Details
| Original language | English |
|---|---|
| Article number | 19LT01 |
| Journal | Journal of Physics B: Atomic, Molecular and Optical Physics |
| Volume | 55 |
| Issue number | 19 |
| Publication status | Published - 2 Sept 2022 |
Abstract
Obtaining a numerical solution of the time-dependent Schrödinger equation requires an initial state for the time evolution. If the system Hamiltonian can be split into a time-independent part and a time-dependent perturbation, the initial state is typically chosen as an eigenstate of the former. For propagation using approximate methods such as operator splitting, we show that both imaginary-time evolution and diagonalization of the time-independent Hamiltonian produce states that are not exactly stationary in absence of the perturbation. In order to avoid artifacts from these non-stationary initial states, we propose an iterative method for calculating eigenstates of the real-time propagator. We compare the performance of different initial states by simulating ionization of a model atom in a short laser pulse and we demonstrate that much lower noise levels can be achieved with the real-time propagator eigenstates.
Keywords
- eigenstates, laser-induced ionization, split-operator method, time-dependent Schrödinger equation, time-independent Schrödinger equation
ASJC Scopus subject areas
- Physics and Astronomy(all)
- Atomic and Molecular Physics, and Optics
- Physics and Astronomy(all)
- Condensed Matter Physics
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In: Journal of Physics B: Atomic, Molecular and Optical Physics, Vol. 55, No. 19, 19LT01, 02.09.2022.
Research output: Contribution to journal › Article › Research › peer review
}
TY - JOUR
T1 - Real-time propagator eigenstates
AU - Oppermann, F.
AU - Eicke, N.
AU - Lein, M.
N1 - Funding Information: The authors acknowledge funding by the Deutsche Forschungsgemeinschaft (DFG) in the frame of the Schwerpunktprogramm (SPP) 1840, Quantum Dynamics in Tailored Intense Fields. We thank S Brennecke for fruitful discussions.
PY - 2022/9/2
Y1 - 2022/9/2
N2 - Obtaining a numerical solution of the time-dependent Schrödinger equation requires an initial state for the time evolution. If the system Hamiltonian can be split into a time-independent part and a time-dependent perturbation, the initial state is typically chosen as an eigenstate of the former. For propagation using approximate methods such as operator splitting, we show that both imaginary-time evolution and diagonalization of the time-independent Hamiltonian produce states that are not exactly stationary in absence of the perturbation. In order to avoid artifacts from these non-stationary initial states, we propose an iterative method for calculating eigenstates of the real-time propagator. We compare the performance of different initial states by simulating ionization of a model atom in a short laser pulse and we demonstrate that much lower noise levels can be achieved with the real-time propagator eigenstates.
AB - Obtaining a numerical solution of the time-dependent Schrödinger equation requires an initial state for the time evolution. If the system Hamiltonian can be split into a time-independent part and a time-dependent perturbation, the initial state is typically chosen as an eigenstate of the former. For propagation using approximate methods such as operator splitting, we show that both imaginary-time evolution and diagonalization of the time-independent Hamiltonian produce states that are not exactly stationary in absence of the perturbation. In order to avoid artifacts from these non-stationary initial states, we propose an iterative method for calculating eigenstates of the real-time propagator. We compare the performance of different initial states by simulating ionization of a model atom in a short laser pulse and we demonstrate that much lower noise levels can be achieved with the real-time propagator eigenstates.
KW - eigenstates
KW - laser-induced ionization
KW - split-operator method
KW - time-dependent Schrödinger equation
KW - time-independent Schrödinger equation
UR - http://www.scopus.com/inward/record.url?scp=85137680448&partnerID=8YFLogxK
U2 - 10.1088/1361-6455/ac8bb9
DO - 10.1088/1361-6455/ac8bb9
M3 - Article
AN - SCOPUS:85137680448
VL - 55
JO - Journal of Physics B: Atomic, Molecular and Optical Physics
JF - Journal of Physics B: Atomic, Molecular and Optical Physics
SN - 0953-4075
IS - 19
M1 - 19LT01
ER -