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arXiv:0901.3790 · Physical Review A

Analysis of electromagnetically induced transparency and slow light in a hot vapor of atoms undergoing collisions

Joyee Ghosh, Rupamanjari Ghosh, Fabienne Goldfarb, J.-L. Le Gouët, Fabien Bretenaker

Published Aug 19, 2009• 44 citations
arXivHTMLPDF

Abstract

We present a detailed theoretical treatment of a three-level $\ensuremath{\Lambda}$ system in a hot atomic vapor interacting with a coupling and a probe field of arbitrary strengths, leading to electromagnetically induced transparency and slow light under the two-photon resonance condition. We take into account all the relevant decoherence processes including collisions. Velocity-changing collisions (VCCs) are modeled in the strong-collision limit effectively, which helps in achieving optical pumping by the coupling beam across the entire Doppler profile. The steady-state expressions for the atomic density-matrix elements are numerically evaluated to yield the experimentally measured response characteristics. The predictions, taking into account a dynamic rate of influx of atoms in the two lower levels of the $\ensuremath{\Lambda}$, are in excellent agreement with the reported experimental results for ${^{4}\text{H}\text{e}}^{\ensuremath{\ast}}$. The role played by the VCC parameter is seen to be distinct from that by the transit time or Raman coherence decay rate.

DOI
10.1103/physreva.80.023817

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We present a realistic theoretical treatment of a three-level Λ system in a hot atomic vapor interacting with a coupling and a probe field of arbitrary strengths, leading to electromagnetically-induced transparency and slow light under the two-photon resonance condition. We take into account all the relevant decoherence processes including collisions. Velocity-changing collisions (VCCs) are modeled in the strong collision limit effectively, which helps in achieving optical pumping by the coupling beam across the entire Doppler profile. We take into account a dynamic rate of influx of atoms in the two lower levels of the Λ, and an outflux from all the three levels. The steady-state expressions for the atomic density-matrix elements are numerically evaluated to yield the experimentally measured response characteristics. Our predictions are in excellent agreement with the reported experimental results for 4He*. The role played by the VCC parameter is seen to be distinct from that by the transit time or Raman coherence decay rate.
We report the experimental observation of transient dynamics in the weak probe coherence under electromagnetically induced transparency (EIT) in hot Rb atoms with a buffer gas. By modulating the control beam in a non-adiabatic fashion, we have examined the corresponding changes in probe transparency. Upon switching the control beam on, the system evolves through multiple dynamical processes before reaching steady-state transparency. We have decoded each of those dynamical processes region by region and notably observed two-photon damped Rabi oscillations, Raman gain, and direct dark state rotation during this evolution. For the theoretical insight, we have numerically solved the time-dependent density matrix elements for a Λ system, incorporating the buffer gas effects phenomenologically into these equations. Our findings provide a detailed understanding of transient and steady-state dynamics in EIT systems, highlighting the interplay between coherent and incoherent processes and the role of the buffer gas in modulating the evolution. The buffer medium extended relevant timescales, thus enhancing the coherence and stability of the atomic system, which are key factors for practical implementations in precision metrology and quantum optics.
For multi-level systems in hot atomic vapors the interplay between the Doppler shift due to atom velocity and the wavenubmer mismatch between driving laser fields strongly influences transmission and absorption properties of the atomic medium. In a three-level atomic ladder-system, Doppler broadening limits the visibility of electromagnetically-induced transparency (EIT) when the probe and control fields are co-propagating, while EIT is recovered under the opposite condition of counter-propagating geometry and kp<kck_{p} < k_{c}kp​<kc​, with kpk_{p}kp​ and kck_{c}kc​ being the wavenumbers of the probe and control fields, respectively. This effect has been studied and experimentally demonstrated as an efficient mechanism to realize non-reciprocal probe light transmission, opening promising avenues for example for realization of magnetic-field free optical isolators. In this tutorial we discuss the theoretical derivation of this effect and show the underlying mechanism to be an avoided crossing of the states dressed by the coupling laser as a function of atomic velocities when $k_{p}
We present a theory of electromagnetically induced transparency (EIT) and slow light in a Doppler broadened three-level ladder (cascade) system incorporating residual Doppler broadening of two-photon coherence and velocity-changing and dephasing collision effects of a buffer gas. Both regimes of wave-vector mismatch occurring when either the probe frequency is higher than that of the (strong) control field or vice versa are considered. It is found that the velocity-changing collisions in general cause narrowing of EIT resonance linewidths which, in a particular wave-vector mismatch regime, can lead to large transparency and slow light generation at relatively low control field intensities. Large collisional dephasing of two-photon coherence in a ladder system, however, tends to mask these effects. A reduction in group velocity by more than 3 orders of magnitude is predicted in the regime where the probe frequency is lesser than that of the control field and in the absence of collisions.
We report a likely observation of cw lasing without inversion in a gas of hot rubidium atoms in an optical cavity under conditions of electromagnetically induced transparency (EIT). The medium is pumped coherently and resonantly by a single ``coupling'' beam which also produces EIT in the lasing transition. The steady-state intensity exhibits thresholds as a function of the atomic density and the strength of the coupling beam. A theoretical model for an effective three-level lambda system indicates that gain without inversion is possible in this system if the two ground states are coupled by depolarizing collisions, and if the decay branching ratios meet certain conditions.
We have experimentally studied electromagnetically induced transparency (EIT) and absorption (EIA) in hot 85Rb atomic vapor using probe and coupling light with comparable power levels. We have shown that strong-probe EIT has different linewidth and appears in fewer configurations than does usual, weak probe EIT. In V-scheme, where optical pumping and saturation are dominant mechanisms, narrow EIT is possible only when a probe is tuned to a closed transition. The width of the EIT resonance increases with laser intensity with non-linear dependence, similar to the weak-probe EIT in Lambda- scheme. The EIT in Lambda- scheme was observed when two transitions had balanced population losses. The EIA was modified for the case of a strong probe as well: in four-level N-scheme with Zeeman sublevels the EIA was observed only for a cycling transition when F'=F+1, where F and F' are the angular momenta of the 5 2S1/2 (ground) and 5 2P3/2 (excited) state hyper-fine levels, respectively. The combination of strong probe and strong coupling laser beam intensities allows observation of an absorption dip due to three-photon resonance in a four-level scheme that involves the Raman transitions via virtual level.