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

Atoms

Saturation Effect Produced by Laser Pulses: Karplus–Schwinger Approach versus Bloch Solution

Valery Alexandrovich Astapenko, V. Lisitsa

Published Oct 10, 2022• 0 citations
Publisher

Abstract

The saturation effect during the excitation of a two-level system by laser pulses is investigated in the framework of two approaches: excitation probability based on Karplus–Schwinger spectral profile and exact solution of Bloch equations. Simple analytical expression for the excitation probability by exponential pulse is derived. The excitation spectra obtained using this expression were compared with the result of solving the Bloch equations for various values of the pulse duration and the Rabi frequency, which describes the strength of the electromagnetic interaction. It is shown that in the case of long pulses, there is a satisfactory correspondence between the two approaches, but in short-pulse limit and strong saturation, the probability description based on Karplus–Schwinger spectral profile and perturbation theory does not provide satisfactory results.

DOI
10.3390/atoms10040111

Related papers

Excitation of a two-level system by a chirped laser pulse

Valery Alexandrovich Astapenko, M. S. Romadanovskiĭ

The excitation of a two-level system by a chirped laser pulse is analyzed using an analytical approach (in the perturbation-theory limit) that involves the modified rotating-wave approximation and the numerical solution to the Bloch equation. The dependence of the population of the upper energy level on the chirp is studied for various radiation intensities and pulse durations. An exact solution is compared with the result obtained using the modified rotating-wave approximation and the perturbation theory. It is demonstrated that, for a certain range of parameters, the excitation probability of a two-level system can be effectively controlled via a variation in the chirp.

Laser Physics•May 1, 2009•19 citations

DYNAMICS OF PULSED SATURATION IN INHOMOGENEOUSLY BROADENED TWO-LEVEL

Vladimir Kuz

On the basis of Bloch's equations an analytical expression is obtained for the pulsed saturation signal of a two-level quantum system with allowance for inhomogeneous line broadening. It is shown that in this case the signal drop is exponential over the initial portion and nonexponential for long times. It is found that starting from a certain time, which depends on the field magnitude, relaxation parameters, and inhomogeneous width of the line, a through appears in the line contour, the depth and width of which increases with an increase in pulse duration. At smaller durations of the pulse, when the line is bell-shaped, an exponential decay of the signal indicates saturation of homogeneously broadened line. Comparison of the results obtained in an experiment on pulsed saturation in ruby shows that at large amplitudes of the field and considerable inhomogeneous broadening, one observes a deviation from the Bloch theory manifesting itself as a biexponential drop in the pulsed saturation signal A conclusion is drawn that the Bloch theory satisfactorily describes the experiment until the effective time of energy transfer to the lattice is smaller than the time of the spectral propagation of excitation.

•Jan 1, 1997•0 citations

Pulsed excitation of a quantum oscillator: A model accounting for damping

Valery Alexandrovich Astapenko, Timur Bergaliyev, Sergey V. Sakhno

Abstract This article proposes a model that accounts for damping of a quantum oscillator (QO) during pulsed excitation. Our model is based on the Schwinger formula, which calculates oscillator’s excitation probability through the energy of an associated classical damped oscillator. We utilize this model to describe the influence of damping on temporal and spectral dependences of QO excitation, induced by electromagnetic pulses with exponential and double exponential envelopes. The oscillator excitation is analyzed in terms of transition probability between stationary states after pulse termination. Here, we present an analytical description of these dependences, along with numerical results. Specifically, we derive analytical expressions that depict the saturation effect during pulsed excitation, taking into account the damping of a QO. The evolution of the temporal dependence of the excitation probability with a change in the damping constant is numerically traced. We demonstrate that the number of maxima in this dependence is determined by the values of pulse parameters and the damping constant.

Open Physics•Jan 1, 2024•0 citations

Saturation of two-level systems under pulsed stochastic resonance conditions

Баруздин Сергей Анатольевич

Pulsed stochastic excitation of a two-level system described by Bloch equations is studied. An equation for the average powers of the components of the state vector of the system is obtained on the basis of the theory of stochastic differential equations, and solved. The dynamical and nonlinear properties of the response of a system under pulsed stochastic resonance conditions are analyzed and the results are compared with the corresponding stationary state. The results obtained can be used in spectroscopy and for analysis of nonlinear filters based on the saturation effect and intended for processing rf and light range signals.

Technical Physics•Dec 1, 1999•1 citation

Free-induction decay after a pulse saturation for systems with random telegraph frequency

Vladimir S. Malinovsky

The free-induction decay (FID) after saturation by a laser radiation pulse of finite duration is studied for systems with spectral diffusion. The exact solution of the FID signal shape has been obtained in the framework of the telegraph noise model. This solution takes into account the finite duration of the saturating field and is valid at arbitrary values of the spectral exchange rate and the amplitude of the coherent field. The exact expression of the FID signal is derived in the weak-external-field limit. It is shown that the FID signal suddenly disappears after a time equal to the pulse width. This confirms the validity of the theorem on coherent transients, which has been proved for the Bloch equations [A. Schenzle, N. C. Wong, and R. G. Brewer, Phys. Rev. A 22, 635 (1980)].

Physical Review A•Dec 1, 1995•8 citations

Resonant pulse excitation leading to ionization

Jay R. Ackerhalt

Laser excitation of a two-level atom is analytically studied for arbitrary pulse shape, area, and energy. The ionization mechanism is modeled as a homogeneous width $\ensuremath{\gamma}$ of the atomic excited state. A transformation of the optical Bloch equations allows the dynamics to be completely described by a single equation for the area of the pulse at time $t$, $\ensuremath{\Phi}(t)$. Analytic solutions for the total bound population for a wide variety of pulse shapes can be found in two regions: $\ensuremath{\Phi}(t)\ensuremath{\approx}sin\ensuremath{\Phi}(t)$ and $\ensuremath{\Omega}(t)>\ensuremath{\gamma}$, where $\ensuremath{\Omega}(t)$ is the resonance Rabi frequency. The generalization of the two-level atom results to the $N$-level atom is discussed.

Physical Review A•Jan 1, 1978•19 citations
The saturation effect during the excitation of a two-level system by laser pulses is investigated in the framework of two approaches: excitation probability based on Karplus–Schwinger spectral profile and exact solution of Bloch equations. Simple analytical expression for the excitation probability by exponential pulse is derived. The excitation spectra obtained using this expression were compared with the result of solving the Bloch equations for various values of the pulse duration and the Rabi frequency, which describes the strength of the electromagnetic interaction. It is shown that in the case of long pulses, there is a satisfactory correspondence between the two approaches, but in short-pulse limit and strong saturation, the probability description based on Karplus–Schwinger spectral profile and perturbation theory does not provide satisfactory results.
The excitation of a two-level system by a chirped laser pulse is analyzed using an analytical approach (in the perturbation-theory limit) that involves the modified rotating-wave approximation and the numerical solution to the Bloch equation. The dependence of the population of the upper energy level on the chirp is studied for various radiation intensities and pulse durations. An exact solution is compared with the result obtained using the modified rotating-wave approximation and the perturbation theory. It is demonstrated that, for a certain range of parameters, the excitation probability of a two-level system can be effectively controlled via a variation in the chirp.
On the basis of Bloch's equations an analytical expression is obtained for the pulsed saturation signal of a two-level quantum system with allowance for inhomogeneous line broadening. It is shown that in this case the signal drop is exponential over the initial portion and nonexponential for long times. It is found that starting from a certain time, which depends on the field magnitude, relaxation parameters, and inhomogeneous width of the line, a through appears in the line contour, the depth and width of which increases with an increase in pulse duration. At smaller durations of the pulse, when the line is bell-shaped, an exponential decay of the signal indicates saturation of homogeneously broadened line. Comparison of the results obtained in an experiment on pulsed saturation in ruby shows that at large amplitudes of the field and considerable inhomogeneous broadening, one observes a deviation from the Bloch theory manifesting itself as a biexponential drop in the pulsed saturation signal A conclusion is drawn that the Bloch theory satisfactorily describes the experiment until the effective time of energy transfer to the lattice is smaller than the time of the spectral propagation of excitation.
Abstract This article proposes a model that accounts for damping of a quantum oscillator (QO) during pulsed excitation. Our model is based on the Schwinger formula, which calculates oscillator’s excitation probability through the energy of an associated classical damped oscillator. We utilize this model to describe the influence of damping on temporal and spectral dependences of QO excitation, induced by electromagnetic pulses with exponential and double exponential envelopes. The oscillator excitation is analyzed in terms of transition probability between stationary states after pulse termination. Here, we present an analytical description of these dependences, along with numerical results. Specifically, we derive analytical expressions that depict the saturation effect during pulsed excitation, taking into account the damping of a QO. The evolution of the temporal dependence of the excitation probability with a change in the damping constant is numerically traced. We demonstrate that the number of maxima in this dependence is determined by the values of pulse parameters and the damping constant.
Pulsed stochastic excitation of a two-level system described by Bloch equations is studied. An equation for the average powers of the components of the state vector of the system is obtained on the basis of the theory of stochastic differential equations, and solved. The dynamical and nonlinear properties of the response of a system under pulsed stochastic resonance conditions are analyzed and the results are compared with the corresponding stationary state. The results obtained can be used in spectroscopy and for analysis of nonlinear filters based on the saturation effect and intended for processing rf and light range signals.
The free-induction decay (FID) after saturation by a laser radiation pulse of finite duration is studied for systems with spectral diffusion. The exact solution of the FID signal shape has been obtained in the framework of the telegraph noise model. This solution takes into account the finite duration of the saturating field and is valid at arbitrary values of the spectral exchange rate and the amplitude of the coherent field. The exact expression of the FID signal is derived in the weak-external-field limit. It is shown that the FID signal suddenly disappears after a time equal to the pulse width. This confirms the validity of the theorem on coherent transients, which has been proved for the Bloch equations [A. Schenzle, N. C. Wong, and R. G. Brewer, Phys. Rev. A 22, 635 (1980)].
Laser excitation of a two-level atom is analytically studied for arbitrary pulse shape, area, and energy. The ionization mechanism is modeled as a homogeneous width $\ensuremath{\gamma}$ of the atomic excited state. A transformation of the optical Bloch equations allows the dynamics to be completely described by a single equation for the area of the pulse at time ttt, $\ensuremath{\Phi}(t)$. Analytic solutions for the total bound population for a wide variety of pulse shapes can be found in two regions: $\ensuremath{\Phi}(t)\ensuremath{\approx}sin\ensuremath{\Phi}(t)$ and $\ensuremath{\Omega}(t)>\ensuremath{\gamma}$, where $\ensuremath{\Omega}(t)$ is the resonance Rabi frequency. The generalization of the two-level atom results to the NNN-level atom is discussed.