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arXiv:1107.0525 · Physical Review A

Effects of thermal motion on electromagnetically induced absorption

E. Tilchin, A. D. Wilson‐Gordon, Ofer Firstenberg

Published May 9, 2011• 6 citations
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Abstract

We describe the effect of thermal motion and buffer-gas collisions on a four-level closed $N$ 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.

DOI
10.1103/physreva.83.053812

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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.
The absorption spectrum of a weak probe, interacting with a driven degenerate two-level atomic system, whose ground and excited hyperfine states are Fg,e,{\mathrm{F}}_{g,e},Fg,e​, can exhibit narrow peaks at line center. When the pump and probe polarizations are different, Fe=Fg+1{F}_{e}{=F}_{g}+1Fe​=Fg​+1 and Fg>0,{F}_{g}>0,Fg​>0, the electromagnetically induced absorption (EIA) peak has been shown to be due to the transfer of coherence (TOC) between the excited and ground states via spontaneous decay. We give a detailed explanation of why the TOC that leads to EIA (EIA-TOC) can only take place when ground-state population trapping does not occur, that is, when Fe=Fg+1.{F}_{e}{=F}_{g}+1.Fe​=Fg​+1. We also explain why EIA-TOC is observed in open systems. We show that EIA can also occur when the pump and probe polarizations are identical and Fe=Fg+1.{F}_{e}{=F}_{g}+1.Fe​=Fg​+1. This EIA is analogous to an effect that occurs in simple two-level systems when the collisional transfer of population (TOP) from the ground state to a reservoir is greater than that from the excited state. For a degenerate two-level system, the reservoir consists of the Zeeman sublevels of the ground hyperfine state, and of other nearby hyperfine states that do not interact with the pump. We will also discuss the four-wave mixing spectrum under the conditions where EIA-TOC and EIA-TOP occur.
We predict the occurrence of electromagnetically induced absorption (EIA) in cycling degenerate two-level transitions where Fe=Fg+1{F}_{e}={F}_{g}+1Fe​=Fg​+1 and Fg>0{F}_{g}>0Fg​>0, interacting with pump and probe lasers with the same polarization. The EIA is due to transfer of population (TOP) between the Zeeman levels of the ground hyperfine state, rather than transfer of coherence (TOC) which occurs for perpendicularly polarized lasers. We model EIA-TOP using a double two-level system (TLS) which we compare with the four-level NNN system, which models EIA-TOC. When the pump intensity is low, both models give an EIA peak at line center. The effect of introducing phase-changing collisions is studied, in the presence and absence of Doppler broadening, for both the double TLS and NNN systems. In the presence of phase-changing collisions, the central EIA peaks are narrowed in both models and persist to higher pump Rabi frequencies than in the absence of collisions. In the double TLS, in the presence of Doppler broadening, the central EIA-TOP peak becomes narrower and does not develop a dip in its center, in contrast to the NNN system. The central dip that appears in the Doppler-broadened EIA-TOC spectrum can be wiped out by adding phase-changing collisions. We demonstrate that EIA-TOP can be obtained for realistic atomic transitions interacting with lasers that have the same polarization.
We discuss the influence of phase-changing collisions on the group velocities in Doppler-broadened, cycling, degenerate two-level systems where Fe=Fg+1{F}_{e}={F}_{g}+1Fe​=Fg​+1 and Fg>0{F}_{g}>0Fg​>0, interacting with pump and probe lasers, that exhibit electromagnetically induced absorption (EIA). Two model systems are considered: the NNN system where the pump and probe are polarized perpendicularly, and EIA is due to transfer of coherence (TOC), and the double two-level system (TLS) where both lasers have the same polarization, and EIA is due to transfer of population (TOP). For the case of Doppler-broadened EIA TOC, which occurs at low pump intensity, there is a switch from positive to negative dispersion and group velocity, as the rate of phase-changing collisions is increased. For the case of EIA TOP at low pump intensity, the dispersion and group velocity remain negative even when the collision rate is increased. Pressure-induced narrowing, accompanied by an increase in the magnitude of the negative dispersion and a decrease in the magnitude of the negative group velocity, occurs in both EIA TOC and EIA TOP, at low pump intensity. When the pump intensity is increased, a switch from negative to positive dispersion and group velocity, with increasing collision rate, also occurs in the double TLS system. However, the effect is far smaller than in the case of the NNN system at low pump intensity.
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.
The absorption/gain spectrum of a weak probe field is theoretically analyzed for an atomic three-level Λ system driven by a strong pump field and perturbed by collisions with buffer-gas atoms. It is assumed that both pump and probe drive the same transition. When the dark state is sufficiently long lived, the probe spectrum exhibits an extremely narrow (possibly subnatural-width) resonance. It is shown that coherence-preserving collisions drastically (both qualitatively and quantitatively) change the probe absorption spectrum even at a low collision frequency, when Dicke narrowing is negligible. Strong coherence effects on the resonance structure at low gas pressures is explained by a change in refractive index due to coherence-preserving collisions for particles in the resonant velocity group.
We investigate the atomic four-level NNN configuration both analytically and numerically, for various pump and probe intensities, with and without transfer of coherence (TOC) and Doppler broadening, and compare the results obtained to those of realistic atomic systems. We find that TOC affects the whole spectrum, in addition to producing an electromagnetically induced absorption (EIA) peak at line center. We show that the EIA peak splits as the pump intensity increases. These results are compared with those of realistic systems. When the pump is ${\ensuremath{\sigma}}^{+}$ polarized and the probe is $\ensuremath{\pi}$ polarized, the results are similar to those of the NNN configuration. When the pump and probe polarizations are both linear with perpendicular polarizations, various NNN-like subsystems contribute to the spectrum. Consequently, the splitting of the EIA peak only occurs at very high pump intensities. We also discuss the influence of the probe on the pump absorption and refraction and find that both the pump and probe show EIA peaks when the pump intensity is low, and complementary behavior when the pump is intense. At both low and high pump intensity, the pump and probe dispersions are of opposite sign.