sqzcomb

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

v0.1.0 (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

Verified against closed forms in the test-suite: vacuum passes a passive cavity unchanged for every coupling 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.

Not yet implemented (the v0.2+ roadmap, in order): the auxiliary-ring photonic molecule and its Purcell extraction of below-threshold modes, soliton-crystal steady-state continuation, supermode decomposition of the multimode covariance, and thermal input noise.

Install and use

pip install -e .

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, including the photonic-molecule extraction that this package's v0.1 does not yet contain.

License

Apache-2.0