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Physical Review A

Resonantly enhanced refractive index without absorption via atomic coherence

Michael Fleischhauer, Christoph H. Keitel, Marlan O. Scully, Chang Su, B. T. Ulrich, Shi-Yao Zhu

Published Aug 1, 1992• 360 citations
Publisher

Abstract

An enhancement of the index of refraction accompanied by vanishing absorption is shown to be possible in an ensemble of phase-coherent atoms (``phaseonium''). A survey of various possible schemes in which coherence is established by certain coherent or incoherent methods is given, and the main results are compared and contrasted. In particular, the influence of processes such as Doppler broadening that degrade coherence is discussed.

DOI
10.1103/physreva.46.1468

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Refractive index enhancement accompanied by vanishing absorption in a four-level atomic system interacting with two control and two probe fields in a regime of four-wave mixing (FWM) has been predicted and studied in the present work. We analyzed the maximal index enhancement in the four-level FWM system and gave index estimates for a real atomic gas of ${}^{40}$K, taking into account its multilevel structure and collisional and Doppler broadenings at large atomic densities. We also discussed how vanishing absorption with no nearby amplification can be realized in a two species system, consisting of a four-level FWM and a two-level system, where the latter provides additional absorption for one of the probe fields. We numerically estimated the index change in a system composed of ${}^{40}$K and ${}^{39}$K gases.

arXiv:1308.3884•Physical Review A•Sep 30, 2013•9 citations
An enhancement of the index of refraction accompanied by vanishing absorption is shown to be possible in an ensemble of phase-coherent atoms (``phaseonium''). A survey of various possible schemes in which coherence is established by certain coherent or incoherent methods is given, and the main results are compared and contrasted. In particular, the influence of processes such as Doppler broadening that degrade coherence is discussed.
. We investigate the possibility of enhancing the refractive properties in a nonabsorbing medium via two fundamentally different schemes. First there is the coherent preparation of three-level atoms where absorption is cancelled due to destructive interference while the refractivity is not hampered in the same way. There also is the possibility of cancelling absorption via a mixture of absorbing and emitting two-level atoms without the need of a coherent preparation. One drawback here, however, is high sensitivity to Doppler broadening, collisions and number fluctuations which makes this scheme practically infeasible. Introduction The various application of atomic coherence in laser physics and quantum optics has recently attracted considerable interest. It has been shown that atomic coherence can lead to absorption cancellation (Alzetta, et al., 1976; and Gray, et al., 1979) and quenching of spontaneous emission noise (Scully, 1985). More recently, the notion of noninversion lasing has received attention, and it was shown that atomic coherence leading to cancellation of absorption does not necessarily influence emission (Harris, 1989; Scully, et al., 1989; and Kocharovskaya and Khanin, 1988). There has been extensive research on many schemes that involve coherence between an upper or lower level laser doublet due to various means: microwave or Raman coherent coupling and spontaneous and incoherent pumping coupling just to name the most important.
Quantum coherence and correlations in atomic and radiation physics have led to many interesting and unexpected consequences. For example, an atomic ensemble prepared in a coherent superposition of states yields the Hanle effect, quantum beats, photon echo, self-induced transparency, and coherent Raman beats. In fact, in Section 1.4, we saw that the quantum beat effect provides one of the most compelling reasons for quantizing the radiation field. A further interesting consequence of preparing an atomic system in a coherent superposition of states is that, under certain conditions, it is possible for atomic coherence to cancel absorption. Such atomic states are called trapping states †. The observation of nonabsorbing resonances via atomic coherence and interference impacts on the concepts of lasing without inversion (LWI),‡ enhancement of the index of refraction accompanied by vanishing absorption, and electromagnetically induced transparency. In lasing without inversion, the essential idea is the absorption cancellation by atomic coherence and interference. This phenomenon is also the essence of electromagnetically induced transparency. Usually this is accomplished in three-level atomic systems in which there are two coherent routes for absorption that can destructively interfere, thus leading to the cancellation of absorption. A small population in the excited state can thus lead to net gain. A related phenomenon is that of resonantly enhanced refractive index without absorption in an ensemble of phase-coherent atoms ( phaseonium ). In a phaseonium gas with no population in the excited level, the absorption cancellation always coincides with vanishing refractivity.
Systems with atomic coherence can have interesting optical properties, such as non-absorbing resonances or an index of refraction at a frequency of vanishing absorption many orders of magnitude larger than is otherwise possible. This chapter shows that phaseonium can display a large nonlinear Kerr-effect near the atomic resonance while retaining complete transparency. Near resonance nonlinearities are usually accompanied by a large absorption of the medium. A three-level atom is initially prepared in a coherent superposition of the two lower levels. This can be achieved for example by a coherent pulse excitation. The Kerr-coefficient is defined as the coefficient of the first nonlinear correction to the index of refraction.
Refractive index enhancement accompanied by vanishing absorption in a four-level atomic system interacting with two control and two probe fields in a regime of four-wave mixing (FWM) has been predicted and studied in the present work. We analyzed the maximal index enhancement in the four-level FWM system and gave index estimates for a real atomic gas of 40{}^{40}40K, taking into account its multilevel structure and collisional and Doppler broadenings at large atomic densities. We also discussed how vanishing absorption with no nearby amplification can be realized in a two species system, consisting of a four-level FWM and a two-level system, where the latter provides additional absorption for one of the probe fields. We numerically estimated the index change in a system composed of 40{}^{40}40K and 39{}^{39}39K gases.