Dicke Narrowing and Line Broadening in Atomic Spectra: Diffusion, Collisions, and Two-Photon Transitions

Overview

MIT OpenCourseWare presents a lecture on line shapes in atomic spectroscopy, emphasizing Dicke narrowing, collisional broadening, diffusion, and two-photon transitions. The talk blends intuitive pictures with a diffusion formalism to connect collisions with spectral linewidths and discusses the spectrum of emitted light and pressure broadening.

Overview

In this lecture from MIT OpenCourseWare, the instructor surveys line shifts and line broadening in atomic systems, highlighting that collisions can narrow lines in addition to broadening them, a phenomenon known as Dicke narrowing. The session connects these effects to broader topics such as buffer-gas traps, mean free paths, coherence times, and the diffusion of trapped atoms. The talk then extends to two related topics in line shapes and line broadening, including the spectrum of emitted light and an introduction to collisional broadening.

Dicke Narrowing and the Diffusion Picture

The lecturer revisits the idea that tightly trapped atoms display a carrier at the excitation frequency with sidebands at the trap frequency, which become smeared when the trap is not well defined. With buffer gas, the particle experiences random collisions, effectively creating an ensemble of traps with varying frequencies. The central question is how to estimate the linewidth of the carrier in this diffusive regime. A key insight is that the coherence time is governed by the mean free path relative to the optical wavelength. If the mean free path is shorter than a wavelength, the atom remains coherent during many collisions, leading to Dicke narrowing. Conversely, when the mean free path exceeds a wavelength, normal Doppler broadening dominates.

Quantitative Formalism: Diffusion and Line Shapes

The lecture introduces a correlation function approach: the line shape equals the Fourier transform of the correlation function of the driving field as experienced by a diffusing atom. The diffusion process is modeled as a random walk with a Gaussian probability distribution for the displacement, yielding an ensemble average that results in an exponentially decaying correlation function. When transformed, this produces a Lorentzian line shape, with a width proportional to K^2 times the diffusion constant D. In the ideal gas limit, the diffusion constant is related to the mean thermal speed and mean free path, leading to a Dicke-narrowing width that scales as K^2 D. The discussion emphasizes that the Doppler width is tied to the momentum spread, while Dicke narrowing arises from collisional randomization and diffusion, not just single-particle motion.

Line Shape Debate: Lorentzian Core and Pedestal

The instructor motivates a conceptual debate between two pictures: a ballistic first-collision model and a diffusive model with a broad pedestal from unresolved sidebands. Both pictures are reconciled by recognizing that in the many-sideband regime the envelope can resemble the Doppler profile, while the central peak remains Lorentzian due to diffusion. The analysis also highlights the limits of the models, noting that the diffusion propagator is valid after the first collision, whereas free motion prior to that can introduce a small Doppler component. The outcome is a consistent picture where Dicke narrowing arises from confined, colliding motion, while residual Doppler effects populate the wings.

Spectrum of Emitted Light and Two-Photon Excitation

The talk then transitions to the spectrum of emitted light after excitation. In the weak-field limit, the central feature is a Lorentzian or a power-broadened Lorentzian, and the emission spectrum can be understood through a two-photon perspective where the incoming and outgoing photons are considered as part of a two-photon process. The speaker discusses the role of two-photon transitions, intermediate virtual states, and rotating wave approximations. He emphasizes that even in a one-photon intuitive picture, a two-photon framework offers a more complete description of light scattering and emission, particularly when the driving field strength approaches or exceeds the natural linewidth.

Pressure Broadening, Collisions, and Microscopic Picture

The final sections cover pressure broadening as a collision-induced effect that adds a broadening rate to the natural linewidth. Two microscopic pictures are presented: (i) knockout collisions that deactivate the excitation, and (ii) phase interruptions where collisions impart random phase jumps to the oscillator. The discussion connects these ideas to how the interaction potential between the active atom and buffer gas modifies the resonance, especially in cold collisions where a single partial wave description may suffice. The wings of the spectral line can reveal details of the molecular potential between the colliding partners, while the central line broadening reflects the collision rate. The lecturer situates these ideas in the context of cold-atom experiments where environment-induced collisions are minimized, and contact with molecular potentials becomes a measure of the interaction landscape.

Two-Photon Excitation: A Bridge to New Regimes

Closing the discussion, the instructor motivates two-photon processes as a natural extension when the laser power is increased or when transitions require bridging large energy gaps with photons of accessible frequencies. A two-photon framework invoked through two driving fields with frequencies Omega1 and Omega2 provides a mechanism to excite otherwise forbidden one-photon transitions. The discussion includes a brief outline of the perturbative calculation, the role of an intermediate virtual state, and the fact that two-photon absorption can be viewed as a two-step process within the dipole approximation. The talk foreshadows more detailed treatment in subsequent lectures and highlights the Doppler-free spectroscopy potential when counterpropagating beams are used.

Takeaway

The lecture provides a coherent picture linking collisional dynamics, diffusion, and line broadening in atomic systems, while offering intuitive and formal tools to understand the spectrum of emitted light and the possibilities of two-photon excitation. It emphasizes the central role of coherence time, mean free path, and diffusion in shaping line shapes, and it frames two-photon processes as a powerful framework for both excitation and spectroscopy in regimes beyond simple one-photon perturbation theory.