Coherent Exciton Phenomena in Quantum Dot Molecules
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UNIVERSITY of CALIFORNIA, SAN DIEGO Exciton Transport
UNIVERSITY OF CALIFORNIA, SAN DIEGO Exciton Transport Phenomena in GaAs Coupled Quantum Wells A dissertation submitted in partial satisfaction of the requirements for the degree Doctor of Philosophy in Physics by Jason R. Leonard Committee in charge: Professor Leonid V. Butov, Chair Professor John M. Goodkind Professor Shayan Mookherjea Professor Charles W. Tu Professor Congjun Wu 2016 Copyright Jason R. Leonard, 2016 All rights reserved. The dissertation of Jason R. Leonard is approved, and it is acceptable in quality and form for publication on microfilm and electronically: Chair University of California, San Diego 2016 iii TABLE OF CONTENTS Signature Page . iii Table of Contents . iv List of Figures . vi Acknowledgements . viii Vita........................................ x Abstract of the Dissertation . xii Chapter 1 Introduction . 1 1.1 Semiconductor introduction . 2 1.1.1 Bulk GaAs . 3 1.1.2 Single Quantum Well . 3 1.1.3 Coupled-Quantum Wells . 5 1.2 Transport Physics . 7 1.3 Spin Physics . 8 1.3.1 D'yakanov and Perel' spin relaxation . 10 1.3.2 Dresselhaus Interaction . 10 1.3.3 Electron-Hole Exchange Interaction . 11 1.4 Dissertation Overview . 11 Chapter 2 Controlled exciton transport via a ramp . 13 2.1 Introduction . 13 2.2 Experimental Methods . 14 2.3 Qualitative Results . 14 2.4 Quantitative Results . 16 2.5 Theoretical Model . 17 2.6 Summary . 19 2.7 Acknowledgments . 19 Chapter 3 Controlled exciton transport via an optically controlled exciton transistor . 22 3.1 Introduction . 22 3.2 Realization . 22 3.3 Experimental Methods . 23 3.4 Results . 25 3.5 Theoretical Model . -
Quantum-Classical Correspondence of Shortcuts to Adiabaticity”
Quantum-Classical Correspondence of Shortcuts to Adiabaticity Manaka Okuyama and Kazutaka Takahashi Department of Physics, Tokyo Institute of Technology, Tokyo 152-8551, Japan (Dated: September 1, 2018) We formulate the theory of shortcuts to adiabaticity in classical mechanics. For a reference Hamiltonian, the counterdiabatic term is constructed from the dispersionless Korteweg–de Vries (KdV) hierarchy. Then the adiabatic theorem holds exactly for an arbitrary choice of time-dependent parameters. We use the Hamilton–Jacobi theory to define the generalized action. The action is independent of the history of the parameters and is directly related to the adiabatic invariant. The dispersionless KdV hierarchy is obtained from the classical limit of the KdV hierarchy for the quantum shortcuts to adiabaticity. This correspondence suggests some relation between the quantum and classical adiabatic theorems. Shortcuts to adiabaticity (STA) is a method control- formulations will allow us to make a link between two ling dynamical systems. The implementation of the theorems. In this letter, we develop the theory of the method results in dynamics that are free from nona- classical STA. First, we formulate the classical STA in a diabatic transitions for an arbitrary choice of time- general way so that the counterdiabatic term can be cal- dependent parameters in a reference Hamiltonian. It was culated, in principle, from the derived formula. Second, developed in quantum systems [1–4] and its applications we show that the adiabatic theorem holds exactly in the have been studied in various fields of physics and engi- classical STA and the adiabatic invariant is obtained di- neering [5]. It is important to notice that this method, rectly from the nonperiodic trajectory. -
The Adiabatic Theorem and Linear Response Theory for Extended Quantum Systems
THE ADIABATIC THEOREM AND LINEAR RESPONSE THEORY FOR EXTENDED QUANTUM SYSTEMS SVEN BACHMANN, WOJCIECH DE ROECK, AND MARTIN FRAAS Abstract. The adiabatic theorem refers to a setup where an evolution equation contains a time- dependent parameter whose change is very slow, measured by a vanishing parameter . Under suitable assumptions the solution of the time-inhomogenous equation stays close to an instanta- neous fixpoint. In the present paper, we prove an adiabatic theorem with an error bound that is independent of the number of degrees of freedom. Our setup is that of quantum spin systems where the manifold of ground states is separated from the rest of the spectrum by a spectral gap. One im- portant application is the proof of the validity of linear response theory for such extended, genuinely interacting systems. In general, this is a long-standing mathematical problem, which can be solved in the present particular case of a gapped system, relevant e.g. for the integer quantum Hall effect. 1. Introduction 1.1. Adiabatic Theorems. The adiabatic theorem stands for a rather broad principle that can be described as follows. Consider an equation giving the evolution in time t of some '(t) 2 B, with B some Banach space: d (1.1) '(t) = L('(t); α ); dt t where L : B × R ! B is a smooth function and αt is a parameter depending parametrically on time. Now, assume that for αt = α frozen in time, the equation exhibits some tendency towards a fixpoint 1 R T 'α, as expressed, for example, by convergence in Cesaro mean T 0 '(t)dt ! 'α, as T ! 1 for any initial '(0). -
Westfälische-Wilhelms-Universität Adiabatic Approximation and Berry
Westfälische-Wilhelms-Universität Seminar zur Theorie der Atome, Kerne und kondensierten Materie Adiabatic Approximation and Berry Phase with regard to the Derivation Thomas Grottke [email protected] WS 14\15 21st January, 2015 Contents 1 Adiabatic Approximation 1 1.1 Motivation . 1 1.2 Derivation of the Adiabatic Theorem . 3 2 Berry Phase 5 2.1 Nonholonomic System . 5 2.2 Derivation of the Berry Phase . 5 2.3 Berry Potential and Berry Curvature . 6 2.4 Summary . 7 Thomas Grottke 1 ADIABATIC APPROXIMATION 1 Adiabatic Approximation 1.1 Motivation Figure 1: Mathematical pendulum with the mass m, the length l and the deflection ϕ To give a short motivation let us have a look at the mathematical pendulum (c.f. Figure 1) with the mass m, the length l and the deflection ϕ. The differential equation is given by g ϕ(t) + ϕ(t) = 0 (1.1) l where g is the acceleration of gravity. Solving this equation leads us to the period T with s l T = 2π . (1.2) g If we move the pendulum from a location A to a location B we can consider two ways doing this. If the pendulum is moved fast it will execute a complicated oscillation not easy to be described. But if the motion is slow enough, the pendulum remains in its oscillation. This motion is a good example for an adiabatic process which means that the conditions respectively the environment are changed slowly. Oscillation is also well known in quantum mechanics systems. A good example is the potential well (c.f. -
Chapter 09584
Author's personal copy Excitons in Magnetic Fields Kankan Cong, G Timothy Noe II, and Junichiro Kono, Rice University, Houston, TX, United States r 2018 Elsevier Ltd. All rights reserved. Introduction When a photon of energy greater than the band gap is absorbed by a semiconductor, a negatively charged electron is excited from the valence band into the conduction band, leaving behind a positively charged hole. The electron can be attracted to the hole via the Coulomb interaction, lowering the energy of the electron-hole (e-h) pair by a characteristic binding energy, Eb. The bound e-h pair is referred to as an exciton, and it is analogous to the hydrogen atom, but with a larger Bohr radius and a smaller binding energy, ranging from 1 to 100 meV, due to the small reduced mass of the exciton and screening of the Coulomb interaction by the dielectric environment. Like the hydrogen atom, there exists a series of excitonic bound states, which modify the near-band-edge optical response of semiconductors, especially when the binding energy is greater than the thermal energy and any relevant scattering rates. When the e-h pair has an energy greater than the binding energy, the electron and hole are no longer bound to one another (ionized), although they are still correlated. The nature of the optical transitions for both excitons and unbound e-h pairs depends on the dimensionality of the e-h system. Furthermore, an exciton is a composite boson having integer spin that obeys Bose-Einstein statistics rather than fermions that obey Fermi-Dirac statistics as in the case of either the electrons or holes by themselves. -
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Adiabatic critical quantum metrology cannot reach the Heisenberg limit even when shortcuts to adiabaticity are applied Karol Gietka, Friederike Metz, Tim Keller, and Jing Li Quantum Systems Unit, Okinawa Institute of Science and Technology Graduate University, Onna, Okinawa 904-0495, Japan We show that the quantum Fisher information attained in an adia- batic approach to critical quantum metrology cannot lead to the Heisen- berg limit of precision and therefore regular quantum metrology under optimal settings is always superior. Furthermore, we argue that even though shortcuts to adiabaticity can arbitrarily decrease the time of preparing critical ground states, they cannot be used to achieve or over- come the Heisenberg limit for quantum parameter estimation in adia- batic critical quantum metrology. As case studies, we explore the appli- cation of counter-diabatic driving to the Landau-Zener model and the quantum Rabi model. 1 Introduction Quantum metrology [1] is concerned with harnessing quantum resources following from the quantum-mechanical framework (in particular, quantum entanglement) to increase the sensitivity of unknown parameter estimation beyond the standard quantum limit [2]. This limitation is a consequence of the central limit theorem which states that if N independent particles (such as photons or atoms) are used in the process of√ estimation of an unknown parameter θ, the error on average decreases as Var[θ] ∼ 1/ N. Taking advantage of quantum resources can further decrease the average error leading to the Heisenberg scaling of precision Var[θ] ∼ 1/N [3] which in arXiv:2103.12939v2 [quant-ph] 25 Jun 2021 the optimal case becomes the Heisenberg limit Var[θ] = 1/N. -
Quantum Adiabatic Theorem and Berry's Phase Factor Page Tyler Department of Physics, Drexel University
Quantum Adiabatic Theorem and Berry's Phase Factor Page Tyler Department of Physics, Drexel University Abstract A study is presented of Michael Berry's observation of quantum mechanical systems transported along a closed, adiabatic path. In this case, a topological phase factor arises along with the dynamical phase factor predicted by the adiabatic theorem. 1 Introduction In 1984, Michael Berry pointed out a feature of quantum mechanics (known as Berry's Phase) that had been overlooked for 60 years at that time. In retrospect, it seems astonishing that this result escaped notice for so long. It is most likely because our classical preconceptions can often be misleading in quantum mechanics. After all, we are accustomed to thinking that the phases of a wave functions are somewhat arbitrary. Physical quantities will involve Ψ 2 so the phase factors cancel out. It was Berry's insight that if you move the Hamiltonian around a closed, adiabatic loop, the relative phase at the beginning and at the end of the process is not arbitrary, and can be determined. There is a good, classical analogy used to develop the notion of an adiabatic transport that uses something like a Foucault pendulum. Or rather a pendulum whose support is moved about a loop on the surface of the Earth to return it to its exact initial state or one parallel to it. For the process to be adiabatic, the support must move slow and steady along its path and the period of oscillation for the pendulum must be much smaller than that of the Earth's. -
Amplitude/Higgs Modes in Condensed Matter Physics
Amplitude / Higgs Modes in Condensed Matter Physics David Pekker1 and C. M. Varma2 1Department of Physics and Astronomy, University of Pittsburgh, Pittsburgh, PA 15217 and 2Department of Physics and Astronomy, University of California, Riverside, CA 92521 (Dated: February 10, 2015) Abstract The order parameter and its variations in space and time in many different states in condensed matter physics at low temperatures are described by the complex function Ψ(r; t). These states include superfluids, superconductors, and a subclass of antiferromagnets and charge-density waves. The collective fluctuations in the ordered state may then be categorized as oscillations of phase and amplitude of Ψ(r; t). The phase oscillations are the Goldstone modes of the broken continuous symmetry. The amplitude modes, even at long wavelengths, are well defined and decoupled from the phase oscillations only near particle-hole symmetry, where the equations of motion have an effective Lorentz symmetry as in particle physics, and if there are no significant avenues for decay into other excitations. They bear close correspondence with the so-called Higgs modes in particle physics, whose prediction and discovery is very important for the standard model of particle physics. In this review, we discuss the theory and the possible observation of the amplitude or Higgs modes in condensed matter physics – in superconductors, cold-atoms in periodic lattices, and in uniaxial antiferromagnets. We discuss the necessity for at least approximate particle-hole symmetry as well as the special conditions required to couple to such modes because, being scalars, they do not couple linearly to the usual condensed matter probes. -
Exciton Binding Energy in Small Organic Conjugated Molecule
1 Exciton Binding Energy in small organic conjugated molecule. Pabitra K. Nayak* Department of Materials and Interfaces, Weizmann Institute of Science, Rehovot, 76100, Israel Email: [email protected] Abstract: For small organic conjugated molecules the exciton binding energy can be calculated treating molecules as conductor, and is given by a simple relation BE ≈ 2 e /(4πε0εR), where ε is the dielectric constant and R is the equivalent radius of the molecule. However, if the molecule deviates from spherical shape, a minor correction factor should be added. 1. Introduction An understanding of the energy levels in organic semiconductors is important for designing electronic devices and for understanding their function and performance. The absolute hole transport level and electron transport level can be obtained from theoretical calculations and also from photoemission experiments [1][2][3]. The difference between the two transport levels is referred to as the transport gap (Et). The transport gap is different from the optical gap (Eopt) in organic semiconductors. This is because optical excitation gives rise to excitons rather than free carriers. These excitons are Frenkel excitons and localized to the molecule, hence an extra amount of energy, termed as exciton binding energy (Eb) is needed to produce free charge carriers. What is the magnitude of Eb in organic semiconductors? Answer to this question is more relevant in emerging field of Organic Photovoltaic cells (OPV), due to their impact in determining the output voltage of the solar cells. A lot of efforts are also going on to develop new absorbing material for OPV. It is also important to guess the magnitude of exciton binding energy before the actual synthesis of materials. -
Pion-Induced Transport of Π Mesons in Nuclei
Central Washington University ScholarWorks@CWU All Faculty Scholarship for the College of the Sciences College of the Sciences 2-8-2000 Pion-induced transport of π mesons in nuclei S. G. Mashnik R. J. Peterson A. J. Sierk Michael R. Braunstein Follow this and additional works at: https://digitalcommons.cwu.edu/cotsfac Part of the Atomic, Molecular and Optical Physics Commons, and the Nuclear Commons PHYSICAL REVIEW C, VOLUME 61, 034601 Pion-induced transport of mesons in nuclei S. G. Mashnik,1,* R. J. Peterson,2 A. J. Sierk,1 and M. R. Braunstein3 1T-2, Theoretical Division, Los Alamos National Laboratory, Los Alamos, New Mexico 87545 2Nuclear Physics Laboratory, University of Colorado, Boulder, Colorado 80309 3Physics Department, Central Washington University, Ellensburg, Washington 98926 ͑Received 28 May 1999; published 8 February 2000͒ A large body of data for pion-induced neutral pion continuum spectra spanning outgoing energies near 180 MeV shows no dip there that might be ascribed to internal strong absorption processes involving the formation of ⌬’s. This is the same observation previously made for the charged pion continuum spectra. Calculations in an intranuclear cascade model or a cascade exciton model with free-space parameters predict such a dip for both neutral and charged pions. We explore several medium modifications to the interactions of pions with internal nucleons that are able to reproduce the data for nuclei from 7Li through Bi. PACS number͑s͒: 25.80.Hp, 25.80.Gn, 25.80.Ls, 21.60.Ka I. INTRODUCTION the NCX data at angles forward of 90° by a factor of 2 ͓3͔. -
Phonon-Exciton Interactions in Wse2 Under a Quantizing Magnetic Field
ARTICLE https://doi.org/10.1038/s41467-020-16934-x OPEN Phonon-exciton Interactions in WSe2 under a quantizing magnetic field Zhipeng Li1,10, Tianmeng Wang 1,10, Shengnan Miao1,10, Yunmei Li2,10, Zhenguang Lu3,4, Chenhao Jin 5, Zhen Lian1, Yuze Meng1, Mark Blei6, Takashi Taniguchi7, Kenji Watanabe 7, Sefaattin Tongay6, Wang Yao 8, ✉ Dmitry Smirnov 3, Chuanwei Zhang2 & Su-Fei Shi 1,9 Strong many-body interaction in two-dimensional transitional metal dichalcogenides provides 1234567890():,; a unique platform to study the interplay between different quasiparticles, such as prominent phonon replica emission and modified valley-selection rules. A large out-of-plane magnetic field is expected to modify the exciton-phonon interactions by quantizing excitons into dis- crete Landau levels, which is largely unexplored. Here, we observe the Landau levels origi- nating from phonon-exciton complexes and directly probe exciton-phonon interaction under a quantizing magnetic field. Phonon-exciton interaction lifts the inter-Landau-level transition selection rules for dark trions, manifested by a distinctively different Landau fan pattern compared to bright trions. This allows us to experimentally extract the effective mass of both holes and electrons. The onset of Landau quantization coincides with a significant increase of the valley-Zeeman shift, suggesting strong many-body effects on the phonon-exciton inter- action. Our work demonstrates monolayer WSe2 as an intriguing playground to study phonon-exciton interactions and their interplay with charge, spin, and valley. 1 Department of Chemical and Biological Engineering, Rensselaer Polytechnic Institute, Troy, NY 12180, USA. 2 Department of Physics, The University of Texas at Dallas, Richardson, TX 75080, USA. -
The Adiabatic Theorem in the Presence of Noise, Perturbations, and Decoherence
The Adiabatic Theorem in the Presence of Noise Michael J. O’Hara ∗ and Dianne P. O’Leary † December 27, 2013 Abstract We provide rigorous bounds for the error of the adiabatic approximation of quan- tum mechanics under four sources of experimental error: perturbations in the ini- tial condition, systematic time-dependent perturbations in the Hamiltonian, coupling to low-energy quantum systems, and decoherent time-dependent perturbations in the Hamiltonian. For decoherent perturbations, we find both upper and lower bounds on the evolution time to guarantee the adiabatic approximation performs within a pre- scribed tolerance. Our new results include explicit definitions of constants, and we apply them to the spin-1/2 particle in a rotating magnetic field, and to the supercon- ducting flux qubit. We compare the theoretical bounds on the superconducting flux qubit to simulation results. 1 Introduction Adiabatic quantum computation [7] (AQC) is a model of quantum computation equivalent to the standard model [1]. A physical system is slowly evolved from the ground state of a simple system, to one whose ground state encodes the solution to the difficult problem. By a physical principle known as the adiabatic approximation, if the evolution is done sufficiently slowly, and the minimum energy gap separating the ground state from higher states is sufficiently large, then the final state of the system should be the state encoding the solution to some arXiv:0801.3872v1 [quant-ph] 25 Jan 2008 problem. The biggest hurdles facing many potential implementations of a quantum computer are the errors due to interaction of the qubits with the environment.