Coherent Control in Three-Level Quantum Systems: Dark States, EIT, and Lasing Without Inversion

MIT OpenCourseWare presents a deep dive into coherence phenomena in three-level quantum systems, focusing on the dark state created when two lasers drive transitions to a common excited state. The talk outlines coherent population trapping, adiabatic transfer (STIRAP), and how a dark state can enable lasing without inversion, followed by a conceptual and qualitative treatment of electromagnetically induced transparency (EIT). Realistic realizations such as hydrogen in an external field and laser dressing of states are discussed, along with the potential for slow light and quantum information storage. This short overview captures the core ideas and their significance for light-mmatter interaction in atomic systems.

Introduction

The lecture examines coherence in a three-level (lambda) system, emphasizing the dark state that arises when two laser fields couple the two ground states to a common excited state. This dark state is a coherent superposition that does not scatter light, enabling robust control of atomic populations even as laser parameters vary.

Dark State and Coherent Population Transfer

The instructor discusses how adiabatic evolution preserves the system in the dark state, a principle behind coherent population transfer and the STIRAP method. This section also covers the concept of a bright and a dark state in the driven three-level Hamiltonian, and how the dark state's identity can shift with changing laser amplitudes.

Lasing Without Inversion

The talk describes lasing without inversion, where destructive interference in absorption allows gain without a conventional population inversion. Two practical realizations are outlined: a hydrogen atom dressed by static or AC fields, and driven systems where a strong control laser creates a dressed state structure that hides population in a dark state while permitting stimulated emission.

Electromagnetically Induced Transparency (EIT)

The core EIT picture is introduced, showing how the interference between excitation pathways creates a narrow transparency window within an otherwise absorbing medium. The width of the EIT feature scales with the coupling laser Rabi frequency, and the effect can dramatically alter the medium's refractive index, enabling slow light and enhanced nonlinearities without absorption.

Interference, Spectra, and Applications

Several qualitative and semi-quantitative pictures are presented, including how detuning and Raman resonances shape the absorption profile and dispersion. The lecturer connects these ideas to practical applications in nonlinear optics, sensitive spectroscopy, and quantum information storage, culminating in a broader view of how dark states and coherence underpin modern light-matter physics.