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Coherent Exciton Phenomena in Quantum Dot Molecules

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Coherent Exciton Phenomena in Quantum Dot Molecules A dissertation presented to the faculty of the College of Arts and Sciences of Ohio University In partial fulfillment of the requirements for the degree Doctor of Philosophy Juan Enrique Rolon Soto November 2011 © 2011 Juan Enrique Rolon Soto. All Rights Reserved. 2 This dissertation titled Coherent Exciton Phenomena in Quantum Dot Molecules by JUAN ENRIQUE ROLON SOTO has been approved for the Department of Physics and Astronomy and the College of Arts and Sciences by Sergio E. Ulloa Professor of Physics and Astronomy Howard Dewald Dean, College of Arts and Sciences 3 Abstract ROLON SOTO, JUAN ENRIQUE, Ph.D., November 2011, Physics and Astronomy Coherent Exciton Phenomena in Quantum Dot Molecules (144 pp.) Director of Dissertation: Sergio E. Ulloa We investigate different aspects of the coherent dynamics of excitons in quantum dot molecules. A theoretical model is developed in order to extract the Forster¨ energy transfer signatures in tunnel coupled quantum dot molecules in the presence of strong interdot tunneling. It is found that Forster¨ coupling can induce spectral doublets in the excitonic dressed spectrum, which is suitable for detection in level anticrossing spectroscopy. The coherent exciton dynamics is investigated both in the closed and open quantum system approach by means of the Lindblad master equation. An adiabatic elimination procedure using the projection operator formalism allows us to extract effective Hamiltonians to describe analytically all relevant anticrossing gaps of the dressed spectrum. It is found that a pair of two indirect excitons can be used as the computational basis of a qubit. An adiabatic control pulse is constructed in order to manipulate the indirect exciton qubit and characterize its coherent dynamics, as well as its decoherence due to spontaneous recombination. On the other hand, recent experiments have shown that indirect excitons in hole tunnel coupled quantum dot molecules exhibit indirect exciton oscillatory relaxation rates, as function of an applied electric field. To this end we developed a model for the experimental results, in which we incorporate relaxation due to exciton-acoustic phonon coupling. We characterize the scattering structure factor and found that it contains an electrically tunable phase relationship between the phonon wave and the hole wave function, which leads to interference effects and oscillatory relaxation rates. Approved: Sergio E. Ulloa Professor of Physics and Astronomy 4 To Anna my daughter, Diana my wife, Maria my mother and Max my brother 5 Acknowledgments I would like to thank the Physics and Astronomy department for developing an encouraging atmosphere to pursue graduate studies in physics at Ohio University. In particular, to those colleagues who never hesitate to share informal conversations about physics and ordinary life matters, who never hesitate to bring out a laugh, or say hello. To the professors who hold graduate students in high regard and encourage them to fulfill themselves as professionals with critical thinking. In this special group, I would deeply thank Prof. Sergio E. Ulloa for being a very supportive advisor, always willing to share his time for discussions even in the busiest of days. I would like also to thank my advisor for creating an atmosphere of friendship and collaboration inside and outside the office, through our weekly group meeting discussions in diverse topics of condensed matter physics, and for its support for students to travel and share their research results with the rest of the world. I would also like to thank my friends and colleagues, Pedro L. Hernandez, Ginetom Diniz, Kushal Wijesundara, David Ruiz, Ahn T. Ngo, Greg Petersen, Mahmoud Asmar and Tejinder Kaur, for all those enjoyable times of traveling and comradeship. Special thanks to professors Dr. Nancy Sandler, Dr. Eric Stinaff, and Dr. Sasha Govorov, who have been excellent mentors inside and outside the classroom. And finally, I would also like to thank my family for their unconditional patience and support during my PhD studies. 6 Table of Contents Page Abstract.........................................3 Dedication........................................4 Acknowledgments....................................5 List of Tables......................................8 List of Figures......................................9 1 Introduction..................................... 16 2 Forster¨ Energy Transfer Signatures in Optically Driven Quantum Dot Molecules. 20 2.1 Introduction.................................. 20 2.2 Model: FRET Coupling in Quantum Dot Molecules............. 21 2.3 Model: Quantum Dot Molecule Hamiltonian................ 24 2.4 Model: Effective Exciton Hamiltonian.................... 26 2.5 Model: Electrically Tunable Molecular Coupling.............. 27 2.6 Model: Coherent Exciton Dynamics and Level Anticrossing Population Maps 30 2.7 Results: Competing Effects of Tunneling and Forster¨ Energy Transfer in Monoexcitons................................. 31 2.8 Results: FRET in Biexciton Optical Signatures............... 36 2.9 Conclusions.................................. 42 3 Coherent Control of Exciton Dynamics in Quantum Dot Molecules....... 43 3.1 Introduction.................................. 43 3.1.1 Coherent control........................... 43 3.2 Effective Subspace Extraction From Level Anticrossing Spectra...... 45 3.2.1 Optical Signatures: Effective Three and Two Level Systems.... 45 3.2.2 Two Level System Optical Signatures: Indirect Exciton Qubits... 47 3.3 Effective Exciton Hamiltonian via Adiabatic Elimination.......... 50 3.3.1 Adiabatic Elimination via Algebra of Projection Operators..... 51 3.3.2 Three Level System Subspaces: Effective Oscillator Strength.... 53 3.3.3 Spatially Indirect Protected Two Level Systems.......... 55 3.4 Coherent Control of Indirect Excitonic Qubits................ 58 3.4.1 Excitonic Density Matrix Dynamics and Control Scheme...... 58 3.4.2 Indirect Exciton Qubit Initialization................. 61 3.4.3 Indirect Exciton Qubit Rotations................... 62 3.4.4 Indirect Exciton Qubit Readout................... 64 7 3.5 Additional dynamical effects......................... 65 3.5.1 Forster¨ Energy Transfer and Biexciton States............ 65 3.6 Dissipative Effects.............................. 66 3.6.1 Numerical Results: Density Matrix................. 66 3.6.2 Analytical Results: Adiabatic Elimination.............. 68 3.7 Discussion and Concluding Remarks..................... 72 3.7.1 Stability of the Control Scheme................... 72 3.7.2 Conclusions.............................. 73 4 Modeling Electrical Control of Indirect Exciton Relaxation Rates in Quantum Dot Molecules.................................... 74 4.1 Introduction.................................. 74 4.2 Oscillatory Relaxation Rates of Indirect Excitons in InGaAs/GaAs QDMs: Experimental Evidence............................ 75 4.3 Phonon Assisted Exciton Relaxation..................... 77 4.3.1 Carrier Phonon Scattering Interaction Mechanisms......... 77 4.3.2 QDM Simplified Model: Electron and Hole Wave Functions.... 81 4.3.3 Uncorrelated Excitons........................ 84 4.3.4 Phonon Induced Hole Scattering Rates................ 88 4.4 Radiative Recombination Rates........................ 100 4.5 Discussion and Concluding Remarks..................... 102 5 Conclusions and Outlook.............................. 104 References........................................ 110 Appendix A: Simulation Parameters.......................... 116 Appendix B: Adiabatic Elimination: Bloch-Feshbach Algebraic Method....... 120 Appendix C: Rabi oscillations and The Rotating Wave Approximation........ 130 Appendix D: Adiabatic Passage............................. 133 Appendix E: Two Level Systems and Qubits..................... 136 Appendix F: Articles and Conferences......................... 142 8 List of Tables Table Page A.1 Constant parameters used in chapters2 and3................... 116 A.2 Parameters used in simulations corresponding to figures 2.5, 2.6 and 2.7.... 116 A.3 Parameters used in simulations corresponding to figures 2.8, 2.9......... 117 A.4 Parameters used for simulations in chapter3................... 118 A.5 Parameters used in simulations for chapter4................... 119 (Λ) B.1 Roots of the polynomial Π (z) at FR ...................... 126 (Λ) B.2 Roots of the polynomial Π (z) at FI ...................... 126 9 List of Figures Figure Page 2.1 Excitation energy transfer between molecular complexes Q1 and Q2. A laser pulse pumps the excited state e1, upon de-excitation electrostatic energy is transfer to Q2; absorption on Q2 leads to the excited state e2. VF is the dipole- dipole Coulomb interaction responsible for this process............. 20 2.2 FRET process in a QDM (a) QDM schematics; two dissimilar disk shaped vertically stacked QDs. (b) Ground state excitons in each QD are represented by an electronic state (blue) and a hole state (red) in the conduction band (CB) and valence band (VB), respectively. A FRET interaction, VF, de-excites an exciton on QD1 and transfers its energy to create an exciton on QD2. (c) 10 The FRET process represented as a single transition between two excitons 10X and 01X. Here an exciton is denoted by e1e2 X, with h ; e being the occupation 01 h1h2 i i numbers on the i-th QD.............................. 22 2.3 Level anticrossing spectroscopy schematics. (left panel) Vertically stacked QD layers are processed into Schottky photo diodes. 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