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Physical Review A

Delay-bandwidth product of electromagnetically induced transparency media

Jonas Tidström, Peter Jänes, L. Mauritz Andersson

Published May 3, 2007• 22 citations

Abstract

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.

DOI: 10.1103/physreva.75.053803

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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.

Delay bandwidth products (DBPs) and physical pulselengths obtainable in media exhibiting electromagnetically induced transparency (EIT) are analyzed. The study is performed in stationary media as well as for dynamic storing of light pulses in such media. In the latter case, the dispersion inherent in storage and readout of the pulses is analyzed. It is shown that absorption and the group velocity dispersion (GVD) are limiting factors. Analytical expressions for the minimum compressed pulselength and DBP are derived, and these expressions show good agreement with simulations of pulse propagation in EIT media.

The influence of a phase-modulated control field on the phenomenon of electromagnetically induced transparency (EIT) is investigated theoretically. We show that the phase modulation changes the dispersive properties of the medium considerably since it results in temporal oscillations of the transparency window in frequency space. This is in marked contrast to the standard EIT setup, where the transparency window is fixed and determined by the two-photon resonance condition. In particular, we find that the phase modulation enables the propagation of probe pulses with disjoint frequency spectra at different times and allows the shifting of the central frequency of a probe pulse almost without distortion of its shape. We employ the time-dependent susceptibility of the medium to explain and analyze our results and demonstrate that this concept yields qualitative as well as quantitative agreement with the numerical integration of Maxwell-Bloch equations. Our theoretical model can be applied to other media with time-dependent susceptibilities.

Optical Sommerfeld-Brillouin precursors significantly ahead of a main field of comparable amplitude have been recently observed in an opaque medium with an electromagnetically induced transparency window [Wei et al., Phys. Rev. Lett. 103, 093602 (2009)]. We theoretically analyze in this article the somewhat similar results obtained when the transparency is induced by the propagating field itself and we establish an approximate analytic expression of the time delay of the main-field arrival, which fits fairly well the result obtained by numerically solving the Maxwell-Bloch equations.

The propagation of broadband pulse in a medium with electromagnetically induced transparency (EIT) was studied. The results show that if the carrier frequency of pulse is exactly tuned to the center of the transparency window, and the pulse spectrum is broader than transparency window, the pulse is temporally broadened and the delay effect is significant. If the carrier frequency of pulse the is exactly tuned to the region of absorption, and the pulse spectrum is wide with respect to the width of absorption line, the pulse begins to distort after a certain distance and is split into two parts at last. The peak value depends not only on the frequency and intensity of the coupling field, but also on the length of the sample. Under appropriate conditions, strong and time domain narrowed pulse can be obtained in the output light.

One-dimensional pulse propagations in the electromagnetically induced media are studied. The Maxwell–Bloch equations for a three-level medium are simplified with the approximations of slowly varying amplitudes, negligible irreversible relaxations and exact resonances. An analysis is made for the case where the integrable condition is satisfied; the oscillation strengths for the two transitions are equall. Through the Bäcklund transformation, one-soliton solutions including the so-called simulton are derived.