• Electromagnetically-Induced-Transparency
• Fast-light
• Lambda-system
• Metastable Helium
• Slow-light
• Tripod-system.

Electromagnetically induced transparency (EIT) is a quantum interference phenomenon. It consists in the trapping of atoms in a dark-state via absorption-emission cycle, induced by a coupling laser. A weak probe field is used to scan the induced transparency, which occurs in a restricted range (EIT window) for coupling-probe detuning. For metastable Helium at room temperature the EIT width is of order of tens kHz. In this spectral range the group velocity of light undergoes a strong slowdown due to the slope of dispersion curve. This phenomenon is called “slow-light”. Varying the coupling field frequency it is possible to change the dispersion curve and obtain a negative slope, which leads to group velocity greater than c (“fast-light”), or with negative values [1]. The theoretical model used to describe the phenomenon consists in describing the energy level of the atoms with a three-level Λ-system, that interacts with two coherent laser fields (coupling and probe). Using the density matrix formalism, imposing the condition of atoms trapped in a dark state, it is possible to calculate the susceptibility of the medium at steady state regime. I have used these results to elaborate a simulation, with Mathematica, of a Gaussian pulse propagating through a finite medium where EIT phenomenon is obtained and the group velocity undergoes a slowdown. I have also studied the propagation of the beam in the “fast-light” regime. Using a D0 transition for metastable Helium, instead of D1 transition used for the Λ- system, it is possible to isolate a four-level tripod system. By applying a uniform and constant magnetic field to metastable Helium atoms, it is possible to remove the levels degeneracy. In a preliminary work [2] two configurations have been studied: the first with probe and coupling beams respectively perpendicular and parallel to the magnetic field, and the second with probe and coupling beams respectively parallel and perpendicular to the magnetic field. For the first configuration two detuned EIT peaks have been observed. The two peaks are the results of the incoherent superposition of two Λ-systems, in which we can decompose the original tripod configuration. In the second case two detuned EIT peaks have been observed with an extra absorption dip at the line center. The tripod system has been interpreted as the coherent superposition of two Λ-systems that destructively interfere at the line center. During my internship I have participated to the extension of this work. We have analyzed the case of a probe polarization rotated of an angle θ with respect the quantization axis and an orthogonal coupling beam polarization. As θ approaches 45◦ five symmetrically detuned transmission peaks appear. We have interpreted the 4 detuned transmission peaks as EIT resonances of several Λ-systems while the fifth central peak cannot be related to any Λ- system leading us to consider that is not related to an EIT resonance. We have studied a second configuration with non-orthogonal probe and coupling field polarizations. We have observed that changing the angles of the polarization vectors with respect to the quantization axis absorptions dip occur at same detuning at which we have previously observed transmission peaks.
All the experiments have been realized at Laboratoire Aim ́e Cotton where I have spent five months in a training.The Heads of training were Professor Fabien Bretenaker and Assistant Professor Fabienne Golfarb.
References
[1] F. Golfarb, T.Laupretre, J. Ruggiero, F. Bretenaker J. Ghosh, and R. Ghosh. Electromagnetically- induced transparency, slow light, and negative group velocities in a room temperature vapor of 4He*. C.R. Physique, 10, 2009.
[2] S.Kumar, T.Laupretre, R. Ghosh, F. Bretenaker, and F. Goldfarb. Interacting double dark resonances in a hot vapor helium. PRA, 84:023811, 2011.