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

Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIE

Transitions probabilities in the multilevel quantum system at the third order of perturbation theory

Alexander Alexandrovich Biryukov, B. V. Danilyuk

Published Mar 3, 2008• 0 citations
Publisher

Abstract

The transitions between stationary states in multilevel quantum system under the influence of an alternating external electric field are considered in this work. Herewith the strength of external electric field changes with time by the harmonic law. The analytical expressions for quantum transitions probabilities of a system are given at the third order of perturbation theory. The dependencies of quantum transitions probabilities and average energy of a system upon interaction time and frequency of field are investigated in the case when the system is a charged particle in rectangular infinitely deep potential pit.

DOI
10.1117/12.801589

Related papers

Rabi oscillations in many-level quantum system

Alexander Alexandrovich Biryukov, B. V. Danilyuk

The object of the research are the quantum transitions of a many-level system between its stationary states under the influence of an alternating external electric field. The transition amplitudes and probabilities are calculated by the method of perturbation theory in the approximation of a classical external field. It is illustrated that in the case when the external field frequency is equal to the frequency of any quantum transition, then the probability of this transition fluctuate nearly the average value which is oscillating with Rabi frequency. Probabilities of other quantum transitions are very small and change chaotically with time.

Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIE•Mar 3, 2008•3 citations

Time-Dependent Perturbation Theory in Quantum Phase Space

Qian‐Shu Li

Time-dependent perturbation theory is discussed within the quantum phase space representation as formulated by Torres-Vega and Frederick(T-F) and the quantum transition probability is studied.Time-dependent perturbation formula in T-F quantum phase space is established,in accordance with the calculation theory in T-F phase space.As an example,the one dimensional harmonic oscillator system,affected by an external electric field,is used to calculate in T-F phase space,the result indicate that the principle of the method is correct.Quantum transition probability of the system's first excited state in T-F phase space is discussed.

Transactions of Beijing Institute of Technology•Jan 1, 2009•0 citations

Transitions of a Quantum Harmonic Oscillator as a Result of Interaction with an Ultrashort Pulse Field

Dmitry N. Makarov, Mikhail Y. Arkhipov, Polina A. Stremilova

The quantum harmonic oscillator is a model system that is actively used in many applications of quantum and nonlinear physics, molecular chemistry and biophysics. In this paper, a formula is obtained for the probability amplitude of the transition of a quantum harmonic oscillator from an oscillatory state with the number$\nu$to a state with the number$\nu+n$, which is affected by an external force depending on time using a method based on the Magnus and Baker-Campbell-Hausdorff decomposition. A formula is obtained for the special case of interaction of a quantum harmonic oscillator with an ultrashort pulse field. As an example, graphs of the probabilities of the oscillator transition from the first oscillatory state to the second and third, the average energy received and the rms fluctuation of the energy received for different values of the ratio of the carrier frequency of the pulse and the frequency of the oscillator are constructed. Conclusions are drawn about the correctness of using the concept of average energy in relation to this problem.

IEEE International Conference on Problems of Informatics, Electronics and Radio Engineering (PIERE)•Nov 15, 2024•0 citations

Dynamical behavior of the harmonic oscillator in the electric dipole interaction

Yoshio Nishiyama, Ikuo Yamamoto, Yumiko Hirashima +1 more

To understand the time-dependent process in quantum mechanics, an exact expression for the dynamical change of the transition probability and the expectation value of the oscillation energy are presented for the system of the charged harmonic oscillator interacting with an external field through the electric dipole interaction of either type A・p or E・r. The oscillating wave packet is shown to be made from an eigenfunction of the free oscillator Hamiltonian by the interaction during some time. The off-resonance, difference between the field frequency and the proper frequency of the oscillator, controls the number of basis states significant in the transient process. Even on complete resonance, the golden rule holds true only for a short duration and all other nonresonant basis states participate in turn as the interaction time elapses. The difference between two types of dipole interaction exists certainly in the probability distribution in the basis states and the oscillation energy, though it does not in the total current of the oscillator.

•Nov 1, 1997•0 citations

Transition Probabilities Among Fock States of an Ion in Harmonic Trap due to Alternating Electric Field

Wu ., Ying, Yang Yang +1 more

In this paper, we derive the exact analytical expressions of the transition probabilities among the Fock states of an ion in a harmonic trap due to the presence of an alternating electric field.

理论物理通讯：英文版•Jan 1, 2002•0 citations

Transition Probabilities Among Fock States of an Ion in Harmonic Trap due to Alternating Electric Field

Ying Wu, Xiaoxue Yang

In this paper, we derive the exact analytical expressions of the transition probabilities among the Fock states of an ion in a harmonic trap due to the presence of an alternating electric field.

Communications in Theoretical Physics•Jul 15, 2002•1 citation
The transitions between stationary states in multilevel quantum system under the influence of an alternating external electric field are considered in this work. Herewith the strength of external electric field changes with time by the harmonic law. The analytical expressions for quantum transitions probabilities of a system are given at the third order of perturbation theory. The dependencies of quantum transitions probabilities and average energy of a system upon interaction time and frequency of field are investigated in the case when the system is a charged particle in rectangular infinitely deep potential pit.
The object of the research are the quantum transitions of a many-level system between its stationary states under the influence of an alternating external electric field. The transition amplitudes and probabilities are calculated by the method of perturbation theory in the approximation of a classical external field. It is illustrated that in the case when the external field frequency is equal to the frequency of any quantum transition, then the probability of this transition fluctuate nearly the average value which is oscillating with Rabi frequency. Probabilities of other quantum transitions are very small and change chaotically with time.
Time-dependent perturbation theory is discussed within the quantum phase space representation as formulated by Torres-Vega and Frederick(T-F) and the quantum transition probability is studied.Time-dependent perturbation formula in T-F quantum phase space is established,in accordance with the calculation theory in T-F phase space.As an example,the one dimensional harmonic oscillator system,affected by an external electric field,is used to calculate in T-F phase space,the result indicate that the principle of the method is correct.Quantum transition probability of the system's first excited state in T-F phase space is discussed.
The quantum harmonic oscillator is a model system that is actively used in many applications of quantum and nonlinear physics, molecular chemistry and biophysics. In this paper, a formula is obtained for the probability amplitude of the transition of a quantum harmonic oscillator from an oscillatory state with the numberν\nuνto a state with the numberν+n\nu+nν+n, which is affected by an external force depending on time using a method based on the Magnus and Baker-Campbell-Hausdorff decomposition. A formula is obtained for the special case of interaction of a quantum harmonic oscillator with an ultrashort pulse field. As an example, graphs of the probabilities of the oscillator transition from the first oscillatory state to the second and third, the average energy received and the rms fluctuation of the energy received for different values of the ratio of the carrier frequency of the pulse and the frequency of the oscillator are constructed. Conclusions are drawn about the correctness of using the concept of average energy in relation to this problem.
To understand the time-dependent process in quantum mechanics, an exact expression for the dynamical change of the transition probability and the expectation value of the oscillation energy are presented for the system of the charged harmonic oscillator interacting with an external field through the electric dipole interaction of either type A・p or E・r. The oscillating wave packet is shown to be made from an eigenfunction of the free oscillator Hamiltonian by the interaction during some time. The off-resonance, difference between the field frequency and the proper frequency of the oscillator, controls the number of basis states significant in the transient process. Even on complete resonance, the golden rule holds true only for a short duration and all other nonresonant basis states participate in turn as the interaction time elapses. The difference between two types of dipole interaction exists certainly in the probability distribution in the basis states and the oscillation energy, though it does not in the total current of the oscillator.