Coherence in Quantum Systems: Spontaneous Emission, Phase Mapping, and Dark States | MIT OCW Lecture

Overview

This MIT OpenCourseWare lecture delves into coherence in quantum systems, starting from the idea that spontaneous emission is a unitary evolution with no intrinsic randomness. The instructor demonstrates how an excited atom prepared by a laser can have its quantum information mapped onto the emitted photon field, and how the phase of that field relates to the laser phase.

Key Concepts

The talk covers phase in two-level and multi-level atoms, measurement via homodyne detection, and the role of vacuum fluctuations in determining relative phases. It also introduces the idea that coherence can persist or be revealed through careful measurements, even when single-photon states carry large quantum fluctuations. The lecture then expands to three-level systems, dark states, and the phenomenon of electromagnetically induced transparency, highlighting how coherence can enable new optical effects such as slowing or stopping light without population inversion.

Coherence and Spontaneous Emission

The lecture begins with a reframing of spontaneous emission as a unitary process dictated by the Hamiltonian of the total system, showing that no intrinsic randomness is present in the time evolution. The instructor illustrates with a simple scenario: an atom in the ground state, a vacuum cavity, and a short laser pulse that prepares a coherent superposition of ground and excited states. In this setting the quantum information initially residing in the atom is mapped onto the photon field as the excited state decays. The phase imprinted by the laser appears in the superposition and can be extracted from the emitted light, but only as a relative phase between populated amplitudes, not from an overall phase factor.

Phase Measurement and Photon-Atom Mappings

Phase measurement of the emitted photon relies on a homodyne or beat experiment that interferes the emitted light with the local oscillator laser. The distribution of phase measurements depends on the population in the excited state; a fifty fifty superposition yields the most precise phase information, whereas a pure excited or ground state leads to large phase uncertainty. The Bloch vector picture reinforces this, showing the maximum phase definition when the coherence vector lies in the xy plane.

Single vs Ensemble Coherence and Vacuum Fluctuations

For a single photon or a single atom, phase measurements are intrinsically uncertain. In ensembles, repeated measurements average out randomness, reducing uncertainty, but vacuum fluctuations still seed randomness in the emitted field. The discussion also touches on how two atoms can share correlated vacuum fluctuations, potentially producing correlations in the emitted light and laying the groundwork for collective phenomena such as superradiance.

Coherence in Free Level Systems: Lambda and Beyond

The talk then shifts to three-level configurations, with emphasis on the Lambda type where two ground states couple to a shared excited state. Coherent driving can create dark states that suppress scattering, enabling effects like electromagnetically induced transparency (EIT). The speaker explains that such coherence can allow lasing without population inversion and can enable slow or stopped light, as well as quantum memories for quantum information processing.

Coherent Spectroscopy and Delay Detectors

Quantum beat spectroscopy and Ramsey-type delayed detection are presented as techniques to access sub-natural linewidths by exploiting phase information before or after long evolution times. The mathematics shows that delaying detection can sharpen spectral features at the cost of reduced signal, and Fourier analysis reveals how central peaks become narrower with increased delay, provided the phase information is preserved.

Closing and Transition to Multi-Level Coherence

The lecture closes by previewing coherence in more complex systems, including double-field driving in Lambda and ladder configurations, and hints at future topics like electromagnetically induced transparency and quantum memories as essential tools for quantum optics and quantum information science.