function in Quantum Optics (https://www.mathworks.com/matlabcentral/fileexchange/155617-wigner-function-in-quantum-optics), MATLAB Central File Exchange. Retrieved .

General Information

MATLAB Release Compatibility

  • Compatible with R2022b to R2024a

Platform Compatibility

  • Windows
  • macOS
  • Linux
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Version Published Release Notes
1.2.4.1

Found and corrected a mistake in the Squeeze operator

1.2.4.0

Found and corrected a mistake in the Squeeze operator

1.2.3.0

Reorganized the folders, added some features in the classes and extended the examples.
1.2.2.1

Tested the scripts in MATLAB 2022b and they run smoothly.
1.2.2

- Annihilation and Creation operators were added as methods in the two classes, along with applications in the respective examples.
- Squeeze operator was added in FockBasis.m class.
- Squeeze example was introduced as Example_Squeezed_states.m
1.2.1

Calculation of Q-Husimi function was added in the two classes.

1.2

-FockBasis.m : I have changed the way I compute the Displacement operator in the Fock basis. The Displacment matrix is calculated much faster.
- FockBasis_Example_1.m: The above update shortened the execution time of this example by 70%.
1.1

I have added more comments in the scripts and fixed a small bug in FockBasis.m
1.0.0

See release notes for this release on GitHub: https://github.com/Filippos-Dakis/Wigner-Function-Quantum-Optics/releases/tag/v1.0.0
See release notes for this release on GitHub: https://github.com/Filippos-Dakis/Wigner-Function-Quantum-Optics/releases/tag/v1.0.0