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arXiv:1805.03840 · Journal of Physics B Atomic Molecular and Optical Physics

Pulse delay and group velocity dispersion measurement in V-type electromagnetically induced transparency of hot 85 Rb atom

Bankim Chandra Das, Dipankar Bhattacharyya, Arpita Das, Satyajit Saha, Shrabana Chakrabarti, Sankar De

Published Nov 2, 2018• 4 citations
arXivHTMLPDF

Abstract

Abstract Pulse delay with the group velocity dispersion (GVD) characteristics was studied in the V-type electromagnetically induced transparency in the hyperfine levels of 85 Rb atoms with a closed system configuration. The phase coherency between the pump and the probe laser beams was maintained. We studied the pulse delay and the GVD characteristics with the variation of the pump Rabi frequency taking optical density (OD) as a parameter. We observed a maximum of 268 ns pulse delay for 21.24 MHz pump Rabi frequency at OD 5.04 of the Rb vapor cell. For a better understanding of the experimental results, we have derived an analytical solution for the delay characteristics considering the thermal averaging. The analytical solution was derived for a three level V-type system. The theoretical plots of the delay and the GVD show the same characteristics as we observed in the experiment. This analytical approach can be further generalized for the higher level schemes to calculate different quantities such as susceptibility, group velocity delay or GVD characteristics.

DOI
10.1088/1361-6455/aaede0

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Abstract Pulse delay with the group velocity dispersion (GVD) characteristics was studied in the V-type electromagnetically induced transparency in the hyperfine levels of 85 Rb atoms with a closed system configuration. The phase coherency between the pump and the probe laser beams was maintained. We studied the pulse delay and the GVD characteristics with the variation of the pump Rabi frequency taking optical density (OD) as a parameter. We observed a maximum of 268 ns pulse delay for 21.24 MHz pump Rabi frequency at OD 5.04 of the Rb vapor cell. For a better understanding of the experimental results, we have derived an analytical solution for the delay characteristics considering the thermal averaging. The analytical solution was derived for a three level V-type system. The theoretical plots of the delay and the GVD show the same characteristics as we observed in the experiment. This analytical approach can be further generalized for the higher level schemes to calculate different quantities such as susceptibility, group velocity delay or GVD characteristics.
Abstract The dispersive properties of 87 Rb atomic medium in electromagnetically induced transparency (EIT) have been studied experimentally as well as theoretically. To measure the dispersion signal, a balanced homodyne detection technique was used by forming a Mach–Zehnder interferometer. We studied the system in a Λ-type configuration. From the slope of the dispersive EIT signal, the group index ( n g ) of the atomic medium, the group velocity ( ) and the time delay ( ) of the light wave through the atomic medium were calculated. We measured the group index of the atomic medium from the dispersion signal and observed that it non-linearly depends on the pump power. This non-linearity signifies that to achieve the maximum reduced group velocity, optimization of the pump power is needed. We got the maximum reduction in the group velocity of the probe beam as m s −1 . The corresponding time delay was ns. To support our experimental observation, we have performed a theoretical simulation by taking the semi-classical approach of density matrix formalism of a Λ-type three level system. To get the probe response we solved the optical Bloch equation analytically assuming the Lorentzian velocity distribution of the atom. We have observed that our analytical solution matched exactly with the numerical solution. Our experimental observation of non-linear variation of the group index with the pump Rabi frequency matched quite well with both of our numerical and analytical simulations.
Abstract We have theoretically studied the multi-window electromagnetically induced transparency (EIT) and the related dispersive signals in multi-level V-type systems which are formed by the co-propagating circularly polarized pump ( σ − ) and probe ( σ + ) laser fields in the Zeeman sublevels of hyperfine states of 87 Rb-D 2 line. The optical Bloch equations (OBEs) are derived and numerically solved under the steady-state condition to obtain the probe absorption and dispersion spectra. We present the study of a single-window EIT for the three-level, double-window EIT for the four-level and triple-window EIT for the five-level V-type systems under both Doppler-free and Doppler-broadened conditions. The dispersive signals corresponding to the multi EIT windows for each system are also observed separately. From the knowledge of the slopes of the probe dispersion signals, we have calculated group index ( n g ) of the medium considering three different V-type schemes. The effect of temperature on the EIT, dispersion and group index profiles is also studied in detail. It is found that the amplitudes of EIT and dispersion signals and also the positive and negative values of n g are decreased as the temperature of the medium increases. To understand the Doppler-broadening effect on the group index profiles, we have considered three different velocity groups of atoms in the calculation of group index profiles. Moreover, the effects of probe intensity variation on the Doppler-broadened EIT and dispersive signals are studied extensively, and the conversions of EIT to EIA and dispersive positive slope to negative slope are observed under strong probe regime. Also, we have investigated the variation of dispersive slope and group index with the variation of probe intensity and probe frequency, respectively, at the multi-frequency position of the multi-window EIT. Finally, the switching between subluminal (slow light) to superluminal (fast light) propagation of light with the variation of both probe intensity and probe frequency is discussed in detail.
Abstract We report the observation of electromagnetically induced transparency (EIT) in a six-level Λ -type system in atomic Rb vapor containing both 87 Rb and 85 Rb. The experimental observation includes five velocity selective optically pumped (VSOP) absorption dips for both 87 Rb and 85 Rb. The EIT signal appears on the background of one such VSOP absorption dips. The measured EIT linewidth ( ) shows sub-natural ( ) values for both lower and higher values of pump Rabi-frequencies. The density matrix based theoretical model for the six-level system is developed and solved numerically by taking into account the Doppler broadening. A complete analytical solution (non perturbative) for a three level Λ -type system has been obtained and compared with the experimentally observed sub-natural EIT linewidth. The simulated spectra are in good agreement with the experimental findings.
We observe pulse delays of up to twenty times the input pulse duration when 200 ps laser pulses pass through a hot Rb 85 vapor cell. The pulse peak travels with a velocity equal to c/20, and the energy transmission is 5%. For pulses with a linewidth greater than typical features in the atomic dispersion, pulse delay is predicted and observed for all center frequencies near resonance. Pulse advance is never observed. The measurements are in good agreement with a three-level linear-dispersion calculation. We are able to control the amount of delay by using a steady-state laser beam for optical pumping of the ground states prior to sending in the test pulse.
Abstract We report a theoretical investigation of the dispersion resulting from electromagnetically induced transparency (EIT) and the associated group refractive index profiles n g of a four-level inverted Y-type system formed by the interaction of three optical fields (probe, pump and control) with 87Rb atoms. The density matrix equations are derived from the semi-classical Liouville’s equation and solved both numerically and analytically to study the coherent nonlinear optical properties of the medium. We first present the EIT, dispersion and corresponding group index profiles n g under the switch-on/off and on/off-resonance conditions of the pump and control lasers. In presence of both pump and control lasers, an enhancement of the EIT window, a sharp EIT spike and related steeper dispersion slopes are obtained at the line centre of the probe frequency detuning. The group index profiles with the variation of the strengths of individual applied optical fields are studied. The effect of the ground state decoherence rates on the group index profile is examined in detail. It is found that the manipulation of n g values and the corresponding group velocities ν g of the probe light can be easily controlled from subluminal to superluminal values or vice versa by changing the strengths of the applied fields and the ground state decoherence rates. Besides, the EIT-based ‘optical switching’ phenomenon in the medium is explained by studying the variation of the group index with the pump and control Rabi frequencies.
Atomic coherence resonances such as electromagnetically induced transparency (EIT) and electromagnetically induced absorption (EIA) signals are observed in a Doppler broadened multi-level system for the D 2 line of 85 Rb atoms in a vapour cell considering different types of atom–laser coupling schemes. Besides the coherence resonances, the nonlinear resonances like velocity selective optical pumping (VSOP) dips and velocity selective resonances (VSR) are also observed for the non-zero velocity selective groups of atoms. In the presence of pump, control and probe laser fields, we observe two EIT signals in a double Λ-type system and two EIA signals in a double V -type system. We are able to see the EIA signal for the non-zero velocity group of atoms when the pump laser is locked with an open transition by a small red detuning. We also report the experimental observation of simultaneous EIT and EIA signals in a (Λ+ V )-type system. The effect of frequency tuning of the control laser is also studied in the presence of the frequency locked pump laser. A simple theoretical analysis explains the experimental results.