Coherence in Three-Level Quantum Systems: Dark States, STIRAP, and Lasing Without Inversion

In this MIT OpenCourseWare lecture, the instructor introduces coherence in three-level quantum systems, showing how interference between two excitation pathways creates dark states and enables phenomena such as coherent population trapping, electromagnetically induced transparency, and enhanced light propagation. The talk then moves to robust population transfer methods, including stimulated Raman adiabatic passage (STIRAP), which uses a dark state to move population between ground states without populating the excited state. The presentation also discusses lasing without inversion, two-photon Raman transitions, and practical realizations in atoms and alkali systems, highlighting the tradeoffs between coherence time, laser power, and experimental imperfections.

Overview

The lecture introduces coherence in three-level quantum systems consisting of two ground states and one excited state. The two optical fields provide two pathways to the excited state with Rabi frequencies Omega1 and Omega2. Because the two pathways can interfere, a coherent superposition of the ground states can be formed that does not couple to the excited state, creating a dark state. This underpins phenomena such as coherent population trapping and electromagnetically induced transparency, where sharp spectral features and large changes in dispersion enable control of light propagation.

Dark and Bright States

By constructing a basis of dark and bright states, the instructor shows how the dark state is immune to excitation, while the bright state couples strongly to the excited level. Spontaneous emission from the bright state can populate either ground state, while the dark state remains unpopulated by the light field. This framework generalizes optical pumping and explains conditions under which population can be trapped without true population inversion.

Two-Photon Resonance and Raman Processes

The two-photon (Raman) resonance condition is essential: the difference between the two laser frequencies matches the energy splitting of the two ground states. If this condition is satisfied, the dark state remains well defined, and the system can undergo robust population transfer without excitation under certain conditions. The instructor emphasizes that the phase relationship between lasers and atomic states matters, and detuning or phase drift can convert the dark state into a bright state over time.

Stimulated Raman Adiabatic Passage (STIRAP)

STIRAP uses a counterintuitive pulse sequence to move population from one ground state to the other via the dark state. With orange and green pulses applied in the proper order, the dark state becomes the final state, keeping the excited-state population minimal. The transfer is adiabatic if the laser parameters change slowly relative to the system dynamics, which makes the process highly robust to many experimental imperfections. The speaker discusses intuitive versus counterintuitive sequencing and explains why the dark-state picture makes STIRAP seem almost magical, though a small excited-state population is still required to effect the transfer physically.

Coherent vs Incoherent Transfer and Practical Considerations

A central point is that coherent transfer can outperform incoherent methods because the integrated excited-state population scales inversely with the transfer time or inversely with the square of the Rabi frequency, depending on the model. The lecture compares STIRAP to two-photon Raman transitions, noting that both rely on coherence and both are limited by coherence time and laser stability. An incoherent scheme that uses sequential pi-pulses scatters more, or at least as much, into unwanted states if the process is not fully isolated, highlighting the practical advantages of coherent population transfer schemes.

Lasing Without Inversion and Dark Resonances

The talk then turns to lasing without inversion (LWI) and how quantum interference can suppress absorption while leaving stimulated emission intact, enabling gain without population inversion. A simple three-level lambda scheme can exhibit a dark resonance where absorption is canceled, and a cavity can provide a gain channel through a weakly populated excited state. The speaker sketches real-world realizations, including hydrogen in a DC field that creates indistinguishable excitation pathways, and discusses the role of dressed states and AC Stark shifts that position the dark state as the lowest energy state under certain conditions.

Experimental Realizations and Takeaways

Hydrogen in a DC electric field and alkali atoms dressed by light are proposed as accessible laboratories for observing dark resonances and LWI. The lecturer stresses the importance of avoiding unwanted laser fluctuations, maintaining phase coherence, and ensuring Raman detuning remains within the transfer time window set by coherence. The discussion closes with reflections on how these concepts form a coherent framework for three-level quantum systems, tying dark states, CPT, EIT, STIRAP, Raman processes, and LWI into a unified picture governed by interference, adiabaticity, and coherence.