Physics Documentation

The following pages contain white-ups that explain the theoretical basis for the many operations performed by rydiqule.

Equations of Motion Generation

• Equations of Motion Generation
  • Hamiltonian and Rotating Wave Approximation
  • Equations of Motion
  • Removing the Ground State
  • Making the Equations Real

Stacking Conventions

• Stacking Conventions
  • Numpy arrays
  • Stacking
  • Parameter Ordering
  • Doppler

Observables

• Observables
  • Observable Derivation
  • Observable Validation

Doppler Averaging

• Doppler Averaging
  • Assumptions
  • Choosing Velocity Classes to Calculate
  • Maxwell-Boltzmann Distribution
  • Averaging Velocity Classes
  • Rydiqule’s Implementation
    • Migrating Doppler averaging from v1 to v2

Time-Dependence

• Time-Dependence
  • Time-Dependent Couplings
  • Rydiqule Coupling Parameters for Time dependence
  • Example Time-Dependencies
    • RF Heterodyne
    • Non-Rotating Frame
    • Frequency Sweep in the Rotating-Frame
    • Static Phase Offsets
    • Closed-Loops

Solving with Atomic Structure

• Atomic Structure Primer
  • Fine Structure without Magnetic Sublevels
  • Migrating Cell from v1 to v2
    • Original Rydiqule Behavior
    • Current Rydiqule Behavior
• Fine and Hyperfine Structure with Sublevels
  • Sublevels in Sensor
  • Sublevels in Cell
    • State Definition
    • Coherent Coupling Definition
    • Incoherent Coupling Definition
  • Dipole Matrix Element Definitions
    • NLJ
    • FS to FS
    • HFS to HFS
    • HFS to FS