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Physical Review A

Dispersive properties of electromagnetically induced transparency

Stephen E. Harris, J. E. Field, A. Kasapi

Published Jul 1, 1992• 507 citations
Publisher

Abstract

An atomic transition that has been made transparent by applying an additional electromagnetic field exhibits a rapidly varying refractive index with zero group velocity dispersion at line center. A 10-cm-long Pb vapor cell at an atom density of 7\ifmmode\times\else\texttimes\fi{}${10}^{15}$ atoms/${\mathrm{cm}}^{3}$ and probed on its 283-nm resonance transition has a calculated optical delay of 83 ns [(c/${\mathit{V}}_{\mathit{G}}$)=250].

DOI
10.1103/physreva.46.r29

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Journal of Modern Optics•Jul 11, 2024•1 citation
An atomic transition that has been made transparent by applying an additional electromagnetic field exhibits a rapidly varying refractive index with zero group velocity dispersion at line center. A 10-cm-long Pb vapor cell at an atom density of 7\ifmmode\times\else\texttimes\fi{}1015{10}^{15}1015 atoms/cm3{\mathrm{cm}}^{3}cm3 and probed on its 283-nm resonance transition has a calculated optical delay of 83 ns [(c/VG{\mathit{V}}_{\mathit{G}}VG​)=250].
The dispersive properties of the atomic transition in the rubidium D2{D}_{2}D2​ line ($5{S}_{\frac{1}{2}}\ensuremath{-}5{P}_{\frac{3}{2}}$) at 780.0 nm are measured with a Mach-Zehnder interferometer when an additional coupling field at 775.8 nm is applied to an upper transition ($5{P}_{\frac{3}{2}}\ensuremath{-}5{D}_{\frac{5}{2}}$). This ladder-type system is observed to exhibit electromagnetically induced transparency together with a rapidly varying refractive index. A reduction in group velocity for the probe beam (vg=c13.2{v}_{g}=\frac{c}{13.2}vg​=13.2c​) is inferred from the measured dispersion curve with 52.5% suppressed absorption on resonance.
It is now well understood that the characteristics of a nonlinear optical process are the result of the interplay of the linear and nonlinear susceptibilities. In general, as an atomic transition to the ground state is approached, the nonlinear susceptibility is resonantly enhanced, but, at the same time, the media exhibits a rapidly increasing refractive index and becomes opaque. During the last several years we have shown how electromagnetically induced transparency (EIT) may be used to dramatically solve this problem.
As evidenced by this book, there has been a flurry of activity over the last decade on tailoring the dispersive properties of optical materials [1]. What has captured the attention of the research community were some of the early results on creating spectral regions of large normal dispersion [2-4]. Large normal dispersion results in extremely small group velocities, where the group velocity is the approximate speed at which a pulse of light propagates through a material. We denote the group velocity by υg = c/ng, where c is the speed of light in vacuum and ng is known as the group index. In the early experiments, described in greater detail in Chapter 1, a dilute gas of atoms is illuminated by a control or coupling beamwhose frequency is tuned precisely to an optical transition of an atom. This control field modifies the absorption and dispersion properties of another atomic transition that shares a common energy level. A narrow transparencywindow is created on this second transition-a process known as electromagnetically induced transparency (EIT)—and within this window, υg takes on extremely small values. Many experiments have now observed υg ∼ 1 m/s or less, implying ng > 108. This result is remarkable, considering the fact that the refractive index n of a material rarely exceeds 3 in the visible part of the spectrum.What are the implications of such large group indices? What applications are enabled by this basic science discovery?
Abstract Pulse delay with the group velocity dispersion (GVD) characteristics was studied in the V-type electromagnetically induced transparency in the hyperfine levels of 85 Rb atoms with a closed system configuration. The phase coherency between the pump and the probe laser beams was maintained. We studied the pulse delay and the GVD characteristics with the variation of the pump Rabi frequency taking optical density (OD) as a parameter. We observed a maximum of 268 ns pulse delay for 21.24 MHz pump Rabi frequency at OD 5.04 of the Rb vapor cell. For a better understanding of the experimental results, we have derived an analytical solution for the delay characteristics considering the thermal averaging. The analytical solution was derived for a three level V-type system. The theoretical plots of the delay and the GVD show the same characteristics as we observed in the experiment. This analytical approach can be further generalized for the higher level schemes to calculate different quantities such as susceptibility, group velocity delay or GVD characteristics.
By employing the density matrix approach, this study systematically examines the impact of a longitudinal magnetic field on electromagnetically induced transparency (EIT) within the context of the effective three-level Zeeman sublevels associated with the D2-line of 87Rb atomic vapor. Our investigation reveals that a sufficient enhancement in the longitudinal magnetic field induces a discernible narrowing of the EIT linewidth, accompanied by an enhancement in the peak transmission through a Rubidium (Rb) vapor cell. Related to these, we analyse the effect of magnetic field on the dispersive properties of the system, including group delay and group velocity and observed a slight decrement in the group delay and increment in the group velocity, which specifies the transition from slow to fast light under the application of the magnetic field.