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Quantum Electronics

Adiabatons in the nonstationary double resonance on degenerate quantum transitions

А. В. Волков, Дружинина Надежда Александровна, Oleg M. Parshkov

Published Oct 31, 2009• 8 citations
Publisher

Abstract

The nonstationary double resonance is numerically simulated in the Λ-scheme of degenerate energy levels with the quantum number J of the total angular momentum equal to 0, 2, and 1. The analysis is performed in the slowly varying envelope approximation taking into account the inhomogeneous broadening of quantum transition lines. In the case of a high-power input low-frequency pulse of long duration with a flat top switched on before the application of a comparatively weak and short input high-frequency pulse and switched off after the end of the latter, a specific pulsed structure, the so-called double adiabaton, can appear. It differs from an adiabaton known from the theory of electromagnetically induced transparency by the decomposition of the high-frequency pulse into two pulses with oppositely directed elliptic polarisations.

DOI
10.1070/qe2009v039n10abeh014025

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The nonstationary double resonance is numerically simulated in the Λ-scheme of degenerate energy levels with the quantum number J of the total angular momentum equal to 0, 2, and 1. The analysis is performed in the slowly varying envelope approximation taking into account the inhomogeneous broadening of quantum transition lines. In the case of a high-power input low-frequency pulse of long duration with a flat top switched on before the application of a comparatively weak and short input high-frequency pulse and switched off after the end of the latter, a specific pulsed structure, the so-called double adiabaton, can appear. It differs from an adiabaton known from the theory of electromagnetically induced transparency by the decomposition of the high-frequency pulse into two pulses with oppositely directed elliptic polarisations.
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.
We present the results of numerical simulation of the adiabaton emergence process in the lambda scheme of degenerate energy levels with the quantum number of the total angular momentum, J = 0, 2, 1. In the case of linear polarisation of the input highfrequency field and circular polarisation of the input low-frequency field, the energy of the high-frequency component of the adiabaton is shown to focus in two or more pulses: in one of the pulses the field is circularly polarised in a direction opposite to that of the low-frequency input field, whereas in other pulses it is circularly polarised in the same direction as that of the field. This effect is caused by the specific character of electromagnetically induced transparency in the lambda scheme under study and by the trends introduced by self-induced transparency in it.
The evolution of adiabatons in electromagnetically induced transparency in the scheme of degenerate quantum transitions with Doppler broadening of spectral lines has been numerically simulated taking into account the effect of resonance detunings. It is shown that, in the case of linearly polarised fields, an increase in the probe-field resonance detuning (under exact-resonance conditions for the control radiation) leads to a transformation of electromagnetically induced transparency into electromagnetically induced absorption at certain stages. When the control-field resonance detuning is varied, the transparency of the medium for the probe (exactly resonant) radiation monotonically decreases with increasing detuning because of the rising role of single-photon absorption. In the case of circularly polarised control radiation and linearly polarised input probe field, a probe pulse propagating in the medium splits into two pulses with oppositely directed circular polarisations. An increase in the probe pulse resonance detuning (under exact-resonance conditions for the control radiation) leads primarily to an increase in the absorption by the medium of the probe pulse, the direction of circular polarisation for which coincides with the circular-polarisation direction for the control radiation.
The numerical simulation results of the nonadiabacity display in electromagnetically induced transparency are presented. The Λ scheme of degenerate and inhomogeneous quantum transitions J = 0 → J = 1 → J = 2 is examined for the cases of slow and abrupt rises in the leading edge of the input probe radiation pulse. For circularly polarized radiations, it has been shown that the deviation from the condition of adiabatic sequence can lead to a separation of the probe pulse of the adiabaton into a train of subpulses. In the case of linear polarization of the input probe field and the circular polarization of the input control field, the probe radiation pulse is split into two pulses with opposite circular polarizations and a multispike structure of the envelopes. If an abrupt rise of the leading edge of the input probe pulse takes place the precursor pulse arises at a probe radiation frequency and the velocity of its propagation coincides with the speed of light in vacuum.
The results of numerical simulation of the electromagnetically induced transparency phenomenon in the Λ scheme of degenerate quantum transitions J = 0 → J = 1 → J = 2 with Doppler broadening of spectral lines are presented for the cases of continuous and abrupt rises in the leading edge of the input probe radiation pulse. For circularly polarized radiations, it has been shown that the deviation from the condition of adiabatic sequence can lead to a separation of the probe pulse of the adiabaton into a train of subpulses. In the case of linear polarization of the input probe field and the circular polarization of the input control field, the probe radiation pulse is split into two pulses with opposite circular polarizations and a multispike structure of the envelopes. In the case of an abrupt rise in the leading edge of the input probe pulse, regardless of the peak intensity of the latter, the precursor pulse arises at a probe radiation frequency and the velocity of its propagation coincides with the speed of light in vacuum.
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.