Fourier transfer function for generic light pulse storage and retrieval using EIT

Electromagnetically induced transparency (EIT) based light storage and retrieval is a potential technique for quantum information storage, except for the stringent limitations of the delay-bandwidth product. Most of the optical storage studies have been limited to storing Sech, Gaussian or other well-known regular pulse shapes. In this paper, we propose an analytical framework based on a Fourier-domain coherent transfer function for arbitrary pulse shapes and derive a generalized expression for the retrieved light pulse from EIT storage in a three-level Lambda\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\Lambda$$\end{document} system. Starting from the coupled differential equations that govern the retrieval of the stored pulse, we derive a formula using parameters of the control pulses and the atomic system that can be used with any arbitrary pulse shape to be stored. We implements Fourier algebra to separate the effect of storage from the arbitrary shape of the pulse being stored, deriving a generalized formula for arbitrary pulse shape. We compare the results with those presented earlier in the literature, and presented results for storage and retrieval of other pulse shapes, including sharp and flat-top pulses.