The limitations on the delay-bandwidth product (DBP) in an electromagnetically induced transparency medium are investigated analytically by studying the susceptibility of the system, derived through Lindblad's master equation, including dephasing. The effect of inhomogeneous broadening is treated. It is shown that the DBP for a given material is fundamentally limited by the frequency-dependent absorption, while the residual absorption limits the penetration length of a pulse. Simple expression for the optimal choice of parameters to maximize the DBP are derived. Also, the length of a device is presented as a function of DBP and control-field Rabi frequency. Supporting these results, numerical calculations are carried out through the Maxwell-Bloch equations in the slowly varying envelope approximation. The results are scalable, hence they apply to the case of atoms or molecules in a gas as well as quantum dots and wells.
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Tidström et al. (2007) studied this question.
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