Vector magnetometry was studied using the electromagnetically induced transparency (EIT) with linear $perp$ linear ($lin perp lin$) polarization of the probe and the pump beams in $^{87}Rb$ - $D_2$ transition. The dependence of the EIT on the directi
on of the quantization axis and the relative orientation of the polarization of the applied electric fields was studied experimentally. We have shown that from the relative strengths of the $sigma$ and $pi$ EIT peaks, the direction of the magnetic field can be found. Moreover from the relative separation between the $sigma$ and $pi$ EIT peaks, the strengths of the magnetic field can be calculated. We have also demonstrated that the EIT peak amplitudes show oscillatory behaviour depending upon the orientation of the laser polarization relative to the magnetic field direction. Using the positions of the maxima and minima, the direction of the magnetic field can be calculated. To understand the experimental observation, a theoretical study has been done numerically considering all the thirteen Zeeman sub-levels. Apart from the numerical model, a toy model has also been considered to obtain an analytical response of the medium considering the velocity distribution. The dependencies of the magnetic field direction and the polarization direction of the electric fields have been explicitly derived in the analytical model. Further the direction of the magnetic field is calculated using the analytical solution. This study can be helpful in order to make an EIT based atomic vector magnetometer at room temperature.
In this article we have shown that the atomic states can be engineered by tunning the coupling Rabi frequency for a system with $mathcal{N}$-type configuration. Electromagnetically induced transparency (EIT), Electromagnetically induced absorption (E
IA) and Autler-Townes (AT) splitting has been observed experimentally in a four level $mathcal{N}$-type atomic vapor of $^{85}Rb$ atoms in the hyperfine levels of $D_2$ 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 $mathcal{N}$-type system.
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 pum
p and the probe laser beams was maintained. We studied the pulse delay and the group velocity dispersion characteristics with the variation of the pump Rabi frequency taking temperature as a parameter. We observed a maximum of $268$ $ns$ pulse delay for $21.24 MHz$ pump Rabi frequency at $55^0C$ temperature of the Rb vapour 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 group velocity dispersion 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 group velocity dispersion characteristics.
It is shown by theoretical simulation that tuning of the pump power can induce mixing and crossing of Autler-Townes(A-T)components of closely spaced transitions in atoms. Pump radiation also leads to small shifts of the central hole of A-T doublet. O
ff-resonance pumping gives an asymmetry in the A-T components and by controlling pump frequency detuning it is also possible to mix the A-T components.
Inversionless gain is observed in a V-type inhomogeneously broadened system without introducing any incoherent pumping and only by changing the collisional dephasing decay rate. In this system sub-Doppler linewidth is achieved with off-resonance pump detuning.
