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Quantum Electronics

Numerical simulation of the quasi-resonance regime of a transient double resonance in a scheme with a common upper level at a large inhomogeneous broadening of quantum transitions

A E Dmitriev, Oleg M. Parshkov

Published Aug 31, 2005• 0 citations
Publisher

Abstract

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.

DOI
10.1070/qe2005v035n08abeh003411

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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.
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 transient double resonance in the Λ-scheme is numerically investigated for short input laser pulses whose spectral widths exceed noticeably the Doppler width of quantum transitions. The case of the exact resonance is considered, when the frequencies of input pulses coincide with the central frequencies of quantum transitions, and the quasi-resonance case, when this coincidence is slightly violated. It is shown that a pulse with a lower frequency is shortened and considerably amplified during its propagation in a medium. A pulse with a higher frequency transforms to a pulse with a ridge envelope, which virtually does not decay during its propagation despite the presence of irreversible relaxation. Estimates were performed for quantum transitions in the 208 Pb atom.
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.
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.
Nonstationary polarisation effects in a medium with the Λ-scheme of energy levels with the quantum numbers of the total angular momentum equal to 0, 2, and 1 are numerically simulated. The analysis is performed in the slowly varying envelope approximation taking into account the inhomogeneous broadening of quantum transition lines. It is assumed that the lower-frequency (signal) radiation at the input to a resonance medium is considerably weaker than the higher-frequency (pump) radiation. It is shown that the polarisation of the signal pulse inside the medium is quasi-elliptic in the general case and is independent of the input-pulse polarisation. If the 'area' of the input pump pulse in the absence of signal radiation admits the formation of only one 2π-pulse, then the major axes of polarisation ellipses for the signal inside the medium and input pump radiation are collinear, however, the directions of rotation of the electric field strengths of these radiations are mutually opposite. For higher-power pump pulses, the polarisation structure of the signal pulse in the medium becomes considerably more complicated.