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The Need for an Open Quantum System Approach to Describe High-Intensity X-ray Interactions with Matter August 3rd, 2010 Nina Rohringer (Lawrence Livermore National Laboratory) This work performed under the auspices of the U.S. Department of Energy by Lawrence Livermore National Laboratory under Contract DE-AC52-07NA27344. LLNL‐PRES‐448504 Lawrence Livermore National Laboratory Non-linear optical physics in the X-ray regime Linear effects (one-photon one-electron interactions): • Coherent diffractive imaging • Time-resolved photo-absorption spectroscopy (RIXS, XANES) • Time-resolved photoelectron spectroscopy • Spectroscopy of highly-charged ions (EBIT) Quantum optics transferred to the X-ray regime Atomic x-ray lasing with innershell transitions Rabi Flopping 3p 3p 2p 2s 2p 2s 0.5 fs 3 fs 1s Rohringer and London, Phys. Rev. A (2010) Option:UCRL# Resonant Raman Scattering 1s Rohringer and Santra, Phys. Rev. A (2008). Option:Directorate/Department Additional Information 2 Non-resonant versus resonant high-intensity x-ray matter interaction Resonant Auger-electron spectrum L. Young et al., Nature 466, 56 (2010) Rohringer and Santra, Phys. Rev. A (2008) Non-resonant interaction 1st user experiment at LCLS on Neon Sequence of one-photon absorption events followed by Auger or radiative decay Model of kinetic rate equations valid Option:UCRL# Resonant interaction Increased coupling strength on resonance Perturbation theory breaks down Non-linear description necessary Optical Bloch equations for a dissipative system Option:Directorate/Department Additional Information 3 Occupation of a specific chargestate / Inensity [arb. unit.] Focusing LCLS into a gas sample of Neon Parameters: pulse of 100 fs, 1012 photons, ω=1.4 keV, focused to 2 µm Option:UCRL# Time [fs] Rohringer and Santra, Phys. Rev. A, (2008). Option:Directorate/Department Additional Information 4 An atomic inner-shell X-ray laser pumped with XFEL radiation based on Neon 2p 2s 2 fs XFEL pump at 1 keV 1s 2p 2s 1s Inner-core photo-ionization Auger decay 160 fs XFEL pump at 1 keV 2p 2s 2p 2s Lasing transition @ 850 eV 1s Spontaneous emission 1s Inner-core photo-ionization Experimental scheme: Atomic gas volume Focused XFEL beam Option:UCRL# Atomic x-ray laser (amplified spontaneous emission) Option:Directorate/Department Additional Information 5 Small-gain parameters at 1 keV pumping energy I(z,t) = I(0,t) ⋅ e g⋅n⋅z (single atom calculcation) Δω /ω = 3⋅10 −4 Ne 1+ Ne 1+ 2p 2p 2s 2s Ne 2+ Ne 2+ 2p 2p 2s 2s Ne 3+ Ne 4+ 2p2p 2s2s Electron–ion collision times: at 100 eV (slow photoelectrons) ≈ 800 fs 1s 1s 1s 1s (for density of 1019 cm-3) at 800 eV1s(fast Auger 1selectrons) ≈ 570 fs Auger decay Double Auger decay ions are at room temperature ! 6 Option:UCRL# Option:Directorate/Department Additional Information One-dimensional self-consistent gain calculation Upper lasing level: X-ray laser flux in forward and backward direction: Atomic x-ray laser Atomic gas volume Focused LCLS beam j(z,t) (amplified spontaneous emission) jXRL(z,t) 2 μm z=L z=0 5 mm Expected output of atomic inner-shell x-ray laser 9x109 photons in XRL line Intensity: 7x1016 W/cm2 Duration: 0.5 fs 0.5 fs 0.75 fs n=4x1018 cm-3, LCLS: 100 fs, 1012 photons per pulse, focal diameter 2 μm Saturation of more than one lasing line seems possible Rohringer and London, Phys. Rev. A (2009). XFEL: 2 µm focus, 5x1012 photons per pulse, 100 fs pulse, 1keV energy gas density: 1x1019 atoms/cm3 Option:UCRL# Option:Directorate/Department Additional Information 9 Gain cross section Number of photons 2p 2s 2p 2s Exponential gain regime 2p 2s 1s 1s 2 2+: 1s 2s22p4 1s At saturation 2p 2s 1s 1+: 1s22s22p5 2+: 2p 2s 1s 3+: 1s12s22p4 2p 2s 2p 2s 1s 1s 1s12s22p5 Output at end of amplifying plasma column for 1 keV pump Pathway to multi-color x-ray fs pump-probe experiments E #(photons) Ipeak 850 eV 3x1010 7x1016 W/cm2 862 eV 4x109 1x1016W/cm2 855 eV 6x107 5x1014W/cm2 To determine spectrum, coherence properties, propagation effects, refraction, etc. -> Solve coupled Maxwell-Bloch equations Option:UCRL# Option:Directorate/Department Additional Information 11 Scheduled experiment of XRL lasing scheme in Sept. 2010 Photo-ionization pumping scheme at different wavelengths Beam waist: ≈1 mm aperture slit ≈2 μm focused LCLS beam (divergence 1 mrad) XRL beam (divergence 0.5 mrad) Gas cell filled with neon (1 atm.) ≈1 m LCLS beam focusing chamber Hutch 1 (AMO) Option:UCRL# AMO high-field chamber CCD grating Chamber for spectrometer Hutch 2 (SXR) Option:Directorate/Department Additional Information 12 Non-linear optical physics in the X-ray regime Atomic x-ray lasing with inner-shell transitions Resonant Raman Scattering Rabi Flopping 3p 3p 2p 2s 2p 2s 3 fs 1s 1s 0.5 fs Option:UCRL# Rohringer and Santra, Phys. Rev. A (2008). 2p 2s 2p 2s 1s 1s Option:Directorate/Department Additional Information 13 Resonant Auger effect at high X-ray intensities, Ne 1s-3p transition, Wave-function approach Coupling strength (Rabi frequency) 3p 3p 2p 2s 2p 2s Ω(t) = E(t) ⋅ 3p z 1s 3p z 1s ≈ 0.01 a.u. 3 fs 1s 1s Rohringer and Santra, Phys. Rev. A (2008) Option:UCRL# Option:Directorate/Department Additional Information 14 Resonant Auger-electron spectrum gets broadened Coherent Gaussian Pulse Single SASE pulse Single SASE pulse Ensemble Average averageover ensemble of pulses Rohringer Option:UCRL# and Santra, Phys. Rev. A (2008) Option:Directorate/Department Additional Information 15 Generalized Bloch equations for open quantum system Calculate time-dependent ionic density matrix Valence Ionization Auger Decay Resonant Coupling 2p 2s 2p 2s 2p 2s 2p 2s 1s 1s 1s or 1s Loss of coherence, Open Quantum System, Unobserved photo electrons ⎡ −iδt R* (t) ⎤ ρ˙11 = ⎢ie ρ21 + cc ⎥ + σ 1 j(t) p0 (t) 2 ⎣ ⎦ R(t) ⎡ ⎤ ρ˙ 22 = −Γ2 ρ22 + ⎢ie iδt ρ12 + cc ⎥ 2 ⎣ ⎦ Γ2 R* (t) −iδt ρ˙12 = − ρ12 + ie ( ρ22 − ρ11 ) 2 2 Rohringer and Santra, work in progress Option:UCRL# Option:Directorate/Department Additional Information 16 Self-Stimulated Resonant Raman Scattering Atomic x-ray lasing with inner-shell transitions Resonant Raman Scattering Rabi Flopping 3p 3p 2p 2s 2p 2s 3 fs 1s 1s 0.5 fs Option:UCRL# Option:Directorate/Department Additional Information 17 Proposed experiment: Resonant pumping scheme 3p 2p 2s K-edge: 1140eV LCLS pump @ 1174 eV 2p 2s 2p 2s ….… 1s 1s Inner-core Auger decay Photo-ionization Ne 1+ Ne 2+ Strong non-linear coupling !! 2p 2s 1174 eV 1s Li-Ne 7+ 2p 2s 1018 eV 3p 2p 2s 3p 1s Resonant excitation He-like Ne 8+ Time 1s 1072 eV 1s Pathway will depend On x-ray intensity ! Comparable oscillator strengths! 3p 174 eV 2p 2s 2p 2s 1008 eV 1s 1s Self-stimulated resonant Raman scattering Option:UCRL# Option:Directorate/Department Additional Information 18 Proposal: Stochastic wave function approach Adopt stochastic wave-function approach from quantum optics Ionic reduced density matrix sampled by ensemble of pure states Ionic wave function evolves deterministic (resonant interaction with XFEL) + random (stochastic) quantum jumps to simulate -photo ionization processes -Auger decay -eventually treat electron impact ionization, excitation, de-phasing Quantum jump approach: Jump operators: derived by semiclassical approximation ? Test on single-atom case by comparing to generalized optical Bloch equations (equivalent descriptions of determining ionic reduced density matrix) dense gas volume/ clusters Focused XFEL beam Option:UCRL# Scattered x-ray light Option:Directorate/Department Additional Information 19 Acknowledgements LLNL: Richard London James Dunn Felicie Albert Sebastien Le Pape Alexander Graf CSU: Jorge Rocca Duncan Ryan Mike Purvis SLAC: John Bozek Christoph Bostedt CFEL: Robin Santra We acknowledge support of this project by LLNLʼs LDRD (Laboratory Directed Research and Development) program. Option:UCRL# Option:Directorate/Department Additional Information 20