Study of multi-window electromagnetically induced transparency (EIT) and related dispersive signals in V-type systems in the Zeeman sublevels of hyperfine states of⁸⁷Rb-D₂line

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 87Rb-D2 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.

Theoretical study of coherent optical phenomena in a three lasers driven four-level ladder-type system involving a Rydberg state

“…Particularly, we are interested to study both the two-and three-photon induced coherent optical phenomena, such as EIT, EIA, TPEIT, TPEIA and their related dispersion spectra, group index, FWM, etc by the detection of probe field. To study these various coherent phenomena in the three lasers driven four-level laddertype system involving a Rydberg state, we set up the density matrix equations which are derived from the semi-classical Liouville's equation of motion [17,19,47],…”

“…The values of the spontaneous decay rates are taken from [34,46] as Γ 21 = 2π × 6.10 MHz, Γ 32 = 2π × 0.66 MHz and Γ 41 = Γ 43 = 2π × 10.00 kHz. In this work, we have neglected any collisional dephasing effects as they are very small compared to the values of the spontaneous decay rates [47].…”

“…The laser field-induced non-linear optical properties of the atomic medium under one-, two-and three-photon coherences are observed by the probe absorption/transmission (dispersion), which is related to the imaginary part (real part) of the complex susceptibility (χ) [37,47],…”

“…The reason behind such conversion from EIT to EIA and related dispersive slopes can be explained by the fact that as the strength of the probe Rabi frequency is gradually increased up to the order of the pump Rabi frequency, the atomic population is transfered by the probe itself between the probe laser-coupled energy levels. Ultimately the competition between the optical pumping by the strong probe and pump fields results in the formation of both EIT and EIA in the Doppler-broadened probe absorption spectrum [47,49]. Besides, the probe absorption profile shows a wavelength mismatching effect [k pr ̸ = k p ] around ∆ pr = 0 and also shows a power broadening effect with the increase of probe strength.…”

Electromagnetically induced transparency in a V-system with 87Rb vapour in the hyperfine Paschen-Back regime

“…V-EIT is the least studied of these because there is no stable dark state [11], as both of the singly coupled states are excited states and can decay to the ground state. Nevertheless, V-EIT has been extensively studied [6,[12][13][14][15][16][17][18][19][20][21][22][23][24][25], and provides an interesting testing ground for ascertaining the relative importance of coherent and incoherent mechanisms in the generation of the transparency window [16,26,27].…”