Rotating wave approximation (RWA) plays a key rule in quantum optics to solve some Schrödinger equation approximately. For example, it is well known that RWA has been used to calculate the transition probability. However, so far no one shows the validity of RWA. Recently Larson [J. Larson, Phys. Rev. Lett. 108, 033601 (2012)] gave the first example showing that the application of RWA in the Jaynes-Cummings model may lead to false conclusions. In this paper, we analytically and numerically show that the application of RWA leads to false conclusions about the transition probability for the near or exact resonance.Rotating wave approximation (RWA) plays a key rule in quantum optics to solve some Schrödinger equation approximately. For example, it is well known that RWA has been used to calculate the transition probability. However, so far no one shows the validity of RWA. Recently Larson [J. Larson, Phys. Rev. Lett. 108, 033601 (2012)] gave the first example showing that the application of RWA in the Jaynes-Cummings model may lead to false conclusions. In this paper, we analytically and numerically show that the application of RWA leads to false conclusions about the transition probability for the near or exact resonance.

arXiv:1511.06122Nov 19, 20150 citations

A remark on transition probability

Huzihiro Araki, G. A. Raggio

Letters in Mathematical PhysicsMay 1, 198233 citations

Transition Probabilities

Robert L. Brooks

Undergraduate lecture notes in physicsJan 1, 20131 citation

Sum rules and expansion formula for Stark radiative transitions in the hydrogen atom

David R. Herrick

An expansion formula for Stark effect transition probabilities is derived in terms of field-free (spherical) transition probabilities. Expansion coefficients are squares of Clebsch-Gordan coefficients from the SO(4) = SU(2) \ifmmode\times\else\texttimes\fi{} SU(2) description of the hydrogen atom. The method provides new sum rules for Stark transitions which explain regularities in previous calculations. Accurate formulas for average Stark transition probabilities obtain from application of the method to an empirical model for field-free transition probabilities. The approximation permits estimation of Stark lifetimes in the large- $n$ regime.An expansion formula for Stark effect transition probabilities is derived in terms of field-free (spherical) transition probabilities. Expansion coefficients are squares of Clebsch-Gordan coefficients from the SO(4) = SU(2) \ifmmode\times\else\texttimes\fi{} SU(2) description of the hydrogen atom. The method provides new sum rules for Stark transitions which explain regularities in previous calculations. Accurate formulas for average Stark transition probabilities obtain from application of the method to an empirical model for field-free transition probabilities. The approximation permits estimation of Stark lifetimes in the large-$n$ regime.

Physical Review ANov 1, 197524 citations

Transition probabilities

Pieter E. Vermaas

Cambridge University Press eBooksFeb 5, 20100 citations

Exact transition probabilities in a 6-state Landau–Zener system with path interference

N A Sinitsyn

We identify a nontrivial multistate Landau–Zener (LZ) model for which transition probabilities between any pair of diabatic states can be determined analytically and exactly. In the semiclassical picture, this model features the possibility of interference of different trajectories that connect the same initial and final states. Hence, transition probabilities are generally not described by the incoherent successive application of the LZ formula. We discuss reasons for integrability of this system and provide numerical tests of the suggested expression for the transition probability matrix.We identify a nontrivial multistate Landau–Zener (LZ) model for which transition probabilities between any pair of diabatic states can be determined analytically and exactly. In the semiclassical picture, this model features the possibility of interference of different trajectories that connect the same initial and final states. Hence, transition probabilities are generally not described by the incoherent successive application of the LZ formula. We discuss reasons for integrability of this system and provide numerical tests of the suggested expression for the transition probability matrix.

arXiv:1501.06083Journal of Physics A Mathematical and TheoreticalApr 23, 201532 citations

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