Population inversion X-ray laser oscillator Aliaksei Halavanaua, Andrei Benediktovitchb, Alberto A. Lutmanc , Daniel DePonted, Daniele Coccoe , Nina Rohringerb,f, Uwe Bergmanng , and Claudio Pellegrinia,1 aAccelerator Research Division, SLAC National Accelerator Laboratory, Menlo Park, CA 94025; bCenter for Free Electron Laser Science, Deutsches Elektronen-Synchrotron, Hamburg 22607, Germany; cLinac & FEL division, SLAC National Accelerator Laboratory, Menlo Park, CA 94025; dLinac Coherent Light Source, SLAC National Accelerator Laboratory, Menlo Park, CA 94025; eLawrence Berkeley National Laboratory, Berkeley, CA 94720; fDepartment of Physics, Universitat¨ Hamburg, Hamburg 20355, Germany; and gStanford PULSE Institute, SLAC National Accelerator Laboratory, Menlo Park, CA 94025 Contributed by Claudio Pellegrini, May 13, 2020 (sent for review March 23, 2020; reviewed by Roger Falcone and Szymon Suckewer) Oscillators are at the heart of optical lasers, providing stable, X-ray free-electron lasers (XFELs), first proposed in 1992 transform-limited pulses. Until now, laser oscillators have been (8, 9) and developed from the late 1990s to today (10), are a rev- available only in the infrared to visible and near-ultraviolet (UV) olutionary tool to explore matter at the atomic length and time spectral region. In this paper, we present a study of an oscilla- scale, with high peak power, transverse coherence, femtosecond tor operating in the 5- to 12-keV photon-energy range. We show pulse duration, and nanometer to angstrom wavelength range, that, using the Kα1 line of transition metal compounds as the but with limited longitudinal coherence and a photon energy gain medium, an X-ray free-electron laser as a periodic pump, and spread of the order of 0.1% (11). They have also been shown a Bragg crystal optical cavity, it is possible to build X-ray oscillators to be a very effective pump for creating population inversion in producing intense, fully coherent, transform-limited pulses. As an an atomic gain medium, because of the high peak power at the example, we consider the case of a copper nitrate gain medium required photon energy. This capability has been demonstrated generating ∼ 5 × 1010 photons per pulse with 37-fs pulse length in experiments of amplified spontaneous emission (ASE) in a Ne and 48-meV spectral resolution at 8-keV photon energy. Our theo- gas (12), Cu metal foils (13), and, recently, Mn solutions (14). An retical study and simulation of this system show that, because of intense pump pulse creates a 1-s core hole, and spontaneously the very large gain per pass, the oscillator saturates and reaches emitted K α1 fluorescence photons along the direction of the full coherence in four to six optical-cavity transits. We discuss the population inversion are amplified. Large values of gain (up to 6 7 feasibility and design of the X-ray optical cavity and other parts 2 × 10 ) were observed, and K α1 ASE pulses of up to 8 × 10 of the oscillator needed for its realization, opening the way to photons per pulse were generated starting from noise (14). How- PHYSICS extend X-ray–based research beyond current capabilities. ever, ASE pulses typically have a large energy bandwidth and are not transform limited. X-ray laser j amplified spontaneous emission j X-ray cavity j Most XFELs operate also in ASE, or self-amplified sponta- transform-limited pulses neous emission (SASE), as it is called in the XFEL community. In SASE mode (15, 16), the X-ray pulse starts from electron shot noise. To improve longitudinal coherence and fluctuations, seed- ince the time Maiman built the first ruby laser in 1960, ing with external lasers has been successfully implemented for Sdeveloping an X-ray laser has been a major goal in laser wavelengths larger than a few nanometers (17–22). For harder physics. A laser generating high-intensity, coherent X-ray pulses X-rays, self-seeding systems have been employed to reduce the at angstrom wavelength and femtosecond pulse duration—the energy bandwidth by an order of magnitude, e.g., at Linac Coher- characteristic time and length scale for atomic and molecular ent Light Source (LCLS) from about 10−3 to 10−4, but the phenomena—allows imaging of periodic and nonperiodic sys- pulses are not transform limited and suffer from large intensity tems, noncrystalline states, studies of dynamical processes in fluctuations (23–31). To produce transform-limited free-electron systems far from equilibrium, nonlinear interactions, and X-ray laser (FEL) pulses, one can reduce the pulse duration down quantum optics, opening a window into electronic, atomic, and molecular phenomena of interest to biology, chemistry, materials science, and physics (1). Significance In the atom-based population-inversion laser approach, this task was extremely difficult, because of the very short lifetime An X-ray oscillator generating fully coherent pulses at the of excited atom-core quantum-energy levels, as pointed out ini- characteristic length and time scale of atomic and molecu- tially by Schawlow and Townes (2). Chapline and Wood of lar phenomena, angstrom wavelength, and femtosecond time Lawrence Livermore National Laboratory (LLNL) estimated duration has been a dream of laser physics from the 1960s. The that the radiative lifetime of an X-ray laser transition would be paper presents a study of an X-ray oscillator based on popula- about 1 fs times the square of the wavelength in angstroms (3). tion inversion of Kα electrons in a transition-metal compound, The short lifetime and large energy needed to excite inner-shell generating fully coherent, transform-limited, high-power radi- atomic levels, 1 to 10 keV compared to about 1 eV for visible ation pulses, in the 3- to <1-A˚ wavelength region, with lasers, requires very large pumping power to attain population a high-energy resolution, about 0.05 eV, showing that the inversion. No pump available at that time could generate the dream can now become a reality. The X-ray laser oscillator will required power. It has been reported that LLNL scientists used open experimental possibilities and research areas in quan- a nuclear device to pump an X-ray laser in the 1980s (4). The tum optics, chemical dynamics, imaging, spectroscopy, and development of high-peak-power, short-pulse, visible-light lasers interferometric measurements. made possible another approach: pumping cylindrical plasmas, in some cases also confining the plasma with magnetic fields. Author contributions: A.H., U.B., and C.P. designed research; A.H., D.D., D.C., and U.B. X-rays from the hot plasma pumped the laser. These experi- performed research; A.B. and N.R. contributed new reagents/analytic tools; A.H., A.B., ments led to X-ray lasing around 18 nm with gain of about 100 in A.A.L., N.R., and C.P. analyzed data; and A.H., A.A.L., U.B., and C.P. wrote the paper.y 1985 (5, 6). More work has been done from that time, and las- Reviewers: R.F., University of California Berkeley; and S.S., Princeton University.y ing has been demonstrated at several wavelengths in the soft The authors declare no competing interest.y X-ray region, however, with limited peak power and tunability. Published under the PNAS license.y A review of the most recent work and developments with this 1 To whom correspondence may be addressed. Email: [email protected] approach is given in ref. 7. www.pnas.org/cgi/doi/10.1073/pnas.2005360117 PNAS Latest Articles j 1 of 6 Downloaded by guest on September 25, 2021 Excited state X-Ray Laser Oscillator Delay Auger 1 The X-ray laser oscillator (XLO) system described here and KB mirrors shown in Fig. 1 starts with a SASE pump pulse that creates a 1-s Liquid jet core hole population inversion followed by ASE in a liquid jet. Ground state SASE pulse train To study the physics of the system, we consider, as an example, a lasing medium formed by a jet of concentrated cupric nitrate [Cu(NO3)2] solution, with 4.2 Cu atoms per cubic nanometer. CRLs We have chosen a cupric nitrate solution as a gain medium because the copper K α1 photon energy at 8 keV is widely used Outcoupling crystal in X-ray science. Furthermore, cupric nitrate is soluble in high concentrations, does not contain any heavy elements that would reduce the gain by absorbing 8-keV photons, and is straightfor- ward to handle. It is important to note that our results for copper apply, with only minor changes, to other elements, providing a Fig. 1. XLO schematics. A train of SASE pump pulses with spacing τ passes lasing range of 5 to 12 keV. After the ASE gain in the first pass, through a semitransparent crystal and impinges on a liquid jet sample, cre- the K α1 signal was recirculated through the cavity and matched ating population inversion. The first pulse generates ASE of the Kα1 line, with the arrival of subsequent XFEL pulses. This created seeded which is recirculated through a cavity with a roundtrip time that matches τ, stimulated emission in each subsequent pass, including losses in seeding the stimulated emission in the subsequent passes. When saturation the cavity. is reached after four to eight passes, the XLO pulse is outcoupled by rapidly To analyze the XLO performance, we first considered the switching the outcoupling crystal into an off-Bragg condition. Note that in amplification process in the lasing medium. The emission from the figure, the separation between X-ray pump pulses and the cavity size is the population-inverted medium was calculated by using a not to scale. The energy diagram for population inversion (top right) and principles of ASE (middle left) and seeded stimulated emission (bottom left) correlation-function approach (49, 50).