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arXiv:0801.3660 · Physical Review A

Theory of thermal motion in electromagnetically induced transparency: Effects of diffusion, Doppler broadening, and Dicke and Ramsey narrowing

Ofer Firstenberg, M. Shuker, Rami Pugatch, Donald R. Fredkin, Nir Davidson, A. Ron

Published Apr 23, 2008• 63 citations
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Abstract

We present a theoretical model for electromagnetically induced transparency (EIT) in vapor that incorporates atomic motion and velocity-changing collisions into the dynamics of the density-matrix distribution. Within a unified formalism, we demonstrate various motional effects, known for EIT in vapor: Doppler broadening of the absorption spectrum; Dicke narrowing and time-of-flight broadening of the transmission window for a finite-sized probe; diffusion of atomic coherence during storage of light and diffusion of the light-matter excitation during slow-light propagation; and Ramsey narrowing of the spectrum for a probe and pump beams of finite size.

DOI
10.1103/physreva.77.043830

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We present a theoretical model for electromagnetically induced transparency (EIT) in vapor that incorporates atomic motion and velocity-changing collisions into the dynamics of the density-matrix distribution. Within a unified formalism, we demonstrate various motional effects, known for EIT in vapor: Doppler broadening of the absorption spectrum; Dicke narrowing and time-of-flight broadening of the transmission window for a finite-sized probe; diffusion of atomic coherence during storage of light and diffusion of the light-matter excitation during slow-light propagation; and Ramsey narrowing of the spectrum for a probe and pump beams of finite size.
We describe the effect of thermal motion and buffer-gas collisions on a four-level closed NNN system interacting with strong pump(s) and a weak probe. This is the simplest system that experiences electromagnetically induced absorption (EIA) due to transfer of coherence via spontaneous emission from the excited state to the ground state. We investigate the influence of Doppler broadening, velocity-changing collisions (VCC), and phase-changing collisions (PCC) with a buffer gas on the EIA spectrum of optically active atoms. In addition to exact expressions, we present an approximate solution for the probe absorption spectrum, which provides physical insight into the behavior of the EIA peak due to VCC, PCC, and the wave-vector difference between the pump and probe beams. VCC are shown to produce a wide pedestal at the base of the EIA peak, which is scarcely affected by the pump-probe angular deviation, whereas the sharp central EIA peak becomes weaker and broader due to the residual Doppler-Dicke effect. Using diffusionlike equations for the atomic coherences and populations, we construct a spatial-frequency filter for a spatially structured probe beam and show that Ramsey narrowing of the EIA peak is obtained for beams of finite width.
Dicke narrowing is a phenomenon that dramatically reduces the Doppler width of spectral lines, due to frequent velocity-changing collisions. A similar phenomenon occurs for electromagnetically induced transparency (EIT) resonances, and facilitates ultranarrow spectral features in room-temperature vapor. We directly measure the Dicke-like narrowing by studying EIT line shapes as a function of the angle between the pump and probe beams. The measurements are in good agreement with an analytic theory with no fit parameters. The results show that Dicke narrowing can increase substantially the tolerance of hot-vapor EIT to angular deviations. We demonstrate the importance of this effect for applications such as imaging and spatial solitons using a single-shot imaging experiment, and discuss the implications for the feasibility of storing images in atomic vapor.
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Electromagnetically induced transparency (EIT) can make an otherwise opaque medium transparent by utilizing quantum coherence. EIT has attracted great interest since the 1990s for its wide applications in metrology, nonlinear and quantum optics, and quantum information science. We present a review on spectral line narrowing mechanisms in EIT-related systems, accounting for linewidths much narrower than expected from the standard mechanisms of Doppler broadening, transit time broadening, magnetic field inhomogeneity and power broadening. Topics covered include Dicke narrowing, atomic-motion-induced Ramsey narrowing, motional narrowing, density narrowing, laser induced narrowing and power-broadening-free resonance. Intuitive pictures are provided to describe the essential physics of each mechanism.
We present a numerical scheme to study the dynamics of slow light and light storage in an electromagnetically-induced-transparency (EIT) medium at finite temperatures. Allowing for the motional coupling, we derive a set of coupled Schr\"odinger equations describing a boosted closed three-level EIT system according to the principle of Galilean relativity. The dynamics of a uniformly moving EIT medium can thus be determined by numerically integrating the coupled Schr\"odinger equations for atoms plus one ancillary Maxwell-Schr\"odinger equation for the probe pulse. The central idea of this work rests on the assumption that the loss of ground-state coherence at finite temperatures can be ascribed to the incoherent superposition of density matrices representing the EIT systems with various velocities. Close agreements are demonstrated in comparing the numerical results with the experimental data for both slow light and light storage. In particular, the distinct characters featuring the decay of ground-state coherence can be well verified for slow light and light storage. This warrants that the current scheme can be applied to determine the decaying profile of the ground-state coherence as well as the temperature of the EIT medium.