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Scientific Reports

Superluminal light propagation in a three-level ladder system

Piotr Gładysz, Szymon Pustelny, Karolina Słowik

Published Jul 2, 2024• 1 citation
Publisher

Abstract

Superluminal light propagation is typically accompanied by significant absorption that might prevent its observation in realistic samples. We propose an all-optical implementation exploiting the two-photon resonance in three-level media to overcome this problem. With several computational methods, we analyze three possible configurations of optically-dressed systems and identify an optimal configuration for superluminal propagation. Due to the far-detuned operating regime with low absorption, this scenario avoids the usual need for population inversion, gain assistance or nonlinear optical response. Our analysis covers a broad parameter space and aims for the identification of conditions where significant pulse advancement can be achieved at high transmission levels. In this context, a figure of merit is introduced accounting for a trade-off between the desired group-index values and transmission level. This quantity helps to identify the optimal characteristics of the dressing beam.

DOI
10.1038/s41598-024-62220-x

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Superluminal light propagation is typically accompanied by significant absorption that might prevent its observation in realistic samples. We propose an all-optical implementation exploiting the two-photon resonance in three-level media to overcome this problem. With several computational methods, we analyze three possible configurations of optically-dressed systems and identify an optimal configuration for superluminal propagation. Due to the far-detuned operating regime with low absorption, this scenario avoids the usual need for population inversion, gain assistance or nonlinear optical response. Our analysis covers a broad parameter space and aims for the identification of conditions where significant pulse advancement can be achieved at high transmission levels. In this context, a figure of merit is introduced accounting for a trade-off between the desired group-index values and transmission level. This quantity helps to identify the optimal characteristics of the dressing beam.
We investigate a light-pulse propagation with negative group velocity in a nonlinear coherent medium. We show that the necessary conditions for nonlinear superluminal effects to be observable are realized in a three-level $\ensuremath{\Lambda}$ system interacting with a linearly polarized laser field in the presence of a static magnetic field. The initially prepared Zeeman coherence cancels the resonant absorption of the medium almost completely, but preserves its dispersion anomalous and very high. In this medium the light pulse propagates superluminally in the sense that the peak of the transmitted pulse exits the medium before the peak of the incident pulse enters. At the same time the pulse group velocity is intensity dependent, which leads to the self-steepening of the pulse trailing edge due to the fact that the more intense parts of the pulse travel slower. This is in contrast with the shock wave generation in a nonlinear medium with normal dispersion. The predicted effect can be easily observed in the well-known schemes employed in the studies of nonlinear magneto-optical rotation. The upper bound of sample length is found from the criterion that the pulse self-steepening and group-advance time are observable without pulse distortion caused by the group-velocity dispersion.
We analyse the group velocity of a laser pulse in an optically dressed atomic system. A Λ system with an additional close upper level and an incoherent pump is specially investigated. The group velocity of a pulse is strongly dependent on the optical properties of the system which can be modified by changing the amplitude or detuning of a strong coupling field or of an incoherent pump between the two lower levels of the system. Depending on the parameters, the medium may have alternatively absorptive or gain properties and the dispersion can be changed from anomalous into a normal one. The ranges of parameters are especially investigated in which absorption (gain) is not too strong, with dispersion being not too steep. The group velocity of a pulse propagating through a sample with such optical properties can be switched from the subinto superluminal regime. The dynamics of propagation in the case of negative group velocities of a small absolute value is especially interesting. In such a regime the peak of the transmitted pulse exits the sample before the peak of the incoming pulse reaches the medium. The transmitted pulse splits into two pulses - one of them propagates forward behind the medium and the other propagates backward and is cancelled at the entrance of the sample by the incoming pulse. Ranges of parameters are seeked in which the shape of the pulse is changed and the group velocity as a single parameter is not sufficient to describe the pulse propagation.
A dressed-state study of lasing without population inversion from a three-level atom interacting with a bichromatic laser field in the ladder configuration is being formulated. The system is allowed to be dressed by both laser-field photons (double dressing). The temporal behavior of the system under consideration is being explored numerically. Although the use of dressed-basis density matrix equations introduces major complexity into the equations, this procedure has crucial importance to the understanding of the atomic spectrum and the underlying physics of the processes involved. The system is found to possess a gain without population inversion, as well as a regular gain with inversion for various transitions, both in the transient and steady-state regimes. Enhancement of the refractive index accompanied by vanishingly small absorption was also found. The frequency response of various transitions is explored via numerical Fourier analysis. Some transitions are found to exhibit a dispersion-like line shape, clear evidence of a quantum-coherent interference effect. The spectrum consists of two distinct quintets centered about the coupling and probe-laser frequencies. The spectral features consisting of each quintet are located symmetrically (at resonance conditions only) around the line center at positions shifted from the center by the generalized Rabi and double Rabi frequencies.
In this paper we investigate the dispersive and absorptive properties of a system of three-level cascade atoms driven by a strong coherent field. Three characteristic features are found. First, for the same set of atom-light interaction parameters, the indices of refraction are large at three different frequencies where the absorption vanishes. These three frequencies are determined by the resonance transition frequencies between dressed states produced by the strong driving field. Second, negative dispersion without absorption, which leads to superluminal light propagation, is achievable in the central resonance structure of the dispersion spectrum. Third, the whole absorption spectrum displays, in general, three pairs of absorption peaks and three pairs of gain (negative absorption) peaks. The minimal spacing between dressed states determines whether the outer adjacent gain peaks are separated from each other.
We demonstrate that significant effects in the "superluminal propagation" of light pulses cannot be observed without involving systems whose gain explodes outside the pulse spectrum. We explicitly determine the minimum norm of the gain to attain given superluminal effects and the transfer function of the corresponding optimal system. The gain norms, which would be required with the most efficient systems considered up to now (dispersive media, photonic barriers) to attain the same effects, are shown to exceed the minimum by several orders of magnitude. We finally estimate the largest superluminal advances which could be attained in a realistic experiment.
Pulse propagation through 1-dimensional stratified media is studied. The general features of pulse propagation in relation to the delay or advancement of the pulse are discussed. It is shown that in a lossless system with spatial symmetry the reflected and the transmitted pulses have the same delay or advancement. The phase times and the explicit output pulse profiles for an input Gaussian pulse are calculated. While recalling recent results for a variety of systems (resonant absorbers or heterogeneous medium in a Fabry-Perot cavity, a slab of negative index medium, a left-handed/right-handed periodic structure, etc.), new results involving coupled waveguides and a high finesse cavity containing an electromagnetically induced transparency (EIT) medium are presented. Calculations clearly show that for pulses with a carrier tuned at the resonance of the stratified media, one generally has subluminal propagation. Alternatively, in stop gaps or away from the resonances one ends up with superluminal transit. In the case of the EIT cavity it is shown that the large dispersion offered by the intracavity medium can lead to substantial superluminality (ng≃−106) with peak transmission as high as 20%. This is in sharp contrast to large signal attenuation for usual superluminal transit. Note also that EIT, to the best of the authors knowledge, has so far been used to achieve only slow light.