Springer Series in CHEMICAL PHYSICS Springer-Verlag Berlin Heidelberg GmbH ONLINE LIBRARY Physics and Astronomy http://www.springer.de/phys/ Springer Series in CHEMICAL PHYSICS Series Editors: F. P. Schafer J. P. Toennies W. Zinth The purpose of this series is to provide comprehensive up-to-date monographs in both well established disciplines and emerging research areas within the broad fields of chemical physics and physical chemistry. The books deal with both fun damental science and applications, and may have either a theoretical or an experi mental emphasis. They are aimed primarily at researchers and graduate students in chemical physics and related fields. 63 Ultrafast Phenomena XI Editors: T. Elsaesser, J.G. Fujimoto, D.A. Wiersma, and W. Zinth 64 Asymptotic Methods in Quantum Mechanics Application to Atoms, Molecules and Nuclei By S.H. Patil and K.T. Tang 65 Fluorescence Correlation Spectroscopy Theory and Applications Editors: R. Rigler and E.S. Elson 66 Ultrafast Phenomena XII Editors: T. Elsaesser, S. Mukamel, M.M. Murnane, and N.F. Scherer 67 Single Molecule Spectroscopy Nobel Conference Lectures Editors: R. Rigler, M. Orrit, T. Basche 68 Nonequilibrium Nondissipative Thermodynamics With Application to Low-Pressure Diamond Synthesis By J.-T. Wang 69 Selective Spectroscopy of Single Molecules By I.S. Osad'ko Series homepage - http://www.springer.de/phys/books/chemical-physics/ Volumes 1-62 are listed at the end of the book Igor S. Osad'ko Selective Spectroscopy of Single Molecules With 87 Figures i Springer Professor Igor S. Osad'ko Lebedev Physical Institute of RAS Department of Luminescence Leninsky Pr., 53 119991 Moscow, Russia Series Editors: Professor EP. Schăfer Professor W. Zinth Max-Planck-Institut fiir Biophysikalische Chemie Universităt Miinchen, 37077 Gottingen-Nikolausberg, Germany Institut fiir Medizinische Optik Ottingerstr. 67 Professor J.P. Toennies 80538 Miinchen, Germany Max-Planck-Institut fiir Stromungsforschung Bunsenstrasse 10 37073 Gottingen, Germany ISSN 0172-6218 ISBN 978-3-642.-07903-0 Library of Congress Cataloging-in-Publication Data applied for. Die Deutsche Bibliothek -CIP-Einheitsaufnahme Osad'ko, Igor' S.: Selective spectroscopy of single molecules/Igor S. Osad'ko. - Berlin; Heidelberg; New York; Hong Kong; London; Milan; Paris; Tokyo: Springer, 2002 (Springer series in chemical physics; 69) (Physics and astronomy online library) ISBN 978-3-642-07903-0 ISBN 978-3-662-05248-8 (eBook) DOI 10.1007/978-3-662-05248-8 This work is subject to copyright. AII rights are reserved, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, reproduction on microfilm or in any other way, and storage in data banks. Duplication of this publication or parts thereof is permitted only under the provisions of the German Copyright Law of September 9, 1965, in its current version, and permission for use must always be obtained from Springer-Verlag. Violations are liable for prosecution under the German Copyright Law. http://www.springer.de © Springer-Verlag Berlin Heidelberg 2003 Originally published by Springer-Verlag Berlin Heidelberg New York in 2003 Sofl:cover reprint of the hardcover 1St edition 2003 The use of general descriptive names, registered names, trademarks, etc. in this publication does not imply, even in the absence of a specific statement, that such names are exempt from the relevant protective laws and regulations and therefore free for general use. Typesetting: Camera-ready copy by the author Cover concept: eStudio Calamar Steinen Cover production: design & production GmbH, Heidelberg Printed on acid-free paper SPIN: 10867292 57/3141 -5 43210 Preface The main topic in this book is the low temperature selective spectroscopy of impurity centers. It deals not only with the well developed methods of selective spectroscopy of molecular ensembles such as spectral hole-burning, fluorescence line-narrowing and femtosecond photon echoes, but also new methods of nanospectroscopy such as single-molecule spectroscopy. Both the ory and experimental data are discussed. Theory united with experimental data enables one to organize the experimental facts. This organization is of great importance, especially for young researchers and students, because it can provide better insight into the nature of the rather complicated dynamics of guest molecules in polymers and glasses, where our understanding is still somewhat lacking. The book mainly addresses young researchers and graduate students studying modern methods of spectroscopy of solid solutions. For this rea son, all formulas commonly used in practice are derived in this book. The reader will also find new approaches and formulas which have been used by the author, but are not well known to the majority researchers. When the derivation of a formula seems rather complicated, it is included in appendix. The reader is then free to look the derivation up if he or she is interested. Oth erwise, the book can be read without reference to these sections. The book includes many examples where theory helps us to interpret experimental data of various types, for instance, the data on line- and hole-broadening. The theory presented in the book includes my original results. These were obtained in collaboration with my students S.N. Gladenkova, A.U. Jal mukhambetov, S.A. Kulagin, M.A. Mikhailov, A.A. Shtygashev, S.L. Solda tov, L.B. Yershova, and N.N. Zaitsev. I thank them and Dr. L.A. Bykovskaya for their help, criticism and collaboration. I am also grateful to Prof. Michel Orrit for valuable discussions when I started research on single molecules in his group at Bordeaux University. Some problems presented in the book have already been discussed in my lectures for graduate students at the Moscow State Pedagogical University and for Soros teachers in Russian schools. This experience was used while writing the book. I thank Prof. M.D. Galanin for comments on the Russian version of the book issued by Nauka Publishing House and graduate student Michel Savin who prepared the J5\TEX version of this book. Moscow, July 2002 1. S. Osad 'ko Contents Introduction. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 Part I. Single Atom in Thansverse Electromagnetic Field 1. Quantum Principles of Two-Level Atomic Spectroscopy. . . 7 1.1 Hamiltonian of an Electron-Photon System. . . . . . . . . . . . . . . . 7 1.2 Transverse Electromagnetic Field as a Photon Gas. . . . . . . . . . 9 1.3 Electron-Photon Interaction. Rabi Frequency. . . . . . . . . . . . .. 13 1.4 Equations for Transition Amplitudes. . . . . . . . . . . . . . . . . . . . .. 16 1.5 Density Matrix of the System. Relation to Transition Amplitudes. . . . . . . . . . . . . . . . . . . . . . .. 18 2. Two-Photon Start-Stop Correlator . . . .. . . . . . . . . . . . . . . . . .. 21 2.1 Photon Counting in the Start-Stop Regime. . . . . . . . . . . . . . .. 21 2.2 Spontaneous Fluorescence. Temporal Evolution of Fluorescence Line Shape . . . . . . . . . . .. 22 2.3 Optical Absorption Line. Equations for Transition Amplitudes. . . . . . . . . . . . . . . . . . . . .. 27 2.4 Temporal Evolution of Probabilities. . . . . . . . . . . . . . . . . . . . . .. 30 2.5 Temporal Evolution of Absorption Line Shape ............. 33 2.6 Two-Photon Start--Stop Correlator ....................... 35 3. Full Two-Photon Correlator ... . . . . . . . . . . . . . . . . . . . . . . . . . .. 39 3.1 Counting All Photon Pairs. . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 39 3.2 Infinite Set of Equations for Transition Amplitudes. Discussion of Main Approximations. . . . . . . . . . . . . . . . . . . . . .. 40 3.3 Equations Governing the Full Two-Photon Correlator . . . . . .. 43 3.4 Relating the Full and Start-Stop Two-Photon Correlators. . . . . . . . . . . . . . . . . .. 46 3.5 Frequency and Time Dependence of Full and Start-Stop Two-Photon Correlators ............ 48 VIII Contents Part II. Phonons and Tunneling Excitations 4. Adiabatic Interaction. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 55 4.1 Theoretical Description of Interacting Electrons and Nuclei.. 55 4.2 Franck-Condon and Herzberg-Teller Interactions. . . . . . . . . .. 57 5. Natural Vibrations of Solids. . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 61 5.1 Acoustic and Optical Phonons ........................... 61 5.2 Localized Phonon Modes. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 65 6. Tunneling Systems in Solids ..... . . . . . . . . . . . . . . . . . . . . . . . .. 75 6.1 Tunneling Degrees of Freedom in Complex Molecules and Amorphous Solids .............. 75 6.2 Rate Equations for Tunneling Systems .................... 78 6.3 One-Phonon Transition Probabilities in Tunneling Systems .. 80 6.4 Kinetics of Tunneling Systems ........................... 84 6.5 Tunneling Systems in Polymers and Glasses. . . . . . . . . . . . . . .. 86 6.6 Two-Level Systems (TLS). Tunnelons. Tunnelon-Phonon and Elect ron-Tunnelon Interaction. . . . . .. 90 Part III. Spectroscopy of a Single Impurity Center 7. Density Matrix for an Impurity Center. . . . . . . . . . . . . . . . . .. 95 7.1 Transition Amplitudes in the Electron-Phonon-Tunnelon System. . . . . . . . . . . . . . . .. 95 7.2 Equations for the Density Matrix. . . . . . . . . . . . . . . . . . . . . . . .. 99 7.3 Reducing Equations for the Full Density Matrix to the Optical Bloch Equations ........................... 104 8. One- and Two-Photon Counting Methods in the Spectroscopy of a Single Impurity Center .......... 109 8.1 Two-Photon Correlator for a Two-Level Impurity Center .... 109 8.2 Influence of a Triplet Level on the Two-Photon Correlator. Photon Bunching and Antibunching ...................... 112 8.3 One-Photon Counting Method. Quantum Trajectories ....... 119 Contents IX Part IV. Optical Band Shape Theory for Impurity Centers 9. Stochastic Theories of Line Broadening ................... 125 9.1 Dynamic and Stochastic Approaches to the Line-Broadening Problem .......................... 125 9.2 Stochastic Theory Due to Anderson and Weiss ............. 126 9.3 Anderson Theory for Optical Lines ....................... 129 9.4 Exchange Model for Line Broadening ..................... 131 10. Dynamical Theory of Electron-Phonon Bands ............ 137 10.1 Absorption Cross-Section and the Probability of Light Emission ..................... 138 10.2 Electron-Phonon Optical Transitions in a Condon Approximation at T = 0 ..................... 139 10.3 Zero-Phonon Line and Phonon Side Band ................. 142 10.4 Influence of Temperature on the ZPL Intensity ............. 149 10.5 Optical Bands for Strong Electron-Phonon Coupling ........ 150 11. Vibronic Spectra of Complex Molecules .................. 153 11.1 Vibronic Spectra in the Condon Approximation. Similarity Rule in Vibronic Spectra ....................... 153 11.2 Influence of the HT Interaction on Optical Bands ........... 156 11.3 Interference of HT and FC Amplitudes. Breakdown of the Mirror Symmetry of Conjugate Absorption and Fluorescence Bands ........... 158 11.4 Theoretical Treatment of Electron-Phonon and Vibronic Spectra ................. 161 12. Dynamical Theory of Line Broadening .................... 167 12.1 Specific Features of the Quadratic FC Interaction ........... 168 12.2 Cumulant Expansion of the Dipolar Correlator ............. 170 12.3 Broadening and Shift of the ZPL at Weak Coupling with Acoustic and Localized Phonons . . . . . . . . . . . . . . . . . . . . . 173 12.4 Quantum Phonon Green Functions ....................... 177 12.5 Temperature Broadening and Shift of the ZPL at Arbitrary Strength of the Quadratic FC Interaction ...... 179 12.6 General Expression for the Cumulant Function of an Electron-Phonon System ........................... 186 12.7 Theoretical Treatment of Experimental Data for Temperature Broadening of the ZPL ................... 187 X Contents Part V. Methods of Selective Spectroscopy 13. Fluorescence Line Narrowing ............................. 195 13.1 Frequency Selection of Molecules by Laser Excitation ....... 195 13.2 Fluorescence Line Narrowing and Its Relation to the Full Two-Photon Correlator ......... 198 13.3 Laser Fluorescence Analysis ............................. 202 14. Spectral Hole Burning in Inhomogeneous Optical Bands .. 205 14.1 Transient Spectral Hole Burning. Relation to the Full Two-Photon Correlator ................ 205 14.2 Persistent Spectral Holes ................................ 209 14.3 Kinetics of Persistent Hole Burning. Hole Shape in the Short Time Limit ...................... 213 14.4 Hole Burning with Photoactive Photoproduct. Antiholes ..... 216 14.5 Polarization Aspects in Spectral Holes and Antiholes ........ 221 14.6 Photon-Gated Persistent Spectral Hole Burning ............ 226 Part VI. Transient Coherent Phenomena in Solids 15. Coherent Radiation of Molecular Ensembles .............. 233 15.1 Dephasing and Energy Relaxation. Coherent Spontaneous Emission . . . . . . . . . . . . . . . . . . . . . . . . . . 233 15.2 Fast Optical Dephasing ................................. 237 16. Photon Echo .............................................. 241 16.1 Interaction of a Single Atom with a Classical Electromagnetic Field .................... 241 16.2 Molecule Interacting with a Classical Electromagnetic Field, Phonons, and Tunnelons ................................ 244 16.3 Simplest Theory of the Two-Pulse Photon Echo ............ 246 16.4 Bloch Vector and Its Temporal Evolution .................. 249 16.5 Exponential Two-Pulse Photon Echo ...................... 251 16.6 Three-Pulse Photon Echo ................................ 255 16.7 Long-Lived 3PE ........................................ 258 16.8 Space Anisotropy of Echo Radiation ...................... 261 17. Nonexponential Photon Echo ............................. 263 17.1 Generalized Bloch Vector ................................ 263 17.2 Long-Lived Stimulated Photon Echo ...................... 265 17.3 Picosecond SPE ........................................ 271 17.4 Two-Pulse Femtosecond Photon Echo ..................... 272 17.5 3PE at Arbitrary Waiting Time tw ....................... 278 Contents XI Part VII. Low Temperature Spectral Diffusion in Polymers and Glasses 18. Theory of Electron~Tunnelon Optical Band ............... 283 18.1 General Expression for the Cumulant Function of the Electron-Tunnelon System. . . . . . . . . . . . . . . . . . . . . . . . . 284 18.2 Tunnelon Green Function ................................ 288 18.3 Temperature Broadening of the Zero Tunnelon Optical Line . 289 18.4 Dipolar Correlator for a Chromophore-TLS System. Solution of the Integral Equation ......................... 292 18.5 Electron-Tunnelon Optical Band Shape Function ........... 294 19. Chromophore Interacting with Phonons and TLSs Which Are not in Thermal Equilibrium ................... 297 19.1 Hamiltonian of the Electron-Phonon-Tunnelon System ...... 297 19.2 Equations for the Density Matrix of the Electron-Phonon-Tunnelon System ................. 299 19.3 Spontaneous and Light-Induced Transitions in TLSs ........ 305 19.4 Interaction with One TLS. Approximate Solution ........... 307 19.5 Interaction with Many TLSs Undergoing Spontaneous Tunneling ....... 310 20. Dynamical Theory of Spectral Diffusion .................. 313 20.1 Absorption Coefficient of a Single Guest Molecule Interacting with Nonequilibrium TLSs ............................... 313 20.2 Dependence of the Optical Dephasing Time T2 on the Time Scale of the Experiment ...................... 317 20.3 Logarithmic Temporal Line Broadening. Deviation from the Logarithmic Temporal Law ............. 321 21. Theory of Tunneling Transitions in TLSs ................. 325 2l.1 General Formulas for the Tunneling Probability ............ 325 2l.2 Inelastic Tunneling Assisted by Acoustic and Localized Phonon Modes ......... 328 2l.3 Elastic Tunneling ....................................... 332 22. Investigating TLS Relaxation by Single-Molecule Spectroscopy .......................... 333 22.1 Two-Photon Corrclator of a Molecule Interacting with TLSs . 333 22.2 Spontaneous and Light-Induced Jumps of the Optical Line. Relation to Hole Burning ................................ 336 22.3 Analysis of Complicated Spectral Trajectories Using the Two-Photon Correlator ........................ 338