Attosecond Control and Measurement: Lightwave Electronics

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1 . 3 AT T O S E C O N D A N D H I G H - F I E L D P H Y S I C S D I V I S I O N GRÜNER et al. Design considerations for table-top, laser-based VUV and X-ray free electron lasers 435 tor below 1.1. Furthermore, CSR can be neglected in agreement with the 1D theory. Experimentally the most demanding constraint is that the Pierce parameter is one order of magnitude smaller than in the test case at 130 MeV, hence the electron (slice) energy spread should be as small as 0.1%. This goal seems to be within reach considering the bubble-transformation scenario mentioned above. Without the effect of wakefields GENESIS simulations have shown that this TT-XFEL scenario with an undulator length of only 5 m yields 8 × 10 11 photons/bunch within ∼ 4 fs and 0.2% bandwidth, a divergence of 10 µrad, and a beam size of 20 µm. However, the wakefields become the dominant degrading effect as the required undulator length is larger and the Pierce parameter reduced, hence also the tolerance with respect to variations in the electron energy. But since there is no initial spacecharge-induced energy chirp, one must find another method for compensating the wakefield-induced energy variation. A suitable method for compensating the wakefields for the TT-XFEL would be tapering, i.e., varying the undulator period along the undulator. Due to the fact that the undulator parameter K is smaller than unity, tapering via K, i.e., by gap variation, could only be used as fine-tuning. Depending on the specific material properties of the undulator surface, our first wake calculations show that the bunch center loses over the entire 5 m undulator length about 10% of its initial energy. Due to the linear wake field variation along the bunch only a fraction of it will undergo SASE. A detailed study will be further investigated in a future paper. 2.3 Experimental status In order to demonstrate practical feasibility, we have built and tested a miniature focusing system and undulator consisting of permanent mag- nets. The focusing triplet consists of mini-quadrupoles with an aperture of just 5 mm, hence allowing for measured gradients of 530 T/m. Their focusing strength was measured with a 600 MeV electron beam (at Mainz Microtron facility MAMI, Mainz, Germany). A first test hybrid undulator with a period of only 5 mm and a peak magnetic field strength of ∼ 1 T has been built, and produced, with a 855 MeV beam (also at MAMI), an undulator radiation spectrum as expected. These results will be published elsewhere. 3 Conclusion We have shown by means of analytical estimates and SASE FEL simulations that laser-plasma accelerator-based FELs can only be operated with meter-scale undulators. The key parameter is the ultra-high electron peak current, which significantly reduces the gain length and increases the tolerance with respect to the energy spread and emittance. The latter would also allow increasing of the TT-XFEL photon energy into the medically relevant range of 20–50 keV, because the limiting quantum fluctuations in the spontaneous undulator radiation, scale with γ 4 [25] and the required electron energy of the TT-XFEL is comparatively small. ACKNOWLEDGEMENTS We thank W. Decking, M. Dohlus, K. Flöttmann, T. Limberg, and J. Rossbach (all DESY) for fruitful discussions. Supported by Deutsche Forschungsgemeinschaft through the DFG-Cluster of Excellence Munich-Centre for Advanced Photonics. This work was also supported by DFG under Contract No. TR18. REFERENCES 1 S.P.D. Mangles, C. Murphy, Z. Najmudin, A. Thomas, J. Collier, A. Dangor, E. Divall, P. Foster, J. Gallacher, C. Hooker, D. Jaroszynski, A. Langley, W. Mori, P. Norreys, F. Tsung, R. Viskup, B. Walton, K. Krushelnick, Nature 431, 535 (2004) 164 Max-Planck-Institut für Quantenoptik • Progress Report 2007/2008 2 C.G.R. Geddes, C. Toth, J. van Tilborg, E. Esarey, C. Schroeder, D. Bruhwiller, C. Nieter, J. Cary, W. Leemans, Nature 431, 538 (2004) 3 J. Faure, Y. Glinec, A. Pukhov, S. Kiselev, S. Gordienko, E. Lefebvre, J.-P. Rousseau, F. Burgy, V. Malka, Nature 431, 541 (2004) 4 W.P. Leemans, B. Nagler, A. Gonsalves, C. Toth, K. Nakamura, C. Geddes, E. Esarey, C. Schroeder, S. Hooker, Nature Phys. 2, 696 (2006) 5 R. Neutze, R. Wouts, D. van der Spoel, E. Weckert, J. Hajdu, Nature 406, 752 (2000) 6 A. Baltus, T. Udem, M. Uiberacker, M. Hentschel, E. Goulielmakis, C. Gohle, R. Holzwarth, V.S. Yakovlev, A. Scrinzi, T.W. Hänsch, F. Krausz, Nature 421, 611 (2003) 7 W. Thomlinson, P. Suortti, D. Chapman, Nucl. Instrum. Methods Phys. Res. A 543, 288 (2005) 8 A. Pukhov, J. Meyer-ter-Vehn, Appl. Phys. B 74, 355 (2002) 9 A. Pukhov, S. Gordienko, Philos. Trans. R. Soc. London A 364, 623 (2006) 10 M. Geissler, J. Schreiber, J. Meyer-ter-Vehn, New J. Phys. 8, 186 (2006) 11 D.J. Spence, A. Butler, S. Hooker, J. Opt. Soc. Am. B 20, 138 (2003) 12 http://www.attoworld.de/research/PFS.html 13 R. Bonifacio, C. Pellegrini, L.M. Narduci, Opt. Commun. 50, 373 (1984) 14 S. Reiche, Nucl. Instrum. Methods Phys. Res. A 429, 243 (1999) 15 M. Xie, Nucl. Instrum. Methods Phys. Res. A 445, 59 (2000) 16 Technical Design Report: http://www.hasylab.desy.de/facility/fel/vuv/ ttf2_update/TESLA-FEL2002-01.pdf 17 M.J. de Loos, S.B. van der Geer, Proc. 5th Eur. Part. Acc. Conf., Sitges, 1241 (1996) 18 M. Dohlus, T. Limberg, Proc. FEL 2004 Conf., 18-21 19 G. Fubiana, J. Qiang, E. Esarey, W.P. Leemans, Phys. Rev. ST Accel. Beams 9, 064 402 (2006) 20 E. Saldin, E.A. Schneidmiller, M.V. Yurkov, Nucl. Instrum. Methods Phys. Res. A 417, 158 (1998) 21 K. Floettmann, Astra User’s Manual, 2000, http://www.desy.de/mpyflo/ 22 M. Ferrario, J.E. Clendenin, D.T. Palmer, J.B. Rosenzweig, L. Serafini, Proc. of the 2nd ICFA Adv. Acc. Workshop on “The Physics of High Brightness Beams”, UCLA, Nov., 1999; see also SLAC-PUB-8400 23 A.W. Chao, Physics of Collective Beam Instabilities in High Energy Accelerators (Wiley, New York, 1993) 24 K. Bane, SLAC-PUB-11829 (2006) 25 M. Sands, Phys. Rev. 97, 470 (1955)
Vol 446 | 5 April 2007 |doi:10.1038/nature05648 1 . 3 . 3 S E L E C T E D R E P R I N T S Attosecond real-time observation of electron tunnelling in atoms ARTICLES M. Uiberacker 1,2 , Th. Uphues 3 , M. Schultze 2 , A. J. Verhoef 2,4 , V. Yakovlev 1 , M. F. Kling 5 , J. Rauschenberger 1,2 , N. M. Kabachnik 3,6 , H. Schröder 2 , M. Lezius 2 , K. L. Kompa 2 , H.-G. Muller 5 , M. J. J. Vrakking 5 , S. Hendel 3 , U. Kleineberg 1 , U. Heinzmann 3 , M. Drescher 7 & F. Krausz 1,2,4 Atoms exposed to intense light lose one or more electrons and become ions. In strong fields, the process is predicted to occur via tunnelling through the binding potential that is suppressed by the light field near the peaks of its oscillations. Here we report the real-time observation of this most elementary step in strong-field interactions: light-induced electron tunnelling. The process is found to deplete atomic bound states in sharp steps lasting several hundred attoseconds. This suggests a new technique, attosecond tunnelling, for probing short-lived, transient states of atoms or molecules with high temporal resolution. The utility of attosecond tunnelling is demonstrated by capturing multi-electron excitation (shake-up) and relaxation (cascaded Auger decay) processes with subfemtosecond resolution. With the invention of the laser in 1960 and subsequent advances in ultrashort light pulse generation, light fields with a strength of several volts per angstrom have become routinely available. They rival the fields acting on valence electrons in atomic systems, allowing their release from atoms, molecules and solids. These advances sparked a revolution in studying the interaction of electrons with light. The primary step in strong-field interactions is the liberation of electrons from their atomic bound state. The revolutionary theory of Keldysh1 and subsequent work2–6 suggested that a valence electron may escape by tunnelling through its atomic binding potential suppressed by the light field (Fig. 1a). If the dimensionless parameter: c ~ vL pffiffiffiffiffiffiffiffiffiffiffiffi 2mWb ð1Þ jejE0 is less than one, under the assumption of "vL = Wb ionization is predicted to be confined to short intervals lasting a fraction of the half oscillation cycle of the light field (Fig. 1b). Here E0 and vL stand for the amplitude and angular frequency of the oscillations of the laser electric field EL(t) 5 E0e(t)cos(vLt 1 Q), with e(t) being the amplitude envelope function, and e, m and Wb the charge, mass and binding energy of the electron. Recent studies6 suggest that tunnelling remains the dominant ionization mechanism even for c substantially exceeding one, that is, under conditions when the potential barrier formed by the atomic binding potential and the ionizing light field varies during tunnelling (non-adiabatic regime). In this work we report what we believe is the first real-time observation of light-induced electron tunnelling. The observation of ionization occurring in subfemtosecond steps spaced by the half laser cycle up to values of the Keldysh parameter as high as three is in good agreement with analytic and numerical calculations. Our approach provides experimental access to all forms of optical field ionization— both adiabatic and nonadiabatic tunnelling, as well as barriersuppression ionization—and allows us to test models of these processes for the first time. Once the process of field ionization is fully understood, the technique of attosecond tunnelling will provide direct time-domain insight into a wide range of multi-electron dynamics and electron– electron interactions, ultimately with a resolution approaching the atomic unit of time (,24 as). We demonstrate this potential by probing shake-up and Auger cascade processes with subfemtosecond resolution. Attosecond probing of electron dynamics Figure 2 illustrates different options for attosecond sampling of electronic motion in atoms or molecules. A subfemtosecond extreme ultraviolet (XUV) pulse triggers the motion by exciting a valence or core electron (Fig. 2a, b). The unfolding excitation and relaxation processes (Fig. 2) could, in principle, be probed by a delayed replica of the pulse. However, the low flux of currently available subfemtosecond XUV pulses and the low two-photon transition probabilities in the XUV and X-ray regimes have thwarted this straightforward extension of conventional pump–probe techniques into the XUV– X-ray spectral range. A few-cycle wave of visible or near-infrared (NIR) light with controlled waveform 7 in combination with a highly nonlinear process may replace the subfemtosecond pulse either in probing or starting electron dynamics. This was first demonstrated by attosecond streaking 8,9 : the strong-field interaction of a few-cycle light wave with free electrons released by a subfemtosecond XUV excitation pulse results in broadening and shifting of their final momentum distribution. Recording the streaked spectra of the emitted photo- and Auger electrons versus delay between the XUV pump and the few-cycle laser probe allowed us to retrieve the XUV pulse 10,11 and the laser field 12 as well as the inner-atomic relaxation dynamics 13 with subfemtosecond resolution. Here, we demonstrate that nonlinear interaction of the same light wave with bound electrons ionizes in subfemtosecond steps and hence offers a means of probing intra-atomic and intra-molecular electron dynamics—including when no free electrons are released— by means of attosecond tunnelling. This approach relies on the fact that energetic photo-excitation as well as subsequent rearrangement 1 Department für Physik, Ludwig-Maximilians-Universität, Am Coulombwall 1, 2 Max-Planck-Institut für Quantenoptik, Hans-Kopfermann-Strasse 1, D-85748 Garching, Germany. 3 Fakultät für Physik, Universität Bielefeld, Universitätsstrasse 25, D-33615 Bielefeld, Germany. 4 Technische Universität Wien, Gusshausstrasse 27, A-1040 Vienna, Austria. 5 FOM- Instituut voor Atoom- en Molecuulfysica (AMOLF), Kruislaan 407, 1098 SJ, Amsterdam, The Netherlands. 6 Institute of Nuclear Physics, Moscow State University, Moscow 119992, Russia. 7 Institut für Experimentalphysik, Universität Hamburg, Luruper Chaussee 149, D-22671 Hamburg, Germany. ©2007 Nature Publishing Group Max-Planck-Institut für Quantenoptik • Progress Report 2007/2008 165 627
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Attosecond Control and Measurement: Lightwave Electronics

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