Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

Journal of Physics B Atomic and Molecular Physics

Quantum transitions between highly excited atomic levels induced by external time-dependent forces

Леонид Петрович Пресняков, A. M. Urnov

Published Oct 1, 1970• 24 citations
Publisher

Abstract

A model of an excited quantum system is considered. An exact solution is obtained for a non-stationary problem in which the interaction potential is an arbitrary function of time and coordinates. The obtained solution reduces in particular cases to well-known results for transition probabilities between highly excited levels of a quantum oscillator.

DOI
10.1088/0022-3700/3/10/001

Related papers

Dynamics of mixed quantum/classical systems

Herman J. C. Berendsen

Introduction We now move to considering the dynamics of a system of nuclei and electrons. Of course, both electrons and nuclei are subject to the laws of quantum mechanics, but since nuclei are 2000 to 200,000 times heavier than electrons, we expect that classical mechanics will be a much better approximation for the motion of nuclei than for the motion of electrons. This means that we expect a level of approximation to be valid, where some of the degrees of freedom (d.o.f.) of a system behave essentially classically and others behave essentially quantum-mechanically. The system then is of a mixed quantum/classical nature. Most often the quantum subsystem consists of system of electrons in a dynamical field of classical nuclei, but the quantum subsystem may also be a selection of generalized nuclear coordinates (e.g., corresponding to high-frequency vibrations) while other generalized coordinates are supposed to behave classically, or describe the motion of a proton in a classical environment. So, in this chapter we consider the dynamics of a quantum system in a non-stationary potential. In Section 5.2 we consider the time-dependent potential as externally given, without taking notice of the fact that the sources of the time-dependent potential are moving nuclei, which are quantum particles themselves, feeling the interaction with the quantum d.o.f. Thus we consider the time evolution of the quantum system, which now involves mixing-in of excited states, but we completely ignore the back reaction of the quantum system onto the d.o.f. that cause the time-dependent potential, i.e., the moving nuclei.

Cambridge University Press eBooks•Jul 12, 2007•0 citations

|2 > |1 >

Z. Ficek, Mohamed Ridza Wahiddin

Figure 2.1 shows a schematic diagram of a two-level system, called a two-level atom, with the ground state |1〉 and the upper (excited) state |2〉. In fact, the electron can make transitions between many energy states, but we can limit the transitions to only between two states. In practice, it is done by a suitable choice of the frequency of an external field that will force the electron to oscillate only between these two selected states [3, 4]. Multi-level transitions involving more than two energy states are much more complex and we are not intend to consider them here, but the formalism presented here can be extended to multi-level cases.a The energy of the electron in the selected states |2〉 and |1〉 is determined by the stationary Schro¨dinger equation HˆA |1〉 = E1 |1〉 , HˆA |2〉 = E2 |2〉 , (2.10) where HˆA is the Hamiltonian of the atom whose explicit form is to be determine.

•Apr 19, 2016•0 citations

Controlled quantum evolutions and transitions

Nicola Cufaro Petroni, S. De Martino, Silvio De Siena +1 more

We study the nonstationary solutions of Fokker-Planck equations associated to either stationary or non stationary quantum states. In particular, we discuss the stationary states of quantum systems with singular velocity fields. We introduce a technique that allows arbitrary evolutions ruled by these equations to account for controlled quantum transitions. As a first signficant application we present a detailed treatment of the transition probabilities and of the controlling time-dependent potentials associated to the transitions between the stationary, the coherent, and the squeezed states of the harmonic oscillator.

arXiv:quant-ph/9910070•Journal of Physics A Mathematical and General•Oct 13, 1999•14 citations

Exact dynamics of a model for a three-level atom

Russell Davidson, John J. Kozak

In this paper we investigate the dynamics of a model for a three-level atom in interaction with a radiation field. The exact solution to the spontaneous-emission problem is derived using methods developed earlier by the authors, and expressions are obtained for the probabilities of the atom’s being in the first or second excited states at any time t. For the special case that the strengths of the coupling between each of the excited states and the λth mode of the field are proportional, detailed conclusions can be drawn concerning the effects of such factors as system size, coupling function, and level splitting on the temporal evolution of the system. The evolution of excited quantum systems having one versus two modes of decay to the ground state is also compared, and similarities and differences in the temporal behavior are noted. Finally the relevance of the theory presented in this paper to experimental problems in radiation chemistry and physics is indicated in our concluding remarks.

Journal of Mathematical Physics•Sep 1, 1976•5 citations

Exact Solutions for Time-Dependent Non-Hermitian Oscillators: Classical and Quantum Pictures

Kevin Zelaya, Óscar Rosas-Ortiz

We associate the stationary harmonic oscillator with time-dependent systems exhibiting non-Hermiticity by means of point transformations. The new systems are exactly solvable, with all-real spectra, and transit to the Hermitian configuration for the appropriate values of the involved parameters. We provide a concrete generalization of the Swanson oscillator that includes the Caldirola–Kanai model as a particular case. Explicit solutions are given in both the classical and quantum pictures.

arXiv:2108.08958•Quantum Reports•Aug 21, 2021•19 citations

Exact analytical solution of theN-level Landau - Zener-type bow-tie model

Valentin N. Ostrovsky, Hiroki Nakamura

The non-stationary Schrödinger equation in a finite basis of states is considered for the Hamiltonian matrix linearly depending on time. Exact analytical solutions of asymptotic transition probabilities are obtained for a bow-tie model, in which an arbitrary number of linear time-dependent diabatic potential curves cross at one point and only a particular horizontal curve has interactions with the others. Based on the contour integral method used, some mathematical aspects such as a possible generalization of the Whittaker functions are also briefly discussed.

Journal of Physics A Mathematical and General•Oct 7, 1997•84 citations
A model of an excited quantum system is considered. An exact solution is obtained for a non-stationary problem in which the interaction potential is an arbitrary function of time and coordinates. The obtained solution reduces in particular cases to well-known results for transition probabilities between highly excited levels of a quantum oscillator.
Introduction We now move to considering the dynamics of a system of nuclei and electrons. Of course, both electrons and nuclei are subject to the laws of quantum mechanics, but since nuclei are 2000 to 200,000 times heavier than electrons, we expect that classical mechanics will be a much better approximation for the motion of nuclei than for the motion of electrons. This means that we expect a level of approximation to be valid, where some of the degrees of freedom (d.o.f.) of a system behave essentially classically and others behave essentially quantum-mechanically. The system then is of a mixed quantum/classical nature. Most often the quantum subsystem consists of system of electrons in a dynamical field of classical nuclei, but the quantum subsystem may also be a selection of generalized nuclear coordinates (e.g., corresponding to high-frequency vibrations) while other generalized coordinates are supposed to behave classically, or describe the motion of a proton in a classical environment. So, in this chapter we consider the dynamics of a quantum system in a non-stationary potential. In Section 5.2 we consider the time-dependent potential as externally given, without taking notice of the fact that the sources of the time-dependent potential are moving nuclei, which are quantum particles themselves, feeling the interaction with the quantum d.o.f. Thus we consider the time evolution of the quantum system, which now involves mixing-in of excited states, but we completely ignore the back reaction of the quantum system onto the d.o.f. that cause the time-dependent potential, i.e., the moving nuclei.
Figure 2.1 shows a schematic diagram of a two-level system, called a two-level atom, with the ground state |1〉 and the upper (excited) state |2〉. In fact, the electron can make transitions between many energy states, but we can limit the transitions to only between two states. In practice, it is done by a suitable choice of the frequency of an external field that will force the electron to oscillate only between these two selected states [3, 4]. Multi-level transitions involving more than two energy states are much more complex and we are not intend to consider them here, but the formalism presented here can be extended to multi-level cases.a The energy of the electron in the selected states |2〉 and |1〉 is determined by the stationary Schro¨dinger equation HˆA |1〉 = E1 |1〉 , HˆA |2〉 = E2 |2〉 , (2.10) where HˆA is the Hamiltonian of the atom whose explicit form is to be determine.
We study the nonstationary solutions of Fokker-Planck equations associated to either stationary or non stationary quantum states. In particular, we discuss the stationary states of quantum systems with singular velocity fields. We introduce a technique that allows arbitrary evolutions ruled by these equations to account for controlled quantum transitions. As a first signficant application we present a detailed treatment of the transition probabilities and of the controlling time-dependent potentials associated to the transitions between the stationary, the coherent, and the squeezed states of the harmonic oscillator.
In this paper we investigate the dynamics of a model for a three-level atom in interaction with a radiation field. The exact solution to the spontaneous-emission problem is derived using methods developed earlier by the authors, and expressions are obtained for the probabilities of the atom’s being in the first or second excited states at any time t. For the special case that the strengths of the coupling between each of the excited states and the λth mode of the field are proportional, detailed conclusions can be drawn concerning the effects of such factors as system size, coupling function, and level splitting on the temporal evolution of the system. The evolution of excited quantum systems having one versus two modes of decay to the ground state is also compared, and similarities and differences in the temporal behavior are noted. Finally the relevance of the theory presented in this paper to experimental problems in radiation chemistry and physics is indicated in our concluding remarks.
The non-stationary Schrödinger equation in a finite basis of states is considered for the Hamiltonian matrix linearly depending on time. Exact analytical solutions of asymptotic transition probabilities are obtained for a bow-tie model, in which an arbitrary number of linear time-dependent diabatic potential curves cross at one point and only a particular horizontal curve has interactions with the others. Based on the contour integral method used, some mathematical aspects such as a possible generalization of the Whittaker functions are also briefly discussed.