Optimal Waveforms for Dipole Moment Estimation with Coherent States:

This code can be used to reproduce results in https://arxiv.org/abs/2509.09807

Code Organization:

The repository is organized into five folders:

1. Figure2_3_4_standard_pulses
   Contains Python code for computing the quantum Fisher information (QFI) of all standard pulses. This code can be used to reproduce Figures 3, 4, and 6. It also includes routines for optimizing the pulse width as a function of the average photon number.

2. Figure4_optimization_real_harmonics
   Provides Python code for optimizing the QFI of an arbitrary real pulse expressed in a harmonic basis, for a given width, as a function of the average photon number. This code can be used to reproduce Figure 5.

3. Figure5_optimization_real_hermite_gaussian
   Extends the above optimization to the Hermite-Gaussian basis, ensuring that no optimal pulse is missed. This code can be used to reproduce Figure 7.

4. Optimization_complex_pulses
   Contains code for optimization in the complex harmonics basis.

5. Long_width_limit
   Provides code that compares the QFI of a coherent state in the long-width limit with that of the single-photon pulse.

Citing:

If you find this code useful in your research, please consider citing our paper:

@article{chinni2025optimal,
  title={Optimal Waveforms for Dipole Moment Estimation with Coherent States},
  author={Chinni, Karthik and Quesada, Nicol{\'a}s},
  journal={arXiv preprint arXiv:2509.09807},
  year={2025}
}

Funding:

Funding for our work has been provided by

• Ministère de l'Économie et de l’Innovation du Québec,
• Natural Sciences and Engineering Research Council of Canada,
• Fonds de recherche du Québec-Nature et technologies (FRQNT) under the Programme PBEEE / Bourses de stage postdoctoral