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Physica Scripta

The analysis of coherent phenomena for both linear and non-linear interactions in a four-level ladder (Ξ)-type configuration using density matrix formalism in dressed state representation

Rejjak Laskar, Md. Mabud Hossain, Jayanta K. Saha

Published Jan 14, 2021• 9 citations
Publisher

Abstract

Abstract In this paper, we present a theoretical study of Autler-Townes (AT) splitting, electromagnetically induced transparency (EIT) and electromagnetically induced absorption (EIA) phenomena in a four-level ladder (Ξ)-type configuration formed by two coupling and one probe laser fields using density matrix formalism in dressed state representation (DSR). The DSR is followed by the analytical solution of the optical Bloch equations (OBEs) under density matrix formalism in bare state representation (BSR). The density matrix elements are presented in both linear and non-linear interaction regimes under DSR. The concept of transfer of population (TOP) mechanism has been shown by calculating the different transition probabilities in DSR. It has been found that the population in a particular dressed state is greatly enhanced by increasing the strength of coupling field and played a key role to manipulate the induced coherence between different energy levels. The present theoretical model of DSR offers an excellent interpretation of the formation of EIT, EIA and conversion from EIT to EIA in both linear and third order non-linear probe absorption profiles. Besides, the dispersion profiles in both linear and non-linear interaction regimes have also been studied and the conversion of normal to anomalous dispersion profile which drastically modifies the optical responses of the medium has been discussed. We have found that the amplitudes of the coherent signals are more sensitive to the third order non-linear interaction compared to first order linear interaction.

DOI
10.1088/1402-4896/abdbf3

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We study phenomenon of electromagnetically induced absorption (EIA) in the Hanle configuration by applying a perturbative method to solve linear system of optical Bloch equations (OBEs) for the case of closed F g = 1 → F e = 2 transition. The method is applied assuming stationary case and a weak laser fields (Ω ≪ Γ, i.e., Rabi frequency small compared to spontaneous emission rate). This way, we calculate (both numerically and analytically) higher order corrections to density matrix. Odd corrections give contributions to optical coherences, while even corrections contribute to populations and Zeeman coherences. The method gives insight into mechanism of transfer of coherences and transfer of populations between Zeeman sublevels. We have found that the ground-state coherences (2nd correction to coherences) are crucial for the 4th correction to the change of populations which brings EIA type behavior of the Hanle spectrum. Using exact analytical expressions we further discuss further the role of decoherence of the ground-state sublevels when forming EIA.

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Abstract In this paper, we present a theoretical study of Autler-Townes (AT) splitting, electromagnetically induced transparency (EIT) and electromagnetically induced absorption (EIA) phenomena in a four-level ladder (Ξ)-type configuration formed by two coupling and one probe laser fields using density matrix formalism in dressed state representation (DSR). The DSR is followed by the analytical solution of the optical Bloch equations (OBEs) under density matrix formalism in bare state representation (BSR). The density matrix elements are presented in both linear and non-linear interaction regimes under DSR. The concept of transfer of population (TOP) mechanism has been shown by calculating the different transition probabilities in DSR. It has been found that the population in a particular dressed state is greatly enhanced by increasing the strength of coupling field and played a key role to manipulate the induced coherence between different energy levels. The present theoretical model of DSR offers an excellent interpretation of the formation of EIT, EIA and conversion from EIT to EIA in both linear and third order non-linear probe absorption profiles. Besides, the dispersion profiles in both linear and non-linear interaction regimes have also been studied and the conversion of normal to anomalous dispersion profile which drastically modifies the optical responses of the medium has been discussed. We have found that the amplitudes of the coherent signals are more sensitive to the third order non-linear interaction compared to first order linear interaction.
Abstract We theoretically study the two- and three-photon coherence in a Ξ−Λ type four-level system for stationary as well moving atoms at the room temperature using density matrix formalism. We discuss the role of dressed states to elucidate the electromagnetically induced transparency and electromagnetically induced absorption phenomena. The presence of the third field induces absorption at the line centre. A negative dispersion slope owing to the enhanced absorption results in super-luminal light propagation and the group index variation with the coupling field is switched from sub- to super-luminal. Group index with probe detuning shows super-luminal light propagation behaviour at the dressed state positions. The three optical fields trigger four-wave mixing as a result of the third order nonlinearity. The transient evolution is also discussed for optimum strengths of the coupling and drive fields to realize the optical switching in the system.
Abstract A comparative theoretical study of two-photon electromagnetically induced transparency (EIT), absorption (EIA) and three-photon electromagnetically induced transparency (TPEIT), absorption (TPEIA) and their associated dispersion and group index profiles are presented by using a four-level ladder-type system of both stationary and moving 85 Rb Rydberg atoms. We have observed EIT, EIA and their respective positive and negative dispersive slopes under two-photon conditions, while the TPEIT, TPEIA signals and the respective multiple positive and negative dispersive slopes at around zero detuning of the probe field are observed under the three-photon conditions. It is found that the control and manipulation of the coherent optical responses under three-photon conditions are much richer than the two-photon conditions. The group index profiles related to the dispersion of the medium have been studied under both two- and three-photon conditions to compare and explain the optical switching between the subluminal and superluminal modes of propagation for both stationary and moving atomic medium. The influence of the ‘pump’ Rabi frequency on the group index has also been investigated to illustrate the action of optical switching. Finally, the existence of the four-wave mixing (FWM) process due to the action of three optical fields in the EIT medium is also discussed.
Electromagnetically induced transparency (EIT) resonance is obtained in a well-studied lambda three level system where an optical coupling field and a probing field interact with two optical transitions. However, both electromagnetically induced absorption (EIA) and EIT can be obtained in a modified quasi-lambda four level system consisting of an optical-radio two-photon coupling field and a probing field. By solving the density matrix equation of motion, a physical account of EIA and EIT is given in terms of a dressed state picture. It can be seen that the optical coupling field in this quasi-lambda four level system has a crucial effect on the forming of EIA and EIT. An EIA is observed under a resonant optical coupling and it evolves into an EIT when there is a detuning. Furthermore, the width of EIA or EIT increases as the optical coupling Rabi frequency increases.
The A-type three-level system coupled by two coherent fields is a basic model to study the electromagnetically induced transparency(EIT).Based on that,the cascade quasi- A-four-level configuration is formed when a radio-frequency(RF)field drives the transition between the excited state and an additional excited state level.The absorption property is studied along with the parameters of the coupling field and the RF driving field by numerically solving the relevant equations of motion of the density matrix.It is shown that under the applying of the coupling field and the RF driving field,both the Autler-Townes doublet and the EIT are observed in the absorptive spectra and it can be explained properly by the theory of dressed state.An important conclusion is that the Autler-Townes doublet originates from the atom system interaction with the strong RF field,while the EIT originates from atom system quantum interference interaction with the coupling field.
In this article we have shown that the atomic states can be engineered by tunning the coupling Rabi frequency for a system with N\mathcal{N}N-type configuration. Electromagnetically induced transparency (EIT), Electromagnetically induced absorption (EIA) and Autler-Townes (AT) splitting has been observed experimentally in a four level N\mathcal{N}N-type atomic vapor of 85Rb^{85}Rb85Rb atoms in the hyperfine levels of D2D_2D2​ transition. It has been shown that the response of the atomic medium can be tunned from highly transparent to highly absorptive in our case. The evolution of the atomic states from the dark state |D> to the non-coupled state |NC> has been studied with the partial dressed state approach which makes the backbone of the modification of the atomic response. In addition, transient solutions in the time domain and steady state solution in the frequency domain has been studied. The population dynamics and the coherence contribution in each case has been analyzed by the time dependent solutions. The experimentally observed steady line-shape profiles has been supported by the steady state solution of optical-Bloch equations considering the Maxwell Boltzmann velocity distributions of the atoms. It has been observed that the crossover between the EIT and the AT splitting has been replaced by the interference contribution of the EIA in this N\mathcal{N}N-type system.
We study phenomenon of electromagnetically induced absorption (EIA) in the Hanle configuration by applying a perturbative method to solve linear system of optical Bloch equations (OBEs) for the case of closed F g = 1 → F e = 2 transition. The method is applied assuming stationary case and a weak laser fields (Ω ≪ Γ, i.e., Rabi frequency small compared to spontaneous emission rate). This way, we calculate (both numerically and analytically) higher order corrections to density matrix. Odd corrections give contributions to optical coherences, while even corrections contribute to populations and Zeeman coherences. The method gives insight into mechanism of transfer of coherences and transfer of populations between Zeeman sublevels. We have found that the ground-state coherences (2nd correction to coherences) are crucial for the 4th correction to the change of populations which brings EIA type behavior of the Hanle spectrum. Using exact analytical expressions we further discuss further the role of decoherence of the ground-state sublevels when forming EIA.