IEEE JOURNAL OF SELECTED TOPICS IN QUANTUM ELECTRONICS, VOL. 18, NO. 1, JANUARY/FEBRUARY 2012 541 Using Quantum Coherence to Generate Gain in the XUV and X-Ray: Gain-Swept Superradiance and Lasing Without Inversion Eyob A. Sete, Anatoly A. Svidzinsky, Yuri V. Rostovtsev, Hichem Eleuch, Pankaj K. Jha, Szymon Suckewer, and Marlan O. Scully (Invited Paper) Abstract—It was shown some time ago that when the excitation of an ensemble of two-level atoms is swept in the direction of lasing, so that atoms are prepared in the excited state just as the radiation from previously excited atoms reaches them, the resulting laser amplifier is “highly anomalous” and yields superradiant emission without population inversion. We here show that transient gain in a three-level system has common features with Dicke superradiance and can yield strong extreme ultraviolet lasing in, for example, He atoms (at 58 nm) or He-like ions such as B 3+ (at 6.1 nm). Index Terms—Extreme ultraviolet (XUV), gain-swept superra- diance (GSS), lasing without inversion (LWI), quantum coherence, X-ray. I. INTRODUCTION G AIN-SWEPT superradiance (GSS) in an ensemble of two- level atoms was extensively studied in the 1970s in con- nection with laser lethargy and coherence brightening in the X-ray laser [1]–[3]. In GSS, the inversion is created by inject- ing a short excitation pulse that produces a gain-swept medium. Among other things, it was found that GSS can yield intense pulses without population inversion. This is closely related to Dicke superradiance 1 [4] in which the maximum emission rate Manuscript received November 1, 2010; revised March 9, 2011; accepted March 22, 2011. Date of publication October 14, 2011; date of current version January 31, 2012. This work was supported by the Office of Naval Research under Awards N00014-07-1-1084, N00014-08-1-0948, and N00014-09-1-0888, the Robert A. Welch Foundation under Award A-1261, and the National Science Foundation under Grant EEC-0540832 (MIRTHE ERC). This work was also supported in part by a grant from King Abdulaziz City of Science and Technol- ogy. The work of E. A. Sete was supported by the Herman F. Heep and Minnie Belle Heep Texas A&M University Endowed Fund held and administered by the Texas A&M Foundation. E. A. Sete, A. A. Svidzinsky, H. Eleuch, and P. K. Jha are with Texas A&M University, College Station, TX 77843-4242 USA (e-mail: eyobas@physics.tamu.edu; asvid@jewel.tamu.edu; hichemeleuch@yahoo.fr; pkjha@physics.tamu.edu). Y. V. Rostovtsev is with the University of North Texas, Denton, TX 76203 USA (e-mail: Yuri.Rostovtsev@unt.edu). S. Suckewer is with the Princeton University, Princeton, NJ 08544-5263 USA (e-mail: suckewer@princeton.edu). M. O. Scully is with the Texas A&M University, College Station, TX 077843- 4242, USA and also with the Princeton University, Princeton, NJ 08544-5263 USA (e-mail: scully@tamu.edu). Color versions of one or more of the figures in this paper are available online at http://ieeexplore.ieee.org. Digital Object Identifier 10.1109/JSTQE.2011.2135339 1 Recently, the GSS concept has been applied to the stand-off detection of trace impurities in the atmosphere (see [5]). Fig. 1. Excitation pulse traveling at the speed of light prepares atoms in an excited state, so that the spontaneous emission from atoms excited earlier can be “simultaneous” with excitation by the pump pulse. (a) For the case of two-level atoms, this can yield GSS. (b), (c) Three-level atoms in Λ or Ξ schemes can yield transient LWI under swept gain conditions. occurs when there are equal number of atoms in the excited and ground states, i.e., when the population inversion is zero [see Fig. 1(a)]. Lasing without inversion (LWI) in an ensemble of three- level atoms, with a coupling laser driving two of the levels was demonstrated in the 1990s [see Fig. 1(b) and (c)]. 2, 3 , 4 Those studies involved continuous pumping and were largely in the visible and IR spectral regimes. Most recently, we have been investigating lasing in the extreme ultraviolet (XUV) using gain-swept excitation together with transient LWI 5 [15]. In this paper, we have explored connections between GSS and transient Raman LWI in He atom (ladder scheme), where we have initial Raman inversion yet the system operates without inversion in the lasing transition. Moreover, we have shown a pure transient LWI using He-like ion B 3+ operating at 6.1 nm. Typical results are shown in Fig. 2(a) for the case of ladder Raman lasing in He as sketched in Fig. 2(b). Here, we see 2 The first suggestion of LWI in a three-level system was given in [6]. 3 For more recent LWI theortical work, see [7]–[9]. 4 For the first LWI oscillator demonstrations, see [10] and [11]. 5 The first clear explanation of transient behavior in LWI was given by Harris and Macklin [12]; see also [13]. The papers of Braunstein and R. Shuker on X-ray LWI in a ladder system also include time-dependence effects (see, e.g., [14]). 1077-260X/$26.00 © 2011 IEEE