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

Communications in Theoretical Physics

Adiabatic Approximation in Interaction Between Two-Level Atom in an External Potential $V{\hat x}$ and Optical Field

Xia-Ji Liu

Published Jul 30, 1998• 0 citations
Publisher

Abstract

In discussion about the detection of the Bose–Einstein condensation, the adiabatic approximation method was taken. According to the perturbation theory, this approximation is studied in detail by a single atom model in this paper.
DOI
10.1088/0253-6102/30/1/13

Related papers

Time-dependent pulses in quantum optics: the use of Light's perturbation theory

Peter Rodgers, S. Swain

The problem of a two-level atom interacting with an external, time-dependent field is solved approximately using Light's perturbation theory. The solutions obtained are compared with accurate numerical solutions for three specific time profiles. The agreement is found to be excellent except for a certain range of detunings, and even in this range the agreement is good. The validity of an adiabatic approximation is also assessed.

Journal of Physics B Atomic and Molecular Physics•Feb 14, 1987•14 citations

Quantum field theory of atoms interacting with photons: Foundations

Maciej Lewenstein, Li You, J. Cooper +1 more

We discuss theoretical foundations of the emerging area of quantum-optical studies of many-body systems: a quantum field theory of atoms interacting with photons. This theory is designed to describe quantum-statistical systems of cooled and trapped atoms undergoing spontaneous and stimulated emission processes. Formulated in the framework of the second quantization, this theory accounts fully for quantum-statistical properties of atoms as bosons or fermions. In particular, it applies to a description of the formation of the Bose-Einstein condensate in bosonic systems, as well as the spectroscopy and other quantum optical properties of the Bose-Einstein condensate. We derive the general second quantized Hamiltonian of this theory and discuss in detail various approximations.

Physical Review A•Sep 1, 1994•106 citations

Adiabaticity in Nonlinear Quantum Dynamics: Bose-Einstein Condensate in a Temporally-Varying Box

Y. B. Band, Boris A. Malomed, Marek Trippenbach

A simple model of an atomic Bose-Einstein condensate in a box whose size varies with time is studied to determine the nature of adiabaticity in the nonlinear dynamics obtained within the Gross-Pitaevskii equation (the nonlinear Schrödinger equation). Analytical and numerical methods are used to determine the nature of adiabaticity in this nonlinear quantum system. Criteria for validity of an adiabatic approximation are formulated.

arXiv:cond-mat/0108114•Aug 7, 2001•0 citations

Adiabaticity in nonlinear quantum dynamics: Bose-Einstein condensate in a time-varying box

Y. B. Band, Boris A. Malomed, Marek Trippenbach

A simple model of an atomic Bose-Einstein condensate in a box whose size varies with time is studied to determine the nature of adiabaticity in the nonlinear dynamics obtained within the Gross-Pitaevskii equation (the nonlinear Schr\"odinger equation). Analytical and numerical methods are used to determine the nature of adiabaticity in this nonlinear quantum system. Criteria for validity of an adiabatic approximation are formulated.

arXiv:cond-mat/0111416•Physical Review A•Feb 7, 2002•35 citations

Interaction between light and a two-level atom

L. Mandeļ, E. Wolf

Light is both radiated and absorbed by atoms, and the interaction between the quantized electromagnetic field and an atom represents one of the most fundamental problems in quantum optics. However, real atoms are complicated systems, and even the simplest real atom, the hydrogen atom, has a non-trivial energy level structure. It is therefore often necessary or desirable to approximate the behavior of a real atom by that of a much simpler quantum system. For many purposes only two atomic energy levels play a significant role in the interaction with the electromagnetic field, so that it has become customary in many theoretical treatments to represent the atom by a quantum system with only two energy eigenstates. This is the most basic of all quantum systems, and it generally simplifies the treatment substantially. In a real atom the selection rules limit the allowed transitions between states, so that, in some cases, a certain state may couple to only one other. Moreover, optical pumping techniques have been developed that allow such preferred states to be prepared in the laboratory, and they have been successfully used in experiments (Abate, 1974). The two-level atom approximation is therefore close to the truth and not merely a mathematical convenience in some experimental situations. In the following we begin by developing the algebra for such a two-level atom. Dynamical variables for a two-level atom We consider an atomic quantum system with the two energy levels shown in Fig. 15.1.

Cambridge University Press eBooks•Sep 29, 1995•0 citations

Mean-field dynamics of a Bose-Einstein condensate in a time-dependent triple-well trap: Nonlinear eigenstates, Landau-Zener models, and stimulated Raman adiabatic passage

Eva-Maria Graefe, H. J. Korsch, Dirk Witthaut

We investigate the dynamics of a Bose-Einstein condensate in a triple-well trap in a three-level approximation. The interatomic interactions are taken into account in a mean-field approximation (Gross-Pitaevskii equation), leading to a nonlinear three-level model. Additional eigenstates emerge due to the nonlinearity, depending on the system parameters. Adiabaticity breaks down if such a nonlinear eigenstate disappears when the parameters are varied. The dynamical implications of this loss of adiabaticity are analyzed for two important special cases: A three-level Landau-Zener model and the stimulated Raman adiabatic passage (STIRAP) scheme. We discuss the emergence of looped levels for an equal-slope Landau-Zener model. The Zener tunneling probability does not tend to zero in the adiabatic limit and shows pronounced oscillations as a function of the velocity of the parameter variation. Furthermore we generalize the STIRAP scheme for adiabatic coherent population transfer between atomic states to the nonlinear case. It is shown that STIRAP breaks down if the nonlinearity exceeds the detuning.

arXiv:quant-ph/0507185•Physical Review A•Jan 20, 2006•139 citations
Adiabatic Approximation in Interaction Between Two-Level Atom in an External Potential Vx^V{\hat x}Vx^ and Optical Field
We discuss theoretical foundations of the emerging area of quantum-optical studies of many-body systems: a quantum field theory of atoms interacting with photons. This theory is designed to describe quantum-statistical systems of cooled and trapped atoms undergoing spontaneous and stimulated emission processes. Formulated in the framework of the second quantization, this theory accounts fully for quantum-statistical properties of atoms as bosons or fermions. In particular, it applies to a description of the formation of the Bose-Einstein condensate in bosonic systems, as well as the spectroscopy and other quantum optical properties of the Bose-Einstein condensate. We derive the general second quantized Hamiltonian of this theory and discuss in detail various approximations.
Light is both radiated and absorbed by atoms, and the interaction between the quantized electromagnetic field and an atom represents one of the most fundamental problems in quantum optics. However, real atoms are complicated systems, and even the simplest real atom, the hydrogen atom, has a non-trivial energy level structure. It is therefore often necessary or desirable to approximate the behavior of a real atom by that of a much simpler quantum system. For many purposes only two atomic energy levels play a significant role in the interaction with the electromagnetic field, so that it has become customary in many theoretical treatments to represent the atom by a quantum system with only two energy eigenstates. This is the most basic of all quantum systems, and it generally simplifies the treatment substantially. In a real atom the selection rules limit the allowed transitions between states, so that, in some cases, a certain state may couple to only one other. Moreover, optical pumping techniques have been developed that allow such preferred states to be prepared in the laboratory, and they have been successfully used in experiments (Abate, 1974). The two-level atom approximation is therefore close to the truth and not merely a mathematical convenience in some experimental situations. In the following we begin by developing the algebra for such a two-level atom. Dynamical variables for a two-level atom We consider an atomic quantum system with the two energy levels shown in Fig. 15.1.
We investigate the dynamics of a Bose-Einstein condensate in a triple-well trap in a three-level approximation. The interatomic interactions are taken into account in a mean-field approximation (Gross-Pitaevskii equation), leading to a nonlinear three-level model. Additional eigenstates emerge due to the nonlinearity, depending on the system parameters. Adiabaticity breaks down if such a nonlinear eigenstate disappears when the parameters are varied. The dynamical implications of this loss of adiabaticity are analyzed for two important special cases: A three-level Landau-Zener model and the stimulated Raman adiabatic passage (STIRAP) scheme. We discuss the emergence of looped levels for an equal-slope Landau-Zener model. The Zener tunneling probability does not tend to zero in the adiabatic limit and shows pronounced oscillations as a function of the velocity of the parameter variation. Furthermore we generalize the STIRAP scheme for adiabatic coherent population transfer between atomic states to the nonlinear case. It is shown that STIRAP breaks down if the nonlinearity exceeds the detuning.