MaxwellBloch Documentation

MaxwellBloch is a Python package for solving the coupled Maxwell-Bloch equations describing the nonlinear propagation of near-resonant light through thermal quantised systems such as atomic vapours.

Propagation of a 4π pulse through a dense atomic vapour. The pulse immediately breaks up on entering the medium and the resultant pulses form two optical solitons each with a pulse area of 2π.

MaxwellBloch is used for theoretical research, for modelling experiments and for undergraduate and graduate teaching.

MaxwellBloch can model two, three or many-level systems with physical effects including:

• Inhomogeneous broadening due to spontaneous decay,

• Doppler broadening in thermal systems,

• Collision dephasing,

• Sub-level structure.

Modules are also available for:

• Generating hyperfine structure for alkali atoms with the correct channels and angular momentum factors for coupling and decay,

• Specral analysis,

• Plotting and animating solutions.

Some phenomena that can be demonstrated:

• Linear absorption and dispersion,

• Fast light,

• Slow light,

• Electromagnetically Induced Transparency (EIT),

• Storage and Retrieval of Light pulses,

• Self-Induced Transparency (SIT) and Optical Solitons,

• Matched Pulses and Simultons,

• Hyperfine Pumping.

See the Examples section below for details.

Installation

• Installing MaxwellBloch

Usage

• Getting Started with the Two-Level Atom
  • Defining the Field and Atom
  • Solving the Maxwell-Bloch Equations
  • Plotting and Analysing Results
  • Defining the System with JSON
  • Spontaneous Decay
  • Using a Natural Unit System
  • Shifting to the Fixed Frame of Reference
• Three-Level Atoms
  • Ladder (Ξ) Configuration
  • Lambda (Λ)
  • Vee (V)
• Structure and Angular Momentum
  • Adding Structure
  • Hyperfine Structure for Single (Outer) Electron Atoms
  • Note on Stength Factors
• Spectral Analysis
  • Results in the Time Domain
  • Results in the Frequency Domain
  • Comparing with Analytic Results
• Velocity Classes for Modelling Doppler Broadening in Thermal Systems
  • Results in the Time Domain
  • Results in the Frequency Domain
  • Adding Inner Steps
• Built-in Time Functions
  • Gaussian
  • Square
  • Ramp On
  • Ramp Off
  • Ramp On and Off
  • Ramp Off and On
  • Sech
  • Sinc
  • Combining Time Functions
• Scripts for Making Movies
  • make-fixed-frame-mp4.py
  • make-ffmpeg-gif.sh

Examples

• Two-level
  • Weak Gaussian Pulses
    • Two-Level: Weak Pulse through Few Atoms
    • Two-Level: Weak Pulse
    • Two-Level: Weak Pulse through More Atoms
    • Two-Level: Weak Pulse with Decay
    • Two-Level: Weak Pulse through More Atoms with Decay
  • Weak Continuous (CW)
    • Two-Level: Weak CW with Decay
    • Two-Level: Weak CW through More Atoms with Decay
  • Weak Square Pulses
    • Two-Level: Weak Square Pulse with Decay
  • Solitons
    • Two-Level: Gaussian Pulse 0.8π
    • Two-Level: Gaussian Pulse 1.8π
    • Two-Level: Sech Pulse 2π — Self-Induced Transparency
    • Two-Level: Sech Pulse 4π — Pulse Breakup
    • Two-Level: Sech Pulse 6π — Pulse Breakup
    • Two-Level: Collision of Two 2π Pulses
• Three-level
  • Λ Configuration
    • Λ-Type Three-Level: Weak Pulse, No Coupling
    • Λ-Type Three-Level: Weak Pulse, With Coupling
    • Λ-Type Three-Level: Weak Pulse with Coupling in a Cloud — Pulse Compression
    • Λ-Type Three-Level: Weak Pulse with Time-Dependent Coupling in a Cloud — Storage and Retrieval
  • V Configuration
    • V-Type Three-Level: 0.5π Sech Pulse, 0.5π Coupling
    • V-Type Three-Level: 0.5π Sech Pulse, 1.5π Coupling — Simulton Propagation
    • V-Type Three-Level: √2π Sech Pulse, √2π Coupling
    • V-Type Three-Level: √8π Sech Pulse, √8π Coupling
    • V-Type Three-Level: √18π Sech Pulse, √18π Coupling
    • V-Type Three-Level: Solitons form Simulton
    • V-Type Three-Level: Weak CW, √2π Coupling: Optical Surfer
    • V-Type Three-Level: Weak CW, √4π Coupling: Double Optical Surfer
  • Ladder (Ξ) Configuration
    • Ladder-Type Three-Level: Weak Pulse with Coupling — EIT
• Structure
  • Rb 87 5s12 5p12
    • Hyperfine Structure: Weak Pulse, q=1, Decay — Optical Pumping
    • Hyperfine Structure: Sech Pulse 2π, q=1 — Self-Induced Transparency

Support

• Troubleshooting