Lindblad Modelling of a SQUID

Final Year Undergraduate Project

This repository contains code and notes related to the quantum modelling of a SQUID (Superconducting Quantum Interference Device) using the Lindblad master equation formalism. The project explores both steady-state and time-dependent dynamics under dissipative evolution.

Overview

The goal of this project is to simulate the quantum behavior of a SQUID in open systems, accounting for decoherence and dissipation using Lindblad operators. It covers:

1. Steady-State Analysis: Solving the Lindblad master equation to find the steady-state density matrix and observables.

2. Time-Dependent Dynamics: Simulating the transient evolution of the system under various initial conditions and external driving.

Key Features

1. Lindblad master equation solver using numerical integration
2. Support for custom Hamiltonians and dissipation channels
3. Visualization tools for density matrix evolution, expectation values, and coherence

Requirements

The project is written in Python. You will need the following libraries:

1. numpy
2. scipy
3. matplotlibq

File Structure

steady_state.py – Code for finding steady-state solutions

time_dynamics.py – Time evolution simulations

hamiltonian.py – Hamiltonian and Lindblad operator definitions

plots/ – Visualizations and figures used in the project

notes/ – Supplementary notes and derivations (if included)

Usage

Modify parameters in the scripts to explore different regimes (e.g., coupling strength, detuning, temperature). Each script is documented for clarity and reproducibility.

Acknowledgments

This work was completed as part of the final year undergraduate physics project. Thanks to Dr. Stephen Duffus for guidance and support.

License

Open for academic and non-commercial use.

Bachelors Thesis - https://drive.google.com/file/d/1w4NweHPtCMsxwigGp6w92vHLy93bRqcn/view?usp=sharing