New paradigms for RIXS: 30meV resolution, and reading the quantum interference pattern

New paradigms for RIXS: 30meV resolution, and reading the quantum interference pattern

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## New paradigms for RIXS: 30meV resolution, and reading the quantum interference pattern

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**New paradigms for RIXS: 30meV resolution, and reading the**quantum interference pattern L. Andrew Wray Advanced Light Source, Lawrence Berkeley National Laboratory IXS 2013**Collaborators**Princeton University M. ZahidHasan Yuqi Xia Su-Yang Xu Nasser Alidoust MadhabNeupane SPring-8 K. Ishii K. Ikeuchi BNL Ignace Jarrige Jinsheng Wen Zhijun Xu Genda Gu LBNL ZahidHussain Yi-De Chuang Jonathan Denlinger Shih-WenHuang Wanli Yang RuiminQiao ElkeArenholz UC Berkeley Z. Q. Qiu Jia Li R. Ramesh Jian Liu APS Yuri Shvyd’ko Harvard University Charles Mathy AIST Hiroshi Eisaki Special thanks to TakamiTohyama Kenji Tsutsui R. Eder K. Wohlfeld Dung-Hai Lee Ronny Thomale SumanHossain Sujoy Roy Padraic Shafer IXS 2013**Talk outline**• 1. Introduction • 2. RIXS at high resolution: dd modes in CoO • “pseudo-anti-Stokes” radiation • beyond the atomic multiplet • 3. Quantum interference in RIXS spectra • 2-slit interference in cuprates • transforming into the time domain • interference in arbitrary experimental spectra • 4. Future directions: into the time domain! • A non-Kramers-Heisenberg calculation • New physics with ultrashort pulses • A momentum-resolved thermometer How does high resolution change what you can study with RIXS? Where does quantum interference fit into RIXS analysis and simulation? IXS 2013**ALS MERLIN beamline (4.0.3)**• RIXS at hv~40-120eV • >~10meV RIXS resolution • Polarization control • ARPES at hv~14-120eV IXS 2013**RIXS at the M-edge**SrCuO2 M2,3: 3p½3d (Mn47eV to Cu 77eV) IXS 2013**2**RIXS at high resolution dd modes in CoO ? t2g-egdd mode eg t2g 200meV resolution 30meV resolution dd mode**Temperature dependence from “any old excitation”**Temperature dependence in a large spin3DAF Mott insulator LSMO MI transition K. Ishii, PRB 2004 Inter-site ZRS in quasi-0D C. Monney, PRL 2013 The observation of effects like this is of existential importance for future pump-probe time resolved RIXS IXS 2013**Pseudo-anti-Stokes**pAS will instantly show where the energy is in pump-probe RIXS (AS will show where energy is after 1-2 scattering events) CoO AS states: 20meV: spin 38meV: spin-orbit 47meV: mixed Wray et al., Phys. Rev. B 88, 035105 (2013) IXS 2013**Shaking up the neighbors**Model vs. Data 12 states/Co atom from 0-150meV Poisson AM calc Wray et al., Phys. Rev. B 88, 035105 (2013) IXS 2013**Mini-Summary**• RIXS at high resolution: • Observed “final state shake-up” excitations • Identified a likely role of electronic instabilities • First identification of “pseudo-anti-Stokes” • Will be an important q-independent signal in the time domain • Just one of many kinds of temperature dependence yet to be seen in RIXS IXS 2013**3**Quantum interference in RIXS spectra When a particle follows two different paths that arrive at the same place, at the same time**Cuprateorbitons (SrCuO2)**RIXS with just two core hole symmetries! You don’t need a ‘real’ AM calculation to understand cuprate RIXS: see Sala et al., New J. Phys. 13, 043026 (2011) IXS 2013**Transforming to the time domain**RIXS with a 100as X-ray pulse: Knowing amplitudes and phases lets you take Kramers-Heisenberg into the time domain! IXS 2013**Direct, indirect and elastic scattering**SIAM Charge Transfer (NiO) ~0.2fs~1/ESOC See definitions in L. Ament review [RMP 83, 705 (2011)] IXS 2013**4**Future directions into the time domain! Have you ever seen the momentum-vs-energy dispersion relation of a Cooper pair? RIXS gives information other spectroscopies are blind to RIXS with sub-fs pulses and time-resolved (pump-probe) capabilities will take X-ray science to new places Wenceslas Hollar, 17th century**Self consistent lifetime correction (SCLC)**SCLC(1): the natural answer for Kramers-Heisenberg SCLC(∞): the non-perturbative answer for a Hamiltonian K. Okada, A. Kotani, H. Ogasawara, Y. Seino, B. T. Thole, PRB 47, 6203 (1993); L. A. Wray et al., PRB 86, 195130 (2012). IXS 2013**Beyond Kramers-Heisenberg**Another way to get a coherent core hole is to use a coherent, sub-femtosecond X-ray pulse. IXS 2013**Changing the core hole clock**L-edge SCLC(∞) KH Core hole decay is ~20% faster on a small time scale, during overlap with the 100as incident pulse. Same effect at the L- and K- edges! IXS 2013**Tracking energy in time and momentum**pAS will instantly show where the energy is in pump-probe RIXS (AS will show where energy is after 1-2 scattering events) CoO AS states: 20meV: spin 38meV: spin-orbit 47meV: mixed Wray et al., Phys. Rev. B 88, 035105 (2013) IXS 2013**K**L M Excitation Mechanisms 1. Atomic monopole shake-up Features: 1. Broad Q-dependence 2. Large resolving power Excitation Mechanisms 1. Atomic multipole 2. Intersite/intrabandmonopole Features: 1. High throughput! 2. Weak elastic line! • Excitation Mechanisms • 1. Strong atomic multipole • 2. 10-30meV resolution: • Final state shake-up • T-dependence • Features: • Strong quantum interference • Surface sensitivity to several unit cells Now Near Future A cleaner elastic tail? • Resolution similar to ARPES • resolving electronic superstructure and susceptibility features Resolution similar to kBT! Flux δE~5meV Laser coherence ?**Summary**• RIXS at high resolution: • Observed temperature dependence in a simple orbiton • First observation of “pseudo-anti-Stokes” radiation • Identified many-body spectral structure in simple orbitons • Quantum interference • Fitted phase information from 2-slit interference in cuprates • Experimental RIXS data transformed into the time domain for the first time • Introduced ζ function to identify interference in arbitrary experimental spectra • QI in core hole decay improves multiplet and ultrafast simulations Color codeblack: M only blue: M, L and K! IXS 2013**M vs L vs K**M Fast resonance processes Elastic Fano effect 1/q~20nm Best current resolution (10meV) • L • 1/q~10nm • Best flux • Large spin-orbit coupling gives strong spin cross section K 1/q<< lattice constant**Energy resolution and the time scale of dynamics**Energy resolution sets the observable time scale. With 200meV resolution, you have ~3fs. With 20meV resolution, you have ~30fs Low energy resolution: local physics High energy resolution: less local physics Excitations that take a long time to emerge can only be studied with high resolution IXS 2013**Fano tails**IXS 2013**The dynamics of RIXS**“What is the RIXS spectral function?” RIXS reveals a spectral decomposition of the many-body quantum state in the time window of core hole decay. Kramers-Heisenberg equation IXS 2013**When is a core hole not a core hole?**Ni orbitals in NiO 2p Electron probability density 3s 3p 3d Radial distance (Angstroms) IXS 2013