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Analytic solutions of Bloch equations with phase term for two-pulse photon echo by the phase modulation pulses

Xiurong Ma, Wenzhong Deng, Yunlong Shan

Optoelectronics LettersJan 12, 20210 citations

Atomic population inversion in a two-level atom for shaped and chirped laser pulses: Exact solutions of Bloch equations with dephasing

Sofiane Grira, Nadia Boutabba, Hichem Eleuch

We perform a theoretical analysis of the Bloch equations of a two-level atom with dephasing. Exact analytical solutions with two different chirped and time-dependent detuned laser pulses are derived. The atomic population inversion as well as the coherence are explored for different initial populations. We show that the stationary population inversion can be controlled.

Results in PhysicsJun 5, 20213 citations

Spectral Resolution and Inversion of the Bloch Equations with Relaxation

Alexander A. Karabanov, David E. Rourke

Letters in Mathematical PhysicsAug 20, 20071 citation

Analytic solutions to the Bloch equations for amplitude- and frequency-modulated fields

Sergey V. Prants, L S Yakupova

Journal of Experimental and Theoretical PhysicsApr 1, 19903 citations

Complete population inversion by a phase jump: an exactly soluble model

Nikolay V. Vitanov

An exact analytic solution to the time-dependent Schrödinger equation is presented for a two-state quantum system coherently driven by a nonresonant pulsed external field. The pulse has a hyperbolic-secant shape, with a sign jump (i.e. a phase step of π) at its maximum, which nullifies the overall pulse area. It is shown that off resonance, for detunings larger than the pulse bandwidth, the transition probability approaches unity as the field intensity increases. The population inversion is robust against small-to-moderate variations in the detuning and the intensity, a feature reminiscent of adiabatic passage. The population inversion, however, is not of adiabatic nature; it is induced by δ-function-shaped nonadiabatic coupling with an area of nearly π. An estimate of the required experimental resources shows that implementation with shaped femtosecond pulses is feasible.An exact analytic solution to the time-dependent Schrödinger equation is presented for a two-state quantum system coherently driven by a nonresonant pulsed external field. The pulse has a hyperbolic-secant shape, with a sign jump (i.e. a phase step of π) at its maximum, which nullifies the overall pulse area. It is shown that off resonance, for detunings larger than the pulse bandwidth, the transition probability approaches unity as the field intensity increases. The population inversion is robust against small-to-moderate variations in the detuning and the intensity, a feature reminiscent of adiabatic passage. The population inversion, however, is not of adiabatic nature; it is induced by δ-function-shaped nonadiabatic coupling with an area of nearly π. An estimate of the required experimental resources shows that implementation with shaped femtosecond pulses is feasible.

New Journal of PhysicsMar 16, 200743 citations

Formation of an optical breather

R. Michalska-Trautman

The generation of an optical breather in coherent, resonant pulse propagation is studied. The initial field envelope is assumed to be in the form of a hyperbolic secant, with one half inverted so that the total area of the pulse is equal to zero. The Maxwell–Bloch equations for an inhomogeneously broadened atomic line are solved by the inverse-scattering method for all values of the independent variables x and t. The scattering amplitudes are found for any value θ of the absolute area of the initial pulse. For θ = 2πn the reflection coefficients are rational functions of the spectral parameter, and the inverse problem can be solved exactly. It is shown that the x-dependent poles of the reflection coefficients are responsible for the transient pulse shape. Such poles appear only in the presence of inhomogeneous broadening. The threshold for transparency is found at θ = 2π. At this value of the area, a breatherlike decaying solution is obtained. At θ = 4π a breather appears. Its energy amounts to approximately 70% of the initial pulse energy. For θ = 2π and 0 = 4π the solutions are analyzed in detail.The generation of an optical breather in coherent, resonant pulse propagation is studied. The initial field envelope is assumed to be in the form of a hyperbolic secant, with one half inverted so that the total area of the pulse is equal to zero. The Maxwell–Bloch equations for an inhomogeneously broadened atomic line are solved by the inverse-scattering method for all values of the independent variables x and t. The scattering amplitudes are found for any value θ of the absolute area of the initial pulse. For θ = 2πn the reflection coefficients are rational functions of the spectral parameter, and the inverse problem can be solved exactly. It is shown that the x-dependent poles of the reflection coefficients are responsible for the transient pulse shape. Such poles appear only in the presence of inhomogeneous broadening. The threshold for transparency is found at θ = 2π. At this value of the area, a breatherlike decaying solution is obtained. At θ = 4π a breather appears. Its energy amounts to approximately 70% of the initial pulse energy. For θ = 2π and 0 = 4π the solutions are analyzed in detail.

Journal of the Optical Society of America BJan 1, 19894 citations

π/2 pulse shaping via analytic inversion of Bloch equations

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