1
|
Ando K. Potential energy surfaces for electron dynamics from a model of localized Gaussian wave packets with valence-bond spin-coupling: High-harmonic generation spectra from H and He atoms. Chem Phys 2023. [DOI: 10.1016/j.chemphys.2023.111883] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 03/19/2023]
|
2
|
Ito R, Takada S, Ludwig A, Wieck AD, Tarucha S, Yamamoto M. Coherent Beam Splitting of Flying Electrons Driven by a Surface Acoustic Wave. PHYSICAL REVIEW LETTERS 2021; 126:070501. [PMID: 33666445 DOI: 10.1103/physrevlett.126.070501] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/23/2020] [Accepted: 01/07/2021] [Indexed: 06/12/2023]
Abstract
We develop a coherent beam splitter for single electrons driven through two tunnel-coupled quantum wires by surface acoustic waves (SAWs). The output current through each wire oscillates with gate voltages to tune the tunnel coupling and potential difference between the wires. This oscillation is assigned to coherent electron tunneling motion that can be used to encode a flying qubit and is well reproduced by numerical calculations of time evolution of the SAW-driven single electrons. The oscillation visibility is currently limited to about 3%, but robust against decoherence, indicating that the SAW electron can serve as a novel platform for a solid-state flying qubit.
Collapse
Affiliation(s)
- R Ito
- Center for Emergent Matter Science, RIKEN, 2-1 Hirosawa, Wako, Saitama 351-0198, Japan
| | - S Takada
- National Institute of Advanced Industrial Science and Technology, National Metrology Institute of Japan, 1-1-1 Umezono, Tsukuba, Ibaraki 305-8563, Japan
| | - A Ludwig
- Angewandte Festkörperphysk, Ruhr-Universität Bochum, D-44780 Bochum, Germany
| | - A D Wieck
- Angewandte Festkörperphysk, Ruhr-Universität Bochum, D-44780 Bochum, Germany
| | - S Tarucha
- Center for Emergent Matter Science, RIKEN, 2-1 Hirosawa, Wako, Saitama 351-0198, Japan
| | - M Yamamoto
- Center for Emergent Matter Science, RIKEN, 2-1 Hirosawa, Wako, Saitama 351-0198, Japan
| |
Collapse
|
3
|
Ando K. Single-electron quantum dynamics in high-harmonic generation spectrum from LiH molecule: Analysis of potential energy surfaces for electrons constructed from a model of localized Gaussian wave packets with valence-bond spin-coupling. J Chem Phys 2020; 152:084306. [DOI: 10.1063/1.5139079] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- Koji Ando
- Department of Information and Sciences, Tokyo Woman’s Christian University, 2-6-1 Zenpukuji, Suginami-ku, Tokyo 167-8585, Japan
| |
Collapse
|
4
|
Wells D, Quiney H. A fast and adaptable method for high accuracy integration of the time-dependent Schrödinger equation. Sci Rep 2019; 9:782. [PMID: 30692569 PMCID: PMC6349856 DOI: 10.1038/s41598-018-37382-0] [Citation(s) in RCA: 6] [Impact Index Per Article: 1.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/16/2018] [Accepted: 11/27/2018] [Indexed: 11/15/2022] Open
Abstract
We present an adaptable, fast, and robust method for integrating the time-dependent Schrödinger equation. We apply the method to calculations of High Harmonic (HHG) and Above Threshold Ionisation (ATI) spectra for a single atomic electron in an intense laser field. Our approach implements the stabilized bi-conjugate gradient method (BiCG-STAB) for solving a sparse linear system to evolve the electronic wavefunction in time. The use of this established method makes the propagation scheme less restrictive compared to other schemes which may have particular requirements for the form of the equation, such as use of a three-point finite-difference approximation for spatial derivatives. Our method produces converged solutions significantly faster than existing methods, particularly if high accuracy is required. We demonstrate that this approach is suitable for a range of different parameters and show that in many circumstances significant gains can be made with the use of a fourth-order time propagator as opposed to the more common second-order Crank-Nicolson (CN) method.
Collapse
Affiliation(s)
- Daniel Wells
- ARC Centre of Excellence for Advanced Molecular Imaging, Theoretical Condensed Matter Physics Group, School of Physics, University of Melbourne, Victoria, 3010, Australia.
| | - Harry Quiney
- ARC Centre of Excellence for Advanced Molecular Imaging, Theoretical Condensed Matter Physics Group, School of Physics, University of Melbourne, Victoria, 3010, Australia
| |
Collapse
|
5
|
Ando K. Potential energy surfaces for electron dynamics modeled by floating and breathing Gaussian wave packets with valence-bond spin-coupling: An analysis of high-harmonic generation spectrum. J Chem Phys 2018. [DOI: 10.1063/1.5012575] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- Koji Ando
- Department of Information and Sciences, Tokyo Woman’s Christian University, 2-6-1 Zenpukuji, Suginami-ku, Tokyo 167-8585, Japan
| |
Collapse
|
6
|
Acocella A, Höfinger S, Haunschmid E, Pop SC, Narumi T, Yasuoka K, Yasui M, Zerbetto F. Structural determinants in the bulk heterojunction. Phys Chem Chem Phys 2018; 20:5708-5720. [PMID: 29410990 DOI: 10.1039/c7cp08435h] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/15/2022]
Abstract
Photovoltaics is one of the key areas in renewable energy research with remarkable progress made every year. Here we consider the case of a photoactive material and study its structural composition and the resulting consequences for the fundamental processes driving solar energy conversion. A multiscale approach is used to characterize essential molecular properties of the light-absorbing layer. A selection of bulk-representative pairs of donor/acceptor molecules is extracted from the molecular dynamics simulation of the bulk heterojunction and analyzed at increasing levels of detail. Significantly increased ground state energies together with an array of additional structural characteristics are identified that all point towards an auxiliary role of the material's structural organization in mediating charge-transfer and -separation. Mechanistic studies of the type presented here can provide important insights into fundamental principles governing solar energy conversion in next-generation photovoltaic devices.
Collapse
Affiliation(s)
- Angela Acocella
- Department of Chemistry "G. Ciamician", University of Bologna, via F. Selmi 2, 40126 Bologna, Italy.
| | | | | | | | | | | | | | | |
Collapse
|
7
|
Ando K. Mixed quantal-semiquantal dynamics with stochastic particles for backreaction. J Chem Phys 2014; 141:144106. [DOI: 10.1063/1.4897532] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
|
8
|
|
9
|
Rakhimov KY, Chaves A, Farias GA, Peeters FM. Wavepacket scattering of Dirac and Schrödinger particles on potential and magnetic barriers. JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2011; 23:275801. [PMID: 21685554 DOI: 10.1088/0953-8984/23/27/275801] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/30/2023]
Abstract
We investigate the dynamics of a charged particle moving in a graphene layer and in a two-dimensional electron gas, where it obeys the Dirac and the Schrödinger equations, respectively. The charge carriers are described as Gaussian wavepackets. The dynamics of the wavepackets is studied numerically by solving both quantum-mechanical and relativistic equations of motion. The scattering of such wavepackets by step-like magnetic and potential barriers is analysed for different values of wavepacket energy and width. We find: (1) that the average position of the wavepacket does not coincide with the classical trajectory, and (2) that, for slanted incidence, the path of the centre of mass of the wavepacket does not have to penetrate the barrier during the scattering process. Trembling motion of the charged particle in graphene is observed in the absence of an external magnetic field and can be enhanced by a substrate-induced mass term.
Collapse
Affiliation(s)
- Kh Yu Rakhimov
- Department of Physics, University of Antwerp, Groenenborgerlaan 171, B-2020 Antwerp, Belgium
| | | | | | | |
Collapse
|
10
|
Sun Z, Yang W. Communication: An exact short-time solver for the time-dependent Schrödinger equation. J Chem Phys 2011; 134:041101. [PMID: 21280676 PMCID: PMC3045215 DOI: 10.1063/1.3549570] [Citation(s) in RCA: 15] [Impact Index Per Article: 1.2] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/04/2010] [Accepted: 01/10/2011] [Indexed: 11/14/2022] Open
Abstract
The short-time integrator for propagating the time-dependent Schrödinger equation, which is exact to machine's round off accuracy when the Hamiltonian of the system is time-independent, was applied to solve dynamics processes. This integrator has the old Cayley's form [i.e., the Padé (1,1) approximation], but is implemented in a spectrally transformed Hamiltonian which was first introduced by Chen and Guo. Two examples are presented for illustration, including calculations of the collision energy-dependent probability passing over a barrier, and interaction process between pulse laser and the I(2) diatomic molecule.
Collapse
Affiliation(s)
- Zhigang Sun
- Department of Chemistry, Duke University, Durham, North Carolina 27708, USA.
| | | |
Collapse
|
11
|
Matsukawa Y. An angular singularity-free method for the dynamics of the rovibrational motion of diatomic molecules. Mol Phys 2009. [DOI: 10.1080/00268970902991406] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/20/2022]
|
12
|
Bauke H, Keitel CH. Canonical transforms and the efficient integration of quantum mechanical wave equations. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2009; 80:016706. [PMID: 19658837 DOI: 10.1103/physreve.80.016706] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/27/2009] [Indexed: 05/28/2023]
Abstract
The integration of time-dependent quantum mechanical wave equations is a fundamental problem in computational physics and computational chemistry. The wave-function's energy spectrum as well as its momentum spectrum impose fundamental limits on the performance of numerical algorithms for the solution of wave equations. We demonstrate how canonical transforms may be applied to negotiate these limitations and to increase the performance of numerical algorithms by up to several orders of magnitude. Our approach includes the so-called Kramers-Henneberger transform as a special case and puts forward modifications toward an improved numerical efficiency.
Collapse
Affiliation(s)
- Heiko Bauke
- Max-Planck-Institut für Kernphysik, Saupfercheckweg 1, 69117 Heidelberg, Germany.
| | | |
Collapse
|
13
|
Ando T, Fujimoto M. Femtosecond pulse propagation in nitrogen: numerical study of (3 + 1)-dimensional extended nonlinear Schrödinger equation with shock-term correction. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2005; 72:026706. [PMID: 16196750 DOI: 10.1103/physreve.72.026706] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/14/2004] [Revised: 03/30/2005] [Indexed: 05/04/2023]
Abstract
We develop an accurate and efficient method for calculating evolution due to the extended nonlinear Schrödinger equation, which describes the propagation behavior of a femtosecond light pulse in a nonlinear medium. Applying Suzuki's exponential operator expansion to the evolution operator based on the finite-differential formulation, we realize the accurate and fast calculation that can be performed without large-scale computing systems even for (3 + 1)-dimensional problems. To study the correspondence between experiments and calculations, we calculate the propagation behavior of a femtosecond light pulse that is weakly focused in nitrogen gas of various pressures and compare the calculation results to the experimental ones. The calculation results reproduce the relative behavior of the spatial light pattern observed during the propagation. Additionally, the multiple-cone formation and interaction between two collimated pulses in nitrogen gas are also demonstrated as applications of the developed method.
Collapse
Affiliation(s)
- Taro Ando
- Hamamatsu Photonics K.K., Central Research Laboratory, Hirakuchi, Hamakita-City, Shizuoka, 434-8601, Japan.
| | | |
Collapse
|
14
|
KAWANO S, MARUYAMA Y. Mathematical Model for Polaronic Effects of Charge Transport in DNA. ACTA ACUST UNITED AC 2005. [DOI: 10.1299/jsmeb.48.456] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/12/2022]
Affiliation(s)
- Satoyuki KAWANO
- Center for Interdisciplinary Research, Tohoku University
- Japan Science and Technology Agency
| | | |
Collapse
|
15
|
Okushima T. Computational method for multidimensional quantal dynamics of polynomially interacting oscillator systems. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2004; 70:016705. [PMID: 15324202 DOI: 10.1103/physreve.70.016705] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/11/2004] [Indexed: 05/24/2023]
Abstract
We propose a numerical algorithm for computing quantal dynamics, which is tailored for a generic multidimensional model of low-energy dynamics, i.e., polynomially interacting oscillator system. This algorithm evaluates symplectic integrators effectively, by using block tridiagonality of the interaction operator, and thus accurately preserves unitarity with time. A practical advantage of this method is that high-order integrators are easily implemented even for time-dependent parameter systems. We demonstrate the accuracy and usefulness by applying it to a phi(4) model.
Collapse
Affiliation(s)
- T Okushima
- Department of Physics, Tokyo Metropolitan University, Minami-Ohsawa, Hachioji, Tokyo 192-0397, Japan.
| |
Collapse
|
16
|
Ren GB, Rorison JM. Eigenvalue problem of the Schrödinger equation via the finite-difference time-domain method. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2004; 69:036705. [PMID: 15089440 DOI: 10.1103/physreve.69.036705] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/30/2003] [Indexed: 05/24/2023]
Abstract
We present a very efficient scheme to calculate the eigenvalue problem of the time-independent Schrödinger equation. The eigenvalue problem can be solved via an initial-value procedure of the time-dependent Schrödinger equation. First, the time evolution of the wave function is calculated by the finite-difference time-domain method. Then the eigenenergies of the electron system can be obtained through a fast Fourier transformation along the time axis of the wave function after some point. The computing effort for this scheme is roughly proportional to the total grid points involved in the structure and it is suitable for large scale quantum systems. We have applied this approach to the three-dimensional GaN quantum dot system involving one million grid points. It takes only 7 h to calculate the confined energies and the wave functions on a standard 2-GHz Pentium 4 computer. The proposed approach can be implemented in a parallel computer system to study more complex systems.
Collapse
Affiliation(s)
- G B Ren
- Department of Electrical and Electronic Engineering, University of Bristol, BS8 1TR, United Kingdom
| | | |
Collapse
|
17
|
Watanabe N, Tsukada M. Efficient method for simulating quantum electron dynamics under the time-dependent Kohn-Sham equation. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2002; 65:036705. [PMID: 11909305 DOI: 10.1103/physreve.65.036705] [Citation(s) in RCA: 9] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/09/2001] [Revised: 08/27/2001] [Indexed: 05/23/2023]
Abstract
A numerical scheme for solving the time evolution of wave functions under the time-dependent Kohn-Sham (TDKS) equation has been developed. Since the effective Hamiltonian depends on the wave functions, the wave functions and the effective Hamiltonian should evolve consistently with each other. For this purpose, a self-consistent loop is required at every time step for solving the time evolution numerically, which is computationally expensive. However, in this paper, we develop a different approach, expressing a formal solution of the TDKS equation, and prove that it is possible to solve the TDKS equation efficiently and accurately by means of a simple numerical scheme without the use of any self-consistent loops.
Collapse
Affiliation(s)
- Naoki Watanabe
- Department of Physics, Graduate School of Science, University of Tokyo, 7-3-1 Hongo, 113-0033 Bunkyo-ku, Tokyo, Japan
| | | |
Collapse
|