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Journal of Optoelectronics·laser

Time Evolution of Atomic Response in an Open Ladder-type System

Tian Shu

Published Jan 1, 2003• 0 citations
OpenAlex

Abstract

Under the conditions of the rotatingwave,slowly varying envelope approximations.It was found that Variation of the driving field Rabi frequency doesn′t vary the oscillation (or nonoscillation) characteristic of the atomic response time evolution and the time needed for reaching to steady state,but will vary size of the oscillation frequency and steady value;increase of incoherent pumping rate doesn′t vary the oscillation frequency and steady value,but will make oscillation times decreasing,oscillation amplitude reducing,time needed for reaching to steady value shorting,however,the steady value of each atomic response doesn′t increase or decrease monotonously with incoherent pumping rate increasing;variation of initial condition of the system doesn′t vary the law of time evolution of atomic response and the steady value of each atomic response.

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The Effects of Phase Fluctuation in an Open Ladder System

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The analytical solutions of the gain,dispersion and population difference in the steady state of an open ladder lasing without inversion(LWI) system are at first given when the phase fluctuation of the driving field is considered.Then the effects of the driving field phase fluctuation on the gain,dispersion and population difference are analyzed by the numerical results from the analytical solutions.Our research shows that the phase fluctuation of the driving field will results in a finite line width;with the line width increasing,the gain decreases monotonously,however,variation of the dispersion isnt monotonous,it has a maximum value when the line width takes some value;the line width varying cant lead to change lasing from without to with population inversion.

Journal of Optoelectronics·laser•Jan 1, 2002•0 citations
Under the conditions of the rotatingwave,slowly varying envelope approximations.It was found that Variation of the driving field Rabi frequency doesn′t vary the oscillation (or nonoscillation) characteristic of the atomic response time evolution and the time needed for reaching to steady state,but will vary size of the oscillation frequency and steady value;increase of incoherent pumping rate doesn′t vary the oscillation frequency and steady value,but will make oscillation times decreasing,oscillation amplitude reducing,time needed for reaching to steady value shorting,however,the steady value of each atomic response doesn′t increase or decrease monotonously with incoherent pumping rate increasing;variation of initial condition of the system doesn′t vary the law of time evolution of atomic response and the steady value of each atomic response.
The law of time evolution of atomic response in an open V type lasing without inversion (LWI) system with two incoherent pumps is investigated by the numerical results.Following conclusions are shown:the time evolution of the populations of the two levels coupled by the probe field has the same oscillation frequency,however,exists a phase difference π;the initial values of the populations affect mainly the oscillation amplitudes of the gain,coherent item and population difference but dont affect their values in the steady state;the ratio of the atomic injection rates increasing will results in an increase of the gain and a decrease of the population difference in the steady state;the atomic exit rate increasing will make both the gain and population difference in the steady state decreasing.
In an open ladder-type resonant atomic system, variation in relative phase between probe and driving fields does not affect the transient evolution of populations, but it has remarkable effects on gain and dispersion of the probe field. No matter whether an incoherent pump is present or absent, transient and stationary gains without inversion (GWI) always can be obtained by choosing an appropriate value of the relative phase. When the incoherent pump is absent, the values of transient and stationary GWIs are much larger and the time interval required to reach the stationary value is longer than those when the incoherent pump is present. Varying the exit rate and the ratio between injection rates can obviously change the phase-dependent GWI. In addition, in the transient evolution process, the phenomenon of high dispersion (refractive index) without absorption occurs at some values of relative phase. In the corresponding closed system, the stationary GWI can be obtained by choosing an appropriate value of relative phase only when incoherent pump exists, moreover the gain is smaller than that in the open system.
The model of an open four-level atomic system is presented on the basis of the closed four-level atomic system. In the rotating wave, slowly varying envelope and mean field approximations, the density-matrix motion equations of the system are solved, and the linear analytical solution in the steady state is obtained. The numerical calculation from the steady-state solution of the open system is presented. It is shown that a change from LWI to lasing with inversion action can occur due to the Rabi frequency of the driving field increasing; another change from lasing with inversion to LWI action can also occur as the exit rate or ratio of injection rates increases; high refractive index without absorption can be obtained; the curve of ρ33-ρ11(vs Δ2) presents the shape of the rectangle wave.
We study the time evolution law of the atomic response in an open Λ type inversionless lasing system when the probe or driving field is off resonance,and compare the law with that obtained when the probe and driving fields are resonant.We find that the detuning has considerable effects on the time evolution law:When the probe or driving fields is off resonance,the dispersive responses for the probe and driving fields are no longer 0 and the two photon coherence is no longer a pure real;The variation of the probe detuning can make the time evolution law of the population distributions and the gain (absorbtion) of the driving field changing obviously;With detuning increasing,the time evolution behavior of the gain (absorbtion),dispersion of the probe field and the two photon coherence will gradually diviate from the evolution law of the standard damped oscillator;With the driving detuning increasing,the oscillating time of the dispersion of the driving field becomes longer,the amplitude and the stationary value increase.
The analytical solutions of the gain,dispersion and population difference in the steady state of an open ladder lasing without inversion(LWI) system are at first given when the phase fluctuation of the driving field is considered.Then the effects of the driving field phase fluctuation on the gain,dispersion and population difference are analyzed by the numerical results from the analytical solutions.Our research shows that the phase fluctuation of the driving field will results in a finite line width;with the line width increasing,the gain decreases monotonously,however,variation of the dispersion isnt monotonous,it has a maximum value when the line width takes some value;the line width varying cant lead to change lasing from without to with population inversion.