Probing Anderson Localization in Absorptive Systems with Fidelity Department of Physics Complex Quantum Dynamics and Mesoscopic Physics Group Joshua D.

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Presentation transcript:

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

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

Determining Anderson Localization Extended: Critical: Localized:

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, (2004)

The Loschmidt Demon

Sensitivity to External Perturbations

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

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

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

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

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

Signatures of Localization

Theoretical Modeling

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

Localized Result Localized Result Localized RMT

RMT versus Localized FIDELITY shows effects of LOCALIZATION! Localized: GHz RMT Delocalized: GHz

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

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

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

Perturbative Regime – Experimental

Conclusions Localization in Absorptive Systems CAN be probed with Fidelity!

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

Wigner Regime – Theory & Numerics

Wigner Regime – Experimental

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