Absorption-free superluminal light propagation in a V-type system arXiv:1001.3131v4 [quant-ph] 19 May 2010 Kh. Saaidi, ∗ B. Ruzbahani, and S. W. Rabiei † Physics Department, University of Kurdistan Sanandaj, Iran M. Mahmoudi ‡ Physics Department, Zanjan University, P. O. Box 45195-313, Zanjan, Iran (Dated: December 13, 2018) Dispersion and absorption properties of a weak probe field in a three-level V-type atomic system is studied. By application of indirect incoherent pump fields the effect of populating upper levels on optical properties of the atomic medium in presence of a strong coherent pump field is investigated. It is shown that the slope of dispersion switches from positive to negative just by changing the intensity of the coherent or indirect incoherent pump fields. It is demonstrated that the absorption- free superluminal and subluminal light propagation appear in this system. PACS numbers: 42.50.Gy, 42.25.Hz, 42.25.Bs In the past few decades, there has been tremendous in- terests in the study of subluminal and superluminal light propagation [1–5]. The group velocity of light pulse can be reduced in Bose-Einstein condensate of sodium atom gas [1], and in hot gases [3], and even halted in vapor of Rb atoms [4]. Also, it can exceed the vacuum light speed, c, and can even become negative [5]. These experiments are based on the fact that electromagnetically induced transparency (EIT) and electro magnetically induced ab- sorption (EIA) [6] lead to a dispersion profile with a sharp positive or negative derivative [7, 8]. Anomalous disper- sion was first studied in mechanical oscillators [9] and was later applied by Sommerfeld and Brillouin [10] to light propagation in absorptive opaque materials. They showed theoretically that inside an absorption line, the dispersion can be anomalous, resulting in a group veloc- ity faster than c, the vacuum speed of light. Such an anomalous velocity appears due to the wave nature of light [11, 12]. Talukder et al. have shown femtosecond laser pulse propagation has switched from superluminal to subluminal velocities in an absorbing dye by changing the dye concentration [13]. Shimizu et al. were able to control the light pulse speed with only a few cold atoms in a high-finesse microcavity by detuning the laser fre- quency from a cavity resonance frequency-locked to the atomic transition [14]. In a series of papers [15–22], Chiao and coworkers showed theoretically that anomalous dis- persion can occur inside a transparent material. It was predicted that by using a gain doublet [18], it is possi- ble to obtain a transparent anomalous dispersion region where the group velocity of light pulse exceeds c with al- most no pulse distortion. Wang et al. used gain-assisted linear anomalous dispersion in atomic cesium gas, and the group velocity of a laser pulse in their experiment exceeded c and could even become negative, while the shape of the pulse was preserved [5]. The incoherent pumping fields can also play an important role in the controlling of the group velocity of light in dispersive media [23, 24]. The double-Λ setup is another scheme which provides a very rich spectrum of phenomena based on atomic coherence [25]. Recently, the dispersion and the absorption properties of a weak probe field in simple multi-level quantum systems have been considered [26– 28]. They showed that, by using a coherent and an indi- rect incoherent pump field the group velocity of light can be controlled. There have been only few experimental and theoretical studies in which both free absorption su- perluminal and subluminal light propagation in a single system have been realized. In this article, the dispersion and the absorption properties of a weak probe field in a three-level V-type atomic system is investigated. By application of indirect incoherent pump fields the effect of populating upper levels on optical properties of the atomic medium in presence of a strong coherent pump field is investigated. It is shown that the slope of disper- sion changes from positive to negative just by adjusting the intensity of the coherent or indirect incoherent pump fields. It is demonstrated that the absorption free super- luminal and subluminal light propagation appear in this system. II. THE MODEL AND DISCUSSIONS I. INTRODUCTION The model consists of a closed three-level V-type atomic system with ground level | 1 〉 and two upper levels | 2 〉 and | 3 〉 as shown in Fig.1. A strong coherent coupling field with Rabi frequency Ω$_{c}$ = ⃗ E$_{c}$. ⃗ ℘$_{12}$/ ℏ drives transition | 1 〉 ↔ | 2 〉 , while a weak tunable probe field with Rabi fre- quency Ω$_{p}$ = ⃗ E$_{p}$. ⃗ ℘$_{13}$/ ℏ is applied to transition | 1 〉 ↔ | 3 〉 . Here, ⃗ ℘$_{1}$$_{j}$ ( j = 2 , 3) are the atomic dipole moments, and E$_{c}$ ( E$_{p}$ ) is the amplitude of the coupling (probe) field. $^{∗}$Electronic address: ksaaidi@uok.ac.ir $^{†}$Electronic address: w.rabiei@uok.ac.ir $^{‡}$Electronic address: mahmoudi@iasbs.ac.ir