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

Physical Review A

Wave-packet dynamics: Level-crossing-induced changes in momentum distributions

Kalle‐Antti Suominen, B. M. Garraway

Published Nov 1, 1993• 16 citations
Publisher

Abstract

We study the changes appearing in Gaussian momentum distributions of quantum-mechanical wave packets after a traversal of a linear level crossing. The numerical results are discussed in terms of the semiclassical Landau-Zener theory. We observe a momentum filtering effect in nondissipative crossings. The results obtained from studies of dissipative level crossings suggest that one can obtain substantial changes in momentum distributions with these systems. The Landau-Zener theory provides qualitative understanding of the processes taking place in the dissipative level crossing.

DOI
10.1103/physreva.48.3811

Related papers

Dissipation effects on wave packets in level crossings: A comparison between two numerical approaches

W. K. Lai, Kalle‐Antti Suominen, B. M. Garraway +1 more

We study the time evolution of wave packets on coupled energy levels including the irreversible effect of spontaneous emission. As a test case we choose a simple two-state level-crossing problem of the Landau-Zener type. The numerical treatment of this situation is demanding, and we explore two approaches based on different views of the quantum-mechanical dynamics. First, we solve the time evolution of the wave packet using the traditional master equation giving directly the ensemble averages. Second, we use the recently developed Monte Carlo simulation method, which gives the individual members of an ensemble of quantum states undergoing spontaneous quantum jumps. The results are compared and found to agree when large enough ensembles are used. We discuss the computational requirements for the two methods and we find both quite demanding but qualitatively different.

Physical Review A•Jun 1, 1993•42 citations

Statistical aspects of dissipation by Landau-Zener transitions

Michael Wilkinson

Considers the effect of slowly varying the parameters X i of a finite-sized quantum mechanical system. The system is excited to higher energies by Landau-Zener transitions at avoided crossing; since this increases the energy of the system, it has the effect of dissipation of the driving motion. The rate of dissipation depends on the level spacing distribution of the system. When the spectral statistics are those of the Gaussian unitary ensemble, the rate of dissipation is proportional to X i 2 , i.e. there is viscous or ohmic damping. When the spectral statistics are of those of the Gaussian orthogonal ensemble, the rate of dissipation is proportional to X i 3 2/.

Journal of Physics A Mathematical and General•Nov 7, 1988•168 citations

Level crossings in a cavity QED model

Jonas Larson

In this paper I study the dynamics of a two-level atom interacting with a standing-wave field. When the atom is subjected to a weak linear force, the problem can be turned into a time-dependent one, and the evolution is understood from the band structure of the spectrum. The presence of level crossings in the spectrum gives rise to Bloch oscillations of the atomic motion. Here I investigate the effects of the atom-field detuning parameter. A variety of different level crossings are obtained by changing the magnitude of the detuning, and the behavior of the atomic motion is strongly affected due to this. I also consider the situation in which the detuning is oscillating in time, and its impact on the atomic motion. Wave-packet simulations of the full problem are treated numerically and the results are compared with analytical solutions given by the standard Landau-Zener and the three-level Landau-Zener models.

arXiv:quant-ph/0601053•Physical Review A•Jan 30, 2006•13 citations

Observation of Landau-Zener dynamics in classical optical systems

Dirk Bouwmeester, Nynke H. Dekker, F. E. van Dorsselaer +3 more

We report the observation of ``tunneling'' effects in a classical optical two-level system. In particular, we present experimental results for the optical implementations of the Landau-Zener model and of a hidden level-crossing model. The experimental results are in good agreement with theory for both the transition probability and the detailed time evolution of the wave function.

Physical Review A•Jan 1, 1995•58 citations

Quantum diffusion in the strong tunneling regime

Nisarga Paul, Ariel Amir

We study the spread of a quantum-mechanical wave packet in a noisy environment, modeled using a tight-binding Hamiltonian. Despite the coherent dynamics, the fluctuating environment may give rise to diffusive behavior. When correlations between different level-crossing events can be neglected, we use the solution of the Landau-Zener problem to find how the diffusion constant depends on the noise. We also show that when an electric field or external disordered potential is applied to the system, the diffusion constant is suppressed with no drift term arising. The results are relevant to various quantum systems, including exciton diffusion in photosynthesis and electronic transport in solid-state physics.

arXiv:1812.04166•Physical review. B./Physical review. B•Jul 26, 2019•3 citations

Dynamical effects at avoided level crossings: A study of the Landau-Zener effect using Rydberg atoms

Jan R. Rubbmark, Michael M. Kash, Michael G. Littman +1 more

We present a study of the dynamics of traversing an avoided energy level crossing. A pair of Stark levels of Rydberg states of lithium are used as a test system for measuring the diabatic transition probability. The experimental conditions are close to those assumed by the Landau-Zener theory. Possible corrections to the Landau-Zener theory are analyzed, and applications of the results to pulsed-field ionization are discussed.

Physical Review A•Jun 1, 1981•280 citations
We study the changes appearing in Gaussian momentum distributions of quantum-mechanical wave packets after a traversal of a linear level crossing. The numerical results are discussed in terms of the semiclassical Landau-Zener theory. We observe a momentum filtering effect in nondissipative crossings. The results obtained from studies of dissipative level crossings suggest that one can obtain substantial changes in momentum distributions with these systems. The Landau-Zener theory provides qualitative understanding of the processes taking place in the dissipative level crossing.
We study the time evolution of wave packets on coupled energy levels including the irreversible effect of spontaneous emission. As a test case we choose a simple two-state level-crossing problem of the Landau-Zener type. The numerical treatment of this situation is demanding, and we explore two approaches based on different views of the quantum-mechanical dynamics. First, we solve the time evolution of the wave packet using the traditional master equation giving directly the ensemble averages. Second, we use the recently developed Monte Carlo simulation method, which gives the individual members of an ensemble of quantum states undergoing spontaneous quantum jumps. The results are compared and found to agree when large enough ensembles are used. We discuss the computational requirements for the two methods and we find both quite demanding but qualitatively different.
Considers the effect of slowly varying the parameters X i of a finite-sized quantum mechanical system. The system is excited to higher energies by Landau-Zener transitions at avoided crossing; since this increases the energy of the system, it has the effect of dissipation of the driving motion. The rate of dissipation depends on the level spacing distribution of the system. When the spectral statistics are those of the Gaussian unitary ensemble, the rate of dissipation is proportional to X i 2 , i.e. there is viscous or ohmic damping. When the spectral statistics are of those of the Gaussian orthogonal ensemble, the rate of dissipation is proportional to X i 3 2/.
In this paper I study the dynamics of a two-level atom interacting with a standing-wave field. When the atom is subjected to a weak linear force, the problem can be turned into a time-dependent one, and the evolution is understood from the band structure of the spectrum. The presence of level crossings in the spectrum gives rise to Bloch oscillations of the atomic motion. Here I investigate the effects of the atom-field detuning parameter. A variety of different level crossings are obtained by changing the magnitude of the detuning, and the behavior of the atomic motion is strongly affected due to this. I also consider the situation in which the detuning is oscillating in time, and its impact on the atomic motion. Wave-packet simulations of the full problem are treated numerically and the results are compared with analytical solutions given by the standard Landau-Zener and the three-level Landau-Zener models.
We study the spread of a quantum-mechanical wave packet in a noisy environment, modeled using a tight-binding Hamiltonian. Despite the coherent dynamics, the fluctuating environment may give rise to diffusive behavior. When correlations between different level-crossing events can be neglected, we use the solution of the Landau-Zener problem to find how the diffusion constant depends on the noise. We also show that when an electric field or external disordered potential is applied to the system, the diffusion constant is suppressed with no drift term arising. The results are relevant to various quantum systems, including exciton diffusion in photosynthesis and electronic transport in solid-state physics.