Theoretical Foundations & Computation

Quantum Analysis

Rigorous mathematical modeling for nonlinear crystal phase-matching using spontaneous parametric down-conversion (SPDC).

01 / ARCHITECTURE

Quantum Analysis Dashboard Mechanics

SPDC State Modeling

The SPDC simulator models the generation of non-classical entangled photon pairs through Spontaneous Parametric Down-Conversion (SPDC) in aperiodically poled nonlinear crystals such as Lithium Niobate (LiNbO₃) and Lithum Tantalate (LiTaO₃). By adjusting crystal temperature, poling period profiles, and pump parameters, we can evaluate spectral and spatical correlations and quantum interference.

Computational Pipeline: Parameter Input to Quantum Observables Engine v0.1
STEP 01
Sellmeier Dispersion
Calculates refractive indices n(λ, T) for a given crystal temperature.
STEP 02
Quasi-Phase Matching
Computes poling period grating Λ(z) along crystal length
STEP 03
Biphoton Wavefunction
Integrates phase matching amplitude with pump envelope function to evaluate the Joint Spectral Amplitude Φ(ωₛ, ωᵢ).
STEP 04
Two-Photon Interference
Calculates Hong-Ou-Mandel (HOM) temporal dips and joint temporal intensity distributions via Fourier transforms.
Input Controls Simulator Sidebar Mapping

Parameter Control Effects

Sidebar Control Physical Meaning Observable Impact
Local Period Crystal spatial modulation Define the type of spatial modulation applied to the crystal. Periodic, polynomial or Chirp
Crystal Physical Characteristics Tune crystal temperature, material, length and material.
Pump Physical Characteristics Tune the pump wavelength for a CW plane wave
Compensation Fabrication compensation Some manufactures wont have a theoretical precision, but we can modelate several fabrication design compensation
Spatial Modulation and Compensation Formulas

Spatial Modulation

The spatial modulation dictates which wavelengths are going to be available for convertion Λ(z). The ones available right now are periodic (periodically polled crystals), polynomial and Chirp.

Λ(z) = a + bz^n
a and b are constants that are obtained by defining the initial period (per_ini) and the final period (per_fin) on the crystal. n is the exponent of the polynomial modulation.
Λ(z) = k_g + D(z -z_0)
k_g is defined as 2π/λ_p and matches a periodically poled crystal, D is a chirp parameter (1/(um * m)) can be positive or negative and z_0 defines a spatial translation of the chirp

Compensation

The spatial modulation can be implemented using photolitography and special equipment. The grating mask can have limited resolution.

Δ_1 and Δ_2
1 implies that the photolitographic process can create grating resolution of 0.1 um, i.e. can create a grating between 17.1 um and 17.2 um. The delta number 2 implies greater resolution of 0.01 um on the fabrication process, i.e. can create a grating between 17.1 um and 17.11 um.

The 5 Diagnostic Curves Explained

Each plot generated in the simulation provides a specific lens into the spatial, spectral, or temporal coherence of the emitted state:

CDS
Phase Tuning Curve
Wavelength vs. local poling period. Plots signal (pink) and idler (cyan) branches showing phase matching branches and degeneracy points.
Local Periods
Domain Grating Profile
Local poling period (μm) as a function of crystal length (mm). Compares theoretical target (teo) against compensated fabrication steps (comp).
JTI
Joint Temporal Intensity
Normalized coincidence amplitude vs. photon arrival time difference Δt (fs). Measures temporal correlation and wavepacket dispersion.
JSI
Joint Spectral Intensity
Normalized spectral amplitude |Φ(ω_s, ω_i)|² across emission wavelengths. Crucial for verifying purity and spectral unentanglement.
HOM
Hong-Ou-Mandel Dip
Coincidence count vs. relative optical delay (fs) across a 50:50 beam splitter.