Metadata-Version: 2.4
Name: sqzcomb
Version: 0.4.0
Summary: Squeezed light in Kerr microcombs: Lugiato-Lefever steady states, linearized quantum noise, and detected output spectra
Author-email: "Tanvir M. Mahim" <tanvir.mahim@bracu.ac.bd>
License: Apache-2.0
Project-URL: Homepage, https://tanvir-mahmud-mahim.github.io/software/
Project-URL: Repository, https://github.com/TaN-MM-Org/sqzcomb
Project-URL: Issues, https://github.com/TaN-MM-Org/sqzcomb/issues
Project-URL: Changelog, https://github.com/TaN-MM-Org/sqzcomb/releases
Keywords: squeezed light,microcomb,Kerr,Lugiato-Lefever,quantum optics,homodyne
Classifier: Development Status :: 3 - Alpha
Classifier: Intended Audience :: Science/Research
Classifier: License :: OSI Approved :: Apache Software License
Classifier: Programming Language :: Python :: 3
Classifier: Topic :: Scientific/Engineering :: Physics
Requires-Python: >=3.9
Description-Content-Type: text/markdown
License-File: LICENSE
Requires-Dist: numpy>=1.22
Provides-Extra: test
Requires-Dist: pytest; extra == "test"
Provides-Extra: interop
Requires-Dist: qutip>=4.7; extra == "interop"
Dynamic: license-file

# sqzcomb

[![PyPI](https://img.shields.io/pypi/v/sqzcomb)](https://pypi.org/project/sqzcomb/) [![DOI](https://img.shields.io/badge/DOI-10.5281%2Fzenodo.22015375-blue)](https://doi.org/10.5281/zenodo.22015375) [![tests](https://github.com/TaN-MM-Org/sqzcomb/actions/workflows/ci.yml/badge.svg)](https://github.com/TaN-MM-Org/sqzcomb/actions)

Squeezed light in Kerr microcombs, computed **end to end**: from the
classical Lugiato-Lefever steady state, through the linearized quantum
fluctuations around it, to the **output quadrature-noise spectrum a
homodyne detector would report**. The package exists because intracavity
squeezing is not the observable; what leaves the extraction port is, and
the coupling that maximizes one does not maximize the other.

## Status

v0.4.0 (alpha). Implemented and tested:

- Lugiato-Lefever solver (Strang splitting; the Kerr step and the
  linear-plus-pump step are each exact)
- homogeneous steady states against the exact cubic
- linearized fluctuation (Bogoliubov) matrix around an arbitrary steady
  state, with a stability guard that refuses above-threshold states
- input-output quadrature spectra with an extraction port and intrinsic
  loss; single-mode and joint two-mode quadratures
- **photonic molecule (new in v0.2)**: the two-ring coupled-mode model
  (`photonic_molecule`), per-mode-coupling output spectra
  (`output_variance_ports`), and the exact instability threshold
  (`molecule_threshold`)
- **multimode comb molecule (new in v0.3)**: every retained comb line of
  the LLE fluctuation matrix coupled to a matching auxiliary-ring mode
  (`molecule_fluctuation_matrix`), with multi-line bus detection and
  joint twin-beam quadratures through the auxiliary ring
- **Gaussian-state interop (new in v0.4)**: steady-state covariance
  matrices of the intracavity Gaussian state (`intracavity_covariance`,
  numpy-only Lyapunov solve), export in the standard xxpp quadrature
  ordering with an explicit hbar convention (`covariance_xxpp`, vacuum
  exactly the identity at hbar = 2), Williamson symplectic spectra
  (`symplectic_eigenvalues`), and a QuTiP adapter (`drift_from_qutip`)
  that turns any quadratic QuTiP Hamiltonian into a drift matrix this
  package's spectra machinery accepts, refusing non-quadratic
  Hamiltonians rather than silently linearizing them. Install
  `sqzcomb[interop]` for the adapter; its test asserts that the released
  two-ring molecule is reproduced exactly from a QuTiP Hamiltonian.

Verified against closed forms in the test-suite: vacuum passes a passive
cavity, and a passive molecule, unchanged for every coupling, port and
frequency; the degenerate parametric oscillator output spectrum is
reproduced to 1e-10; and the textbook result that detectable squeezing
saturates at 3 dB at critical coupling, while full extraction breaks that
limit, emerges from the machinery rather than being asserted.

For the molecule, the test-suite additionally asserts: exact reduction to
the single ring at zero coupling; passive supermodes split by exactly 2J;
the resonant threshold mu = 1 + J^2/gamma (static branch, Hopf branch
1 + gamma beyond J = gamma); the quarter-turn quadrature rotation of the
-iJ hop; the exact zero-frequency equivalence of the auxiliary-ring port
to an effective single mode with escape efficiency
(J^2/gamma)/(1 + J^2/gamma); and a J^2/gamma = 3 molecule reaching 6 dB
detected squeezing through the auxiliary port although the Kerr ring
itself has no extraction port, which is the molecule extraction mechanism
in its simplest form.

For the multimode molecule, the asserts continue in the same spirit: at
one retained line the builder equals the released two-ring matrix to
machine precision; at zero coupling it reduces exactly to the plain
fluctuation matrix and the v0.1 spectra, single-line and twin-beam; a
passive multimode molecule returns exact vacuum through any bus; the
resonant auxiliary ring at zero frequency is exactly the single ring with
J^2/gamma_b extra loss per line and the quarter-turn rotation; and when
J^2/gamma_b exceeds one, twin-beam squeezing detected through the
auxiliary bus is strictly deeper than through the main bus of the same
device. The stability guard is also asserted to refuse a flat state that
is above a pair's modulational-instability threshold once the molecule's
added loss is removed.

Not yet implemented (the v0.4+ roadmap, in order): soliton-crystal
steady-state continuation, supermode decomposition of the multimode
covariance, and thermal input noise.

## Install and use

```
pip install sqzcomb
```

For development, clone the repository and `pip install -e .[test]`.

```python
import numpy as np
from sqzcomb import (lle_evolve, fluctuation_matrix,
                     output_quadrature_variance, squeezing_db)

# steady state at pump F and detuning alpha, anomalous dispersion d2
psi = lle_evolve(np.full(256, 0.05 + 0j), F=1.2, alpha=0.8,
                 dispersion=(-0.02,), t_end=300.0)

M, modes = fluctuation_matrix(psi, alpha=0.8, dispersion=(-0.02,))
i0 = int(np.where(modes == 0)[0][0])
v = output_quadrature_variance(M, eta=0.5, omega=0.0,
                               mode_index=i0, n_modes=modes.size)
print(squeezing_db(v), "dB relative to vacuum")
```

Units are the standard normalized LLE units: time in photon lifetimes,
eta = kappa_ex / kappa, vacuum variance 1/2.

## Methodological basis

> T. M. Mahim, M. M. Rahman and A. S. M. Mohsin, "Overcoming the 3 dB
> squeezing extraction limit in silicon carbide microcombs with a
> photonic molecule" (under review); code for the paper:
> https://github.com/Tanvir-Mahmud-Mahim/sic-molecule-squeezer

This package is the general-purpose engine; the paper repository
reproduces the specific published study. v0.2 adds the two-mode photonic
molecule, the extraction mechanism in its simplest form; the paper's full
multimode comb molecule remains in the paper repository.

## License

Apache-2.0
