1. Probing Anderson Localization in Absorptive Systems with Fidelity Department of Physics Complex Quantum Dynamics and Mesoscopic Physics Group Joshua D. Bodyfelt M.C. Zheng, U. Kuhl, H.-J. Stöckmann, and T. Kottos Collaborators: Research Support: ● Forschergruppe 760 – 'Scattering Systems ● With Complex Dynamics' ● United States–Israel Binational ● Science Foundation (BSF) Dresden, Germany, January 2009

2. Synopsis Introduction What is Anderson Localization? Fidelity – A Measure of Sensitivity Fidelity – Intus Mundus Veris Comin' In & Goin' Out – The Scattering Matrix Scattering Fidelity Experimental Setup & Theoretical Modeling Theory versus Experiment Conclusions

3. Determining Anderson Localization Extended: Critical: Localized:

4. Anderson Localization in Experiments A. Aspect, et al., Nature, 453, 891 (2008) ● BECs in Optical Lattices ● Ultrasound Waves in 3D Elastic Networks B.A. van Tiggelen, et al., Nature Phys. 4, 945 (2008) ● Light Waves in Planar Lattices T. Schwartz, et al., Nature 446, 52 (2007) ● Dynamical Localization in Rough Cavities H. Cao, et al., PNAS, 101, 10498 (2004)

5. The Loschmidt Demon

7. Sensitivity to External Perturbations

8. Fidelity / Loschmidt Echo & Sensitivity F.M. Cucchietti, et al., PRE, 65, 045206 (2002) r p r p H 1 H 2

9. Synopsis Introduction What is Anderson Localization? Fidelity – A Measure of Sensitivity Fidelity – Intus Mundus Veris Comin' In & Goin' Out – The Scattering Matrix Scattering Fidelity Experimental Setup & Theoretical Modeling Theory versus Experiment Conclusions

10. Scattering System Scattering Matrix – Weidenmüller Approach Weidenmüller, Ann. Phys., 158, 120 (1984)

11. From Scattering to Fidelity R. Schäfer, H.J. Stöckmann, T. Gorin, & T.H. Seligman, PRL, 95, 184102 (2005) Theoretical Experimental

12. Quasi-1D Experimental Setup Borland Delphi User Interface Agilent 8720ES Network Analyzer w #1 #2

13. Signatures of Localization Localized Extended A. Genack & A. Chabanov, J. Phys A, 38, 10465 (2005)

14. Signatures of Localization

15. Theoretical Modeling

16. Supersymmetry (RMT) Result R. Schäfer, T. Gorin, et al., PRL 95, 184102 (2005) Delocalized

17. Localized Result Localized Result Localized RMT

18. RMT versus Localized FIDELITY shows effects of LOCALIZATION! Localized: 6.0-7.5 GHz RMT Delocalized: 10.5-12.0 GHz

20. Y. Fyodorov, PRL, 73, 2688 (1994) J. Bodyfelt, M. Zheng, et al., in preparation (2009) Perturbative Regime – Theory

21. Perturbative Regime – Theory & Numerics J. Bodyfelt, M. Zheng, et al., in preparation (2009)

22. Perturbative Regime – Experimental J. Bodyfelt, M. Zheng, et al., in preparation (2009)

23. Perturbative Regime – Experimental

24. Conclusions Localization in Absorptive Systems CAN be probed with Fidelity!

25. D. Cohen, T. Kottos, PRE, 72, 027201 (2005) Wigner Regime – Theory

26. Wigner Regime – Theory & Numerics

27. Wigner Regime – Experimental

28. Conclusions, Revisited Fidelity CAN probe Localization! Wigner: Perturbative: