The dependencies of the polarization rotation on the probe ellipticity and the longitudinal magnetic field have been studied both experimentally and theoretically in a V-type electromagnetically induced transparency for 87Rb vapour. The angle of rotation varies periodically with the change in the probe ellipticity and non-linearly with the variation of the magnetic field. We have observed that the plane of polarization is rotated maximum for linearly polarized light and have obtained angle of rotation 0.32° ± 0.01° for B = 0.036 ± 0.001 mT while it was 0.0267° ± 0.0002° without magnetic field. Thus our measurement becomes sensitive to the low magnetic field. A four-level system is considered and the corresponding density matrix equations have been solved analytically to explain these observations theoretically with the help of degenerate and non-degenerate magnetic sub-levels.
Abstract The dependency of polarization rotation with electromagnetically induced transparency (PREIT) in 87 Rb vapor on the angular mismatch between the probe and the pump beams has been studied experimentally and theoretically for a V-type configuration. We have observed a nonlinear variation of the PREIT angle with the angular mismatch. The angular mismatch enhanced the residual Doppler broadening effect, as well as diminishes the two photon coherence contribution, in the medium. We have also systematically studied the effect of optical depth (OD) and the pump beam spot size variations to understand how the number of interacting atoms affect the two photon coherence contribution of the polarization rotation. The value of group velocity of the probe beam has been calculated from the experimentally observed spectrum. We have modeled a three-level V-type system to explain the experimentally observed phenomena by considering the effect of OD and spot size with angular mismatch in the medium. We have considered two-dimensional Maxwell–Boltzmann distribution to calculate the susceptibilities for all atoms of all velocity components. The characteristic variation of the angle of PREIT with the angular mismatch matches well with the experimentally observed result.
Comparison of Electromagnetically Induced Transparency (EIT) Spectra for Six-level Lambda
Λ and Five-level V-type Systems
Electromagnetically induced transparency (EIT) is experimentally studied in a rubidium vapour cell (without buffer gas, both
87Rb and
85Rb present according to their natural abundance) kept within two-layers of
μ(μ)-metal shields to avoid the effect of Earth's magnetic field on the energy levels of atomic rubidium. An external cavity diode laser (ECDL), used as a low power probe laser, is locked to the hyperfine cross-over peak of
F=2→F′=2,3 transitions of
87Rb. The frequency of another ECDL, the pump laser, is set to scan the
F=1→F′=0,1,2 transitions of
87Rb. These form the
Λ-type six level system. In the V-type system, both the pump and the probe lasers share the same
F=2 ground level. The probe beam coming out of the cell is detected by a low noise fast photodetector. The resulting spectra show signature of EIT in the "peak" for the
Λ-type system and in the "dip" for the V-type system. Numerical calculation based simulated spectra are also compared with the experimental spectra. In both the cases very narrow EIT linewidth
(Γt<Γ) is observed even at high value of pump Rabi-frequency
(Ωc≫Γ). Narrower value of EIT linewidth is due to Doppler averaging phenomena.
Vector magnetometry was studied using the electromagnetically induced transparency (EIT) with linear
⊥ linear (
lin⊥lin) polarization of the probe and the pump beams in
87Rb -
D2 transition. The dependence of the EIT on the direction 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
σ and
π EIT peaks, the direction of the magnetic field can be found. Moreover from the relative separation between the
σ and
π 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.
We study the phenomenon of electromagnetically induced transparency (EIT) of
87Rb vapor at the temperature of
325K in a magnetic field. Two linearly polarized orthogonal laser fields act on two dipole-allowed transitions of the
D1 line of
87Rb in the $\ensuremath{\Lambda}$ configuration, respectively. In the absence of magnetic fields, we observe a wide EIT window with the contrast of about 66% while when the magnetic field is applied, the wide EIT window is split into three or four narrower subwindows with contrasts of 32% or 16% due to the lifting of magnetic sublevels' degeneracy. The number of EIT subwindows depends on the magnetic field orientation. Our theoretical simulations and analysis are in good agreement with the experimental results.
Abstract We have studied the phenomenon of electromagnetically induced transparency (EIT) of 87 Rb vapor at room temperature in a magnetic field with an arbitrary angle to the laser propagation direction. Rather than exposing atoms to a parallelled or transverse magnetic field as usual, in our work, we apply a magnetic field (up to 45 Gauss) with an arbitrary angle to the laser propagation direction and the spectra become much more complex. More EIT dips are observed due to the Zeeman splitting on the D 2 line of 87 Rb in a Λ -type configuration. With a 5 Torr N 2 buffer gas in the thermal 2 cm vapor cell, the state 5 2 P 3 / 2 has a very short effective lifetime, corresponding to a large energy broadening, which removes the velocity selective optical pumping effect almost completely and keeps the high resolution EIT spectrum for the energy splitting of 87 Rb in magnetic fields. The shifting of the EIT resonances with the strength of the applied magnetic field coincides well with the theory based on a full matrix Hamiltonian combined with a spectral decomposition method. Our work can be extended to measure the magnetic field vector in space. The effects of the detuning of the probe and coupling beams on the spectral lines are also investigated.