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Quantum Electronics

Linear regime of time-varying double resonance in a medium with Doppler-broadened spectral lines

A E Dmitriev, Oleg M. Parshkov

Published May 31, 1993• 0 citations
Publisher

Abstract

A time-varying regime of a double resonance in a system with a common upper level, with Doppler-broadened spectral lines, is described theoretically. The light field with the lower frequency (the signal) is assumed to be weak in comparison with that with the higher frequency (the pump). The nature of the interaction between the fields is determined substantially by the parameter n , which is the square root of the ratio of oscillator strengths in the pump and signal channels. At n > 0.5, and at sufficiently large distances, the resultant optical field is described as a superposition of the fields of a 2π pump pulse and an exponentially growing signal pulse of steady-state shape which is coupled with the pump pulse. The signal gain coefficient is described as a function of the pump frequency and the pump pulse energy by means of a probability integral of complex argument. At n < 0.5, the signal pulse undergoes a pronounced dispersive spreading with increasing distance traversed, and the rate of amplification of this pulse is lower than exponential. The shaping of the signal pulse is studied as a function of the detuning from resonance in the signal and pump channels.

DOI
10.1070/qe1993v023n05abeh003058

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Physical Review A•Jun 1, 1993•18 citations
A time-varying regime of a double resonance in a system with a common upper level, with Doppler-broadened spectral lines, is described theoretically. The light field with the lower frequency (the signal) is assumed to be weak in comparison with that with the higher frequency (the pump). The nature of the interaction between the fields is determined substantially by the parameter n , which is the square root of the ratio of oscillator strengths in the pump and signal channels. At n > 0.5, and at sufficiently large distances, the resultant optical field is described as a superposition of the fields of a 2π pump pulse and an exponentially growing signal pulse of steady-state shape which is coupled with the pump pulse. The signal gain coefficient is described as a function of the pump frequency and the pump pulse energy by means of a probability integral of complex argument. At n < 0.5, the signal pulse undergoes a pronounced dispersive spreading with increasing distance traversed, and the rate of amplification of this pulse is lower than exponential. The shaping of the signal pulse is studied as a function of the detuning from resonance in the signal and pump channels.
A theoretical study is made of a linear, in respect of the field of lower frequency (signal), transient double resonance in a system with a shared upper level. The radiation of higher frequency (pump) is selected to be a 2π pulse which is spectrally much narrower than the contour of the Doppler scatter of the frequencies of a transition which is in resonance with this pulse. A condition is found for the appearance of a signal pulse of constant profile moving at the velocity of the pump pulse and growing exponentially in the course of its propagation into a resonant medium. It is shown that in general the energy of a signal pulse depends nonmonotonically on the energy of the pump pulse: there is an optimal value of the pump energy at which the rate of rise of the signal energy is maximal. A study is made of the efficiency of a double resonance on the detuning from a resonance in the pump and signal channels.
The transient double resonance in the Λ scheme is numerically investigated in the case of a strong inhomogeneous spectral broadening of a medium and nonzero detunings of the frequencies of interacting pulses from the central frequencies of corresponding quantum transitions. It is shown that the signal pulse efficiently interacts with the pump pulse only when a certain condition imposed on the nonzero detunings is satisfied. If this condition is strongly violated at the input to the resonance medium, only a weak field of the rear edge of the input signal pulse mainly interacts with the pump field. In this case, two pulses with different frequencies are formed in the signal channel. This is explained by the specific interaction of radiation with Doppler-broadened quantum transitions.
One consider the amplification of pulses of coherent light in the resonant three-level active media that is excited by short power pulse of coherent light according to the common-upper- level double resonance scheme. The radiation with major frequency (pump) is supposed to be stronger than one with minor frequency (signal). The self-induced transparency is supposed to be established in the pump channel. The exponential growth of stationary shape short signal pulses is studied mainly. One shows that when any described here conditions for initial signal pulse shape are meeting the stationary gained signal pulse of complicated form can be formed. The gains of these pulses are less than ones for signal pulses of quasi-hyperbolic-secant form. Therefore in the case of incomplete condition meeting the competition between the exponentially growing signal pulses with different gains and shapes leads finally to the overwhelming of signal pulse with quasi-hyperbolic-secant-shape form. The effect of inhomogeneous broadening of spectral transition lines on the parameters of signal pulses was studied too. Evaluations that were carried out for any atomic gases show that described in this paper phenomena can be produced at realistic levels of power and duration of pump and signal pulses.
A theoretical investigation is made of an essentially nonstationary double resonance excited in a system with a common upper level in the field of a 2π pump pulse and of constant low-intensity signal radiation. The conditions are found for the formation of an exponentially amplified signal pulse of asymptotically constant profile moving at the velocity of the pump pulse. A study is made of the relationship between the signal pulse parameters and the parameters of the medium and of the pump pulse. It is shown that competition between the local and wave transient processes is responsible for the existence of an optimal pump pulse energy which depends on the values of the detuning from a resonance in the pump and signal channels. When this optimal energy is exceeded, the output signal pulse energy decreases. It is demonstrated that when the initial values of the detuning in the two channels are unequal the formation of a signal pulse is accompanied by pulling of the signal frequency to the value which satisfies the conditions of equality of the detuning values. During the early stages of formation of the signal pulse this results in splitting into a train of several pulses which are shorter than the pump pulse.
Transient regime of common-upper-level scheme double resonance is studied numerically. It was shown that in the presence of resonance detunings in channels of interaction and with taking into account of inhomogeneous broadening of resonant transition lines the process of stationary gained signal pulse forming is accompanied with signal carrier frequency pulling to the value that is corresponding some condition. This relates frequency detunings with transition central frequencies and differs from such conditions for Raman scattering. In some cases. Satisfaction of this condition provides the effective conversion of pump pulse energy into signal one. Depends on frequency detuning values one- or two-pulse structure will arise in signal channel. To vary these detunings it is possible to manipulate of signal pulse magnitudes and of time shift between them
The interaction of a four-level atomic system with two electromagnetic radiations has been studied. The two intermediate levels are closely spaced such that a single radiation frequency can induce transitions from the ground state to both of them. In a cascade-type double resonance, the pump electric-field amplitude is much stronger than the amplitude of the signal field, which can induce transitions from both of the intermediate levels to the upper state. The 15 optical Bloch equations obtained from the Liouville equations are solved analytically to obtain the Doppler-free signal line shape. The computed signals, exhibiting two Lorentzian line profiles, are presented for different pump frequencies. In addition to these one-photon transitions, we obtain a weak two-photon resonance peak. The two-photon resonance becomes weaker when the detuning of the pump frequency from a resonance frequency is increased. When the pump frequency ${\mathrm{\ensuremath{\Omega}}}_{\mathit{p}}$ is intermediate between the pump resonance frequencies ${\mathrm{\ensuremath{\omega}}}_{1}$ and ${\mathrm{\ensuremath{\omega}}}_{2}$, the two-photon resonance is very weak and almost vanishes when ${\mathrm{\ensuremath{\Omega}}}_{\mathit{p}}$=(${\mathrm{\ensuremath{\omega}}}_{1}$+${\mathrm{\ensuremath{\omega}}}_{2}$)/2. When the pump frequency is on resonance with one of the transition frequencies, the Rabi splitting of the signal shows asymmetry because of the presence of a close-lying transition which is pumped off resonance. The intensity-dependent shifts of the transitions are such that they repel each other more and more as the intensity of the pump field is increased. These shifts arise from the nonresonant interaction between the atom and the field.