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arXiv:2607.27466

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

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

quant-phSubmitted Jul 29, 2026• Announced Jul 31, 2026• 0 citations

Abstract

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.

Comments: 14 pages, 5 figures

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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.

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.

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.

Abstract We investigate the dynamics of a two-level quantum system driven by a laser pulse characterized by Lorentzian frequency and sub-Lorentzian amplitude modulations. Complete analytical solutions, expressed via confluent Heun functions, are derived. Our analysis reveals that explicit exact analytical solutions exist under infinite sets of specific parameter conditions. The effects of modulation parameters and initial conditions on the final transition probabilities are examined analytically and numerically. Furthermore, the method is demonstrated to be directly applicable to two closely related models with Lorentzian pulses.

It is shown that any pulse with a time-asymmetric envelope and a constant non-zero detuning excites a two-level quantum system with a probability of nearly one-half provided the pulse is very asymmetric, adiabatic in the slowly rising part of its envelope, sudden in the steep part and the peak Rabi frequency is much greater than the detuning. Three particular cases are considered analytically: the asymmetric hyperbolic-secant, the Bambini-Berman and the exponential pulse, which illustrate the general conclusions. The results are applied to a special three-level 'vee' system whose two transitions are driven by two asymmetric laser pulses of the same Rabi frequencies and the same detunings. Analysis shows that if such a system is prepared initially in its ground state, effective population depletion of this state can be achieved, the results being quite insensitive to variations in the Rabi frequency and the detuning.