Two-level

Linear Absorption & Beer-Lambert Law

Weak probe pulses and continuous-wave fields in a two-level absorber. Demonstrates Beer-Lambert attenuation, the role of spontaneous decay, and how increasing optical depth reshapes the transmitted pulse.

• 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
• Two-Level: Weak CW with Decay
• Two-Level: Weak CW through More Atoms with Decay
• Two-Level: Weak Square Pulse with Decay

Self-Induced Transparency & Optical Solitons

Strong resonant pulses whose area exceeds π can form area-conserving solitons via self-induced transparency (McCall–Hahn). 2π solitons propagate without loss; larger areas break up into multiple 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

Area Theorem: Odd-π Instability

Odd multiples of π are unstable fixed points of the area theorem — a pulse entering at 1π, 3π, or 5π reshapes as it propagates.

• Two-Level: Odd-π Sech Pulses — Area Theorem

Photon Echo & Coherence Time ($T_2$) Measurement

A π/2 pulse followed by a π pulse creates a photon echo at $t = +tau$ in an inhomogeneously broadened (Doppler-broadened) medium. The echo amplitude decays as $e^{-2tau/T_2}$, allowing the homogeneous coherence time $T_2$ to be measured even when the lineshape is dominated by inhomogeneous broadening.

• Two-Level: Two-Pulse Photon Echo