Examples¶
This project includes three representative notebooks that demonstrate correctness, physical consistency, and advanced modeling capabilities.
Each example is designed to highlight a distinct aspect of Gaussian open-system dynamics.
1. Validation: Two-Mode Squeezing under Thermal Loss¶
Notebook:
notebooks/01_validation_two_mode_squeezing_under_loss.ipynb
Repo Link:
Purpose¶
Establishes correctness of Gaussian state evolution under independent thermal dissipation.
Setup¶
Two-mode squeezed vacuum state
Independent Markovian environments
Variable thermal occupation \(\bar{n}\)
Key Results¶
Entanglement decays monotonically to zero
Higher \(\bar{n}\) accelerates disentanglement
Purity behavior distinguishes:
\(\bar{n} = 0\): transient mixing → recovery to pure vacuum
\(\bar{n} > 0\): monotonic decay → thermal steady state
What this demonstrates¶
Correct drift–diffusion implementation
Correct steady-state structure
Quantitative agreement with known Gaussian results
2. Collective Dissipation: Phase-Dependent Entanglement Generation¶
Notebook:
notebooks/02_markov_common_bath_baseline.ipynb
Repo Link:
Purpose¶
Demonstrates environment-induced entanglement and its dependence on squeezing phase.
Setup¶
Two separable single-mode squeezed states
Collective annihilation dissipator
Relative squeezing phase \(\Delta\phi\)
Key Results¶
Aligned squeezing (\(\Delta\phi = 0\)) → maximal steady entanglement
Partial misalignment → reduced entanglement
Orthogonal squeezing (\(\Delta\phi = \pi\)) → suppressed entanglement
What this demonstrates¶
Dissipation can generate entanglement from separable inputs
Squeezing phase controls coupling to dissipative structure
Existence of configurations with no entanglement generation
3. Finite-Memory Environments: OU Pseudomode Embedding¶
Notebook:
notebooks/03_ou_pseudomode_embedding_showcase.ipynb
Repo Link:
Purpose¶
Shows how finite environmental memory modifies Gaussian dynamics using an exact pseudomode embedding.
A. Resonant aligned squeezing¶
Setup
Resonant modes
Aligned squeezing
Comparison: Markov vs OU memory
Key Results
OU dynamics exhibit overshoot and damped oscillations in entanglement
Markov dynamics rapidly reach steady state
OU purity remains lower over long times due to persistent system–memory correlations
Interpretation
Finite memory reshapes the transient pathway to entanglement without eliminating the underlying steady-state mechanism.
B. Detuned orthogonal squeezing¶
Setup
Detuned modes
Orthogonal squeezing
Comparison: Markov vs OU memory
Key Results
Markov case remains effectively disentangled
OU dynamics generate repeated, decaying entanglement bursts
Purity indicates sustained mixing during memory-mediated exchange
Interpretation
Finite memory enables transient entanglement in configurations that are inactive in the Markovian limit.
Summary¶
These examples demonstrate:
Correct Gaussian open-system evolution
Phase-sensitive dissipative structure
Finite-memory effects beyond Markovian dynamics
Together, they provide a progression from validation to physically structured modeling.