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The Journal of Chemical Physics

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

G. S. Vasilev, Nikolay V. Vitanov

Published Oct 31, 2005• 21 citations
Publisher

Abstract

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.

DOI
10.1063/1.2090260

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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 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 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 calculate the propagator and the transition probabilities for a coherently driven three-state quantum system. The energies of the three states change linearly in time, whereas the interactions between them are pulse shaped. We derive a highly accurate analytic approximation by assuming independent pairwise Landau-Zener transitions occurring instantly at the relevant avoided crossings, and adiabatic evolution elsewhere. Quantum interferences are identified, which occur due to different possible evolution paths in Hilbert space between an initial and a final state. A detailed comparison with numerical results for Gaussian-shaped pulses demonstrates a remarkable accuracy of the analytic approximation. We use the analytic results to derive estimates for the half-width of the excitation profile, and for the parameters required for creation of a maximally coherent superposition of the three states. These results are of potential interest in ladder climbing in alkali-metal atoms by chirped laser pulses, in quantum rotors, in transitions between Zeeman sublevels of a J=1J=1J=1 level in a magnetic field, and in control of entanglement of a pair of spin-1∕21∕21∕2 particles. The results for the three-state system can be generalized, without essential difficulties, to higher dimensions.
We present a theoretical study of the excitation of a charged quantum linear oscillator by chirped laser pulse with the use of probability of the process throughout the pulse action. We focus on the case of the excitation of the oscillator from the ground state without relaxation. Calculations were made for an arbitrary value of the electric field strength by utilizing the exact expression for the excitation probability. The dependence of the excitation probability on the pulse parameters was analyzed both numerically and by using analytical formulas.