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arXiv:1212.5657 · Journal of Physics B Atomic Molecular and Optical Physics

Analytical approach on linear and nonlinear pulse propagations in an open Λ-type molecular system with Doppler broadening

Chaohua Tan, Chengjie Zhu, Guoxiang Huang

Published Jan 10, 2013• 9 citations
arXivHTMLPDF

Abstract

We develop a systematic analytical approach on linear and nonlinear pulse propagations in an open Λ-type molecular system with Doppler broadening. In the linear case, using a residue theorem and a spectrum decomposition method, we prove that a crossover from electromagnetically induced transparency (EIT) to Autler–Townes splitting (ATS) exists for a co-propagating configuration of probe and control fields. However, there is no EIT and hence no EIT–ATS crossover for a counter-propagating configuration. We give various explicit formulas, including probe-field spectrum decomposition, the EIT condition, the width of the EIT transparency window, as well as a comparison with the result of cold molecules. Our analytical result agrees well with the experimental one reported recently by Lazoudis et al (2010 Phys. Rev. A 82 023812). In the nonlinear case, using the method of multiple scales, we derive a nonlinear envelope equation for probe-field propagation. We show that stable ultraslow solitons can be realized in the open molecular system.

DOI
10.1088/0953-4075/46/2/025103

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Mixture of Electromagnetically Induced Transparency and Autler–Townes Splitting in a Five-Level Atomic System*

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Abstract Discerning electromagnetically induced transparency (EIT) from Autler–Townes splitting (ATS) is a significant issue in quantum optics and has attracted wide attention in various three-level configurations. Here we present a detailed study of EIT and ATS in a five-level atomic system considered to be composed of a four-level Y-type subsystem and a three-level Λ-type subsystem. In our theoretical calculations with standard density matrix formalism and steady-state approximation, we obtain the general analytical expression of the first-order matrix element responsible for the probe-field absorption. In light of the well-known three-level EIT and ATS criteria, we numerically show an intersection of EIT with ATS for the Y-type subsystem. Furthermore, we show that an EIT dip is sandwiched between two ATS dips (i.e., multi-dip mixture of EIT and ATS) in the absorption line for the five-level system, which can be explained by the dressed-state theory and Fano interference.

Communications in Theoretical Physics•Feb 1, 2017•3 citations
We develop a systematic analytical approach on linear and nonlinear pulse propagations in an open Λ-type molecular system with Doppler broadening. In the linear case, using a residue theorem and a spectrum decomposition method, we prove that a crossover from electromagnetically induced transparency (EIT) to Autler–Townes splitting (ATS) exists for a co-propagating configuration of probe and control fields. However, there is no EIT and hence no EIT–ATS crossover for a counter-propagating configuration. We give various explicit formulas, including probe-field spectrum decomposition, the EIT condition, the width of the EIT transparency window, as well as a comparison with the result of cold molecules. Our analytical result agrees well with the experimental one reported recently by Lazoudis et al (2010 Phys. Rev. A 82 023812). In the nonlinear case, using the method of multiple scales, we derive a nonlinear envelope equation for probe-field propagation. We show that stable ultraslow solitons can be realized in the open molecular system.
We investigate electromagnetically induced transparency (EIT) and Autler-Townes splitting (ATS) in an open V-type molecular system. Through detailed analytical calculations of the absorption spectrum of a probe laser field using the residue theorem and spectrum decomposition, we find that EIT may occur and a crossover from EIT to ATS exists for hot molecules. However, there is no EIT and hence no EIT-ATS crossover for cold molecules. Furthermore, we prove that for hot molecules EIT is allowed even for a counter-propagating configuration. We provide explicit formulas of EIT conditions and widths of EIT transparency windows of the probe field when hot molecules work in copropagating and counter-propagating configurations, respectively. Our theoretical result agrees well with the recent experimental ones reported by Lazoudis et al. [Phys. Rev. A 83, 063419 (2011)].
We present a systematic theoretical study to deal with linear and nonlinear light propagations in a Doppler-broadened three-level $\ensuremath{\Lambda}$ system via electromagnetically induced transparency (EIT), with incoherent population exchange between two lower energy levels taken into account. Through a careful analysis of base state and linear excitation, we show that the EIT condition of the system is given by $|{\ensuremath{\Omega}}_{c}|{}^{2}{\ensuremath{\gamma}}_{31}\ensuremath{\gg}2{\ensuremath{\gamma}}_{21}\ensuremath{\Delta}{\ensuremath{\omega}}_{D}^{2}$, where ${\ensuremath{\Omega}}_{c}$ is half the Rabi frequency of the control field, $\ensuremath{\Delta}{\ensuremath{\omega}}_{D}$ is the Doppler width, and ${\ensuremath{\gamma}}_{\mathit{jl}}$ is the decay rate of the coherence between states $|j\ensuremath{\rangle}$ and $|l\ensuremath{\rangle}$. Under this condition, the effect of incoherent population exchange is insignificant, while dephasing dominates the decoherence of the system. This condition also ensures the validity of the weak nonlinear perturbation theory used in this work for solving the Maxwell-Bloch equations with inhomogeneous broadening. We then investigate the nonlinear propagation of the probe field and show that it is possible to form temporal optical solitons in the Doppler-broadened medium. Such solitons have ultraslow propagating velocity and can be generated in very low light power. The possibility of realizing (1+11+11+1)-dimensional and (2+12+12+1)-dimensional spatial optical solitons in the adiabatic regime of the system is also discussed.
We propose a general theoretical scheme to investigate the crossover from electromagnetically induced transparency (EIT) to Autler–Townes splitting (ATS) in open ladder-type atomic and molecular systems with Doppler broadening. We show that when the wavenumber ratio kc/kp≈−1, EIT, ATS, and EIT-ATS crossover exist for both ladder-I and ladder-II systems, where kc (kp) is the wavenumber of control (probe) field. Furthermore, when kc/kp is far from −1, EIT can occur, but ATS is destroyed if the upper state of the ladder-I system is a Rydberg state. In addition, ATS exists but EIT is not possible if the control field used to couple the two lower states of the ladder-II system is a microwave field. The theoretical scheme developed here can be applied to atoms, molecules, and other systems (including Na2 molecules, and Rydberg atoms), and the results obtained may have practical applications in optical information processing and transformation.
We investigate the linear and nonlinear light pulse propagations in a three-level Λ-type molecular system with permanent dipole moments via electromagnetically induced transparency (EIT). We find that EIT characters in such a system depend strongly on the phase of control field, based on which a phase-controlled optical switch can be designed. We show that the Kerr nonlinearity of the system can be largely enhanced due to the control-field-induced quantum interference effect. We derive a nonlinear Schrödinger equation for the evolution of the probe-field envelope and demonstrate that it is possible to generate stable slow- and weak-light solitons in the system.
We describe in this Letter how inhomogeneous line broadening affects the Autler-Townes (AT) splitting in a three level open molecular cascade system. For moderate Rabi frequencies in the range of 300 to 500 MHz the fluorescence line shape from the uppermost level |3> in this system depends strongly on the frequency ratio of the two laser fields. However, the fluorescence spectrum of the intermediate level |2> appears as expected. We provide a description of the conditions for optimally resolved AT splitting in terms of the probe laser/coupling field frequency ratio and laser propagation geometry based on our theoretical analysis of the Doppler integral. This is important for applications such as molecular angular momentum alignment as well as for the measurement of the transition dipole moment matrix element.
Abstract Discerning electromagnetically induced transparency (EIT) from Autler–Townes splitting (ATS) is a significant issue in quantum optics and has attracted wide attention in various three-level configurations. Here we present a detailed study of EIT and ATS in a five-level atomic system considered to be composed of a four-level Y-type subsystem and a three-level Λ-type subsystem. In our theoretical calculations with standard density matrix formalism and steady-state approximation, we obtain the general analytical expression of the first-order matrix element responsible for the probe-field absorption. In light of the well-known three-level EIT and ATS criteria, we numerically show an intersection of EIT with ATS for the Y-type subsystem. Furthermore, we show that an EIT dip is sandwiched between two ATS dips (i.e., multi-dip mixture of EIT and ATS) in the absorption line for the five-level system, which can be explained by the dressed-state theory and Fano interference.