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

Coherent excitation of a two-state system by a Gaussian field

G. S. Vasilev, Nikolay V. Vitanov

Published Nov 16, 2004• 32 citations
Publisher

Abstract

This work presents an analytic description of the coherent excitation of a two-state quantum system by an external field with a Gaussian temporal shape and a constant frequency. A very accurate analytic approximation to the transition probability is derived by using the Dykhne-Davis-Pechukas approach. This approximation provides analytic expressions for the frequency and amplitude of the probability oscillations, for the excitation profile and excitation linewidth. The linewidth, in particular, shows a weak, logarithmic power broadening.

DOI
10.1103/physreva.70.053407

Related papers

Coherent excitation of a two-state system by a linearly chirped Gaussian pulse

G. S. Vasilev, Nikolay V. Vitanov

This work presents an analytic description of coherent excitation of a two-state quantum system by an external field with a Gaussian temporal shape and a linear frequency sweep. A very accurate analytic approximation to the transition probability in terms of the Lambert function is derived by using the Dykhne-Davis-Pechukas approach. This approximation provides analytic expressions for the frequency and the amplitude of the probability oscillations and for the ranges of interaction parameters where high transition probability is obtained.

The Journal of Chemical Physics•Oct 31, 2005•21 citations

Coherent excitation of two-state system by a Lorentzian filed

G. S. Vasilev, Nikolay V. Vitanov

This work presents an analytic description of the coherent excitation of a two-state quantum system by an external field with a Lorentzian temporal shape and a constant frequency. An exact analytical solution for the differential equation of the model is derived in terms of Confluent Heun functions. Also a very accurate analytic approximation to the transition probability is derived by using the Dykhne-Davis-Pechukas approach. This approximation provides analytic expressions for the frequency and amplitude of the probability oscillations.

arXiv:1402.5119•Feb 20, 2014•0 citations

Coherent excitation of a two-state system by a Lorentzian field

Aida Shiroyan, Genko S. Vasilev, Nikolay V. Vitanov

We study the coherent excitation of a two-state quantum system by a field with a Lorentzian temporal envelope and constant carrier frequency. The associated differential equation admits an exact local representation in terms of confluent Heun functions. For the transition probability we develop a Dykhne-Davis-Pechukas (DDP) description based on the two relevant complex transition points and their interference. The DDP action is analyzed directly in the weak- and strong-coupling limits, yielding explicit asymptotic expressions for the oscillation phase, oscillation envelope, far-detuned line shape, and near-resonant behavior. In particular, the strong-coupling asymptotics imply a linewidth proportional to the inverse peak Rabi frequency for resonant odd-$π$ pulses, thereby exhibiting the power-narrowing characteristic of the Lorentzian pulse.

quant-pharXiv:2607.27466•Jul 31, 2026•0 citations

Adiabatic passage for a lossy two-level quantum system by a complex time method

Ghassen Dridi, S. Guérin

Using a complex time method with the formalism of Stokes lines, we establish a generalization of the Davis–Dykhne–Pechukas formula which gives in the adiabatic limit the transition probability of a lossy two-state system driven by an external frequency-chirped pulse-shaped field. The conditions that allow this generalization are derived. We illustrate the result with the dissipative Allen–Eberly and Rosen–Zener models.

Journal of Physics A Mathematical and Theoretical•Apr 19, 2012•8 citations

Resonant excitation amidst dephasing: An exact analytic solution

Elica S. Kyoseva, Nikolay V. Vitanov

An exact analytic solution is presented for coherent resonant excitation of a two-state quantum system driven by a time-dependent pulsed external field with a hyperbolic-secant shape in the presence of dephasing. Analytic results are derived for the amplitude and phase shift of the damped Rabi oscillations.

arXiv:0804.3315•Physical Review A•May 31, 2005•21 citations

Two-level-atom excitation probability for single- and N -photon wave packets

Hemlin Swaran Rag, Julio R. Gea-Banacloche

We study how the transient excitation probability of a two-level atom by a quantized field depends on the temporal profile of the incident pulse, in the presence of external losses, for both coherent and Fock states, and in two complementary limits: when the pulse contains only one photon (on average), and when the number of photons $N$ is large. For the latter case we derive analytical expressions for the scaling of the excitation probability with $N$ that can be easily evaluated for any pulse shape.

arXiv:1707.02351•Physical Review A•Sep 11, 2017•15 citations
This work presents an analytic description of the coherent excitation of a two-state quantum system by an external field with a Gaussian temporal shape and a constant frequency. A very accurate analytic approximation to the transition probability is derived by using the Dykhne-Davis-Pechukas approach. This approximation provides analytic expressions for the frequency and amplitude of the probability oscillations, for the excitation profile and excitation linewidth. The linewidth, in particular, shows a weak, logarithmic power broadening.
This work presents an analytic description of coherent excitation of a two-state quantum system by an external field with a Gaussian temporal shape and a linear frequency sweep. A very accurate analytic approximation to the transition probability in terms of the Lambert function is derived by using the Dykhne-Davis-Pechukas approach. This approximation provides analytic expressions for the frequency and the amplitude of the probability oscillations and for the ranges of interaction parameters where high transition probability is obtained.
This work presents an analytic description of the coherent excitation of a two-state quantum system by an external field with a Lorentzian temporal shape and a constant frequency. An exact analytical solution for the differential equation of the model is derived in terms of Confluent Heun functions. Also a very accurate analytic approximation to the transition probability is derived by using the Dykhne-Davis-Pechukas approach. This approximation provides analytic expressions for the frequency and amplitude of the probability oscillations.
We study the coherent excitation of a two-state quantum system by a field with a Lorentzian temporal envelope and constant carrier frequency. The associated differential equation admits an exact local representation in terms of confluent Heun functions. For the transition probability we develop a Dykhne-Davis-Pechukas (DDP) description based on the two relevant complex transition points and their interference. The DDP action is analyzed directly in the weak- and strong-coupling limits, yielding explicit asymptotic expressions for the oscillation phase, oscillation envelope, far-detuned line shape, and near-resonant behavior. In particular, the strong-coupling asymptotics imply a linewidth proportional to the inverse peak Rabi frequency for resonant odd-πππ pulses, thereby exhibiting the power-narrowing characteristic of the Lorentzian pulse.
We study how the transient excitation probability of a two-level atom by a quantized field depends on the temporal profile of the incident pulse, in the presence of external losses, for both coherent and Fock states, and in two complementary limits: when the pulse contains only one photon (on average), and when the number of photons NNN is large. For the latter case we derive analytical expressions for the scaling of the excitation probability with NNN that can be easily evaluated for any pulse shape.