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arXiv:2503.08243

Dynamic Bragg microcavities in collisions of unipolar light pulses of unusual shape in two- and three-level medium

Rostislav M. Arkhipov, Mikhail V. Arkhipov, Nikolay N. Rosanov

Published Mar 11, 2025• 0 citations
arXivHTMLPDF

Abstract

Unipolar light pulses with a non-zero electric area due to the unidirectional action on charged particles can be used for the ultrafast control of the properties of quantum systems. To control atomic properties in an efficient way, it is necessary to vary the temporal shape of the pulses used. This has led to the problem of obtaining pulses of an unusual shape, such as a rectangular one. A number of new phenomena, not possible with conventional multi-cycle pulses, were discovered by analyzing the interaction of such unipolar pulses with matter. These include the formation of dynamic microcavities at each resonant transition of a multilevel medium when such pulses collide with the medium. In this work, we compare the behavior of dynamic microcavities in a two-level and a three-level medium when unipolar pulses of unusual shape (rectangular) are collided with the medium. We do this on the basis of the numerical solution of the system for the density matrix of the medium and the wave equation for the electric field. Medium parameters correspond to atomic hydrogen. It is shown that for rectangular pulses in a three-level medium, the dynamics of the cavities can be very different from the two-level model, as opposed to pulses of other shapes (e.g. Gaussian shape). When the third level of the medium is taken into account, the self-induced transparency-like regime disappears. Differences in the dynamics of resonators in a three-level medium are revealed when the pulses behave like 2π pulses of self-induced transparency.

DOI
10.48550/arxiv.2503.08243

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Unipolar light pulses with a non-zero electric area due to the unidirectional action on charged particles can be used for the ultrafast control of the properties of quantum systems. To control atomic properties in an efficient way, it is necessary to vary the temporal shape of the pulses used. This has led to the problem of obtaining pulses of an unusual shape, such as a rectangular one. A number of new phenomena, not possible with conventional multi-cycle pulses, were discovered by analyzing the interaction of such unipolar pulses with matter. These include the formation of dynamic microcavities at each resonant transition of a multilevel medium when such pulses collide with the medium. In this work, we compare the behavior of dynamic microcavities in a two-level and a three-level medium when unipolar pulses of unusual shape (rectangular) are collided with the medium. We do this on the basis of the numerical solution of the system for the density matrix of the medium and the wave equation for the electric field. Medium parameters correspond to atomic hydrogen. It is shown that for rectangular pulses in a three-level medium, the dynamics of the cavities can be very different from the two-level model, as opposed to pulses of other shapes (e.g. Gaussian shape). When the third level of the medium is taken into account, the self-induced transparency-like regime disappears. Differences in the dynamics of resonators in a three-level medium are revealed when the pulses behave like 2π pulses of self-induced transparency.
Abstract We report an analytical and numerical study of the dynamics of electromagnetically induced atomic population gratings during collisions of a sequence of unipolar pulses of unusual temporal shape (rectangular and triangular) in a multilevel resonant medium. The possibility of forming dynamic microcavities with Bragg-like mirrors, the shape of which is different at each resonant transition of the medium, is demonstrated. A simple analytical description of such microresonators is proposed based on an approximate solution of the time-dependent Schrödinger equation when the amplitude of the exciting pulses is small. In the case of high-power pulses, when perturbation theory is not applicable, the results of numerical calculations show the disappearance of microcavities and the emergence of nonharmonic gratings with an increase in the number of collisions between pulses. The studied phenomena demonstrate a possibility of using unipolar pulses of an unusual shape for ultrafast control of the medium properties.
Unipolar light pulses with non-zero electric area enable ultrafast control of quantum systems, requiring tailored temporal shapes like rectangular pulses for efficient atomic manipulation. Such pulses induce unique phenomena, including dynamic microcavities at resonant transitions in multilevel media. Here, we compare microcavity dynamics in two- and three-level media under rectangular unipolar pulse excitation via numerical solutions of the density matrix and wave equations. Unlike Gaussian pulses, rectangular pulses exhibit starkly different dynamics in a three-level medium, disrupting self-induced transparency-like regimes. Key differences emerge when pulses behave as 2 π pulses, highlighting the impact of the third level on microcavity dynamics. These findings establish rectangular unipolar attosecond pulses as a powerful tool for attosecond-scale quantum control, revealing fundamental limits of few-level approximations in extreme nonlinear optics and opening pathways to coherent light–matter engineering in complex atomic systems.
This paper examines the behavior of dynamic microcavities (DMs) in multi-level resonant media when attosecond unipolar pulses of different shapes (Gaussian and rectangular) collide, acting as 2 π -like self-induced transparency pulses. For realistic quasi-unipolar pulses, the influence of the trailing edge of opposite polarity is investigated, and conditions under which the trailing edge’s effect can be ignored are found analytically and then confirmed by a direct numerical calculation. We demonstrate that the collision of sub-cycle pulses in a medium results in a rapid change of the refractive index both in time and space. Thus, the case considered here of a resonant medium under the action of a sequence of pulses is an example of a time-dependent medium. The findings demonstrate the feasibility of creating time-dependent media in an atomic medium with high polarization relaxation times T 2 , and subsequently controlling them with half-cycle pulses at an extremely short timescale of half of an electromagnetic field oscillation.
Abstract The formation of dynamic microcavities (DMs) in the asymmetric collision of a single-cycle π‑pulse and a 2π-pulse of self-induced transparency in a two-level medium is investigated theoretically. The numerical solution of the Maxwell–Bloch equations demonstrates that the interaction of pulses leads to the emergence of two DMs, which are separated in space within the medium. Controlling the shape of the microcavities is possible by altering the number of collisions between pulses. These results pave the way for the development of ultrafast tunable optical devices.
In the case of coherent interaction with a medium of extremely short light pulses (ESPs) having a carrier frequency and harmonic shape (when the pulse durations are shorter than the population relaxation times T1 and polarization relaxation time T2 of the medium), electromagnetically induced gratings (EMIGs) of the population difference, which have a pronounced harmonic dependence on the coordinates, may appear in it. These structures can occur when pulses do not overlap or overlap in the medium. Recently, the possibility of obtaining unipolar electromagnetic pulses in the optical and adjacent ranges of non-harmonic shape, for example, rectangular and triangular, with a duration less or comparable to the duration of the extremely-short pulse in this range, has attracted interest. In this work, using the numerical solution of the system of Maxwell-Bloch equations, we study EMIG formation by rectangular attosecond pulses in a two-level resonant medium. The possibility of inducing an EMIG of a non-harmonic shape in the form of light-induced channels microresonators, (microcavities) with a size of the order of the wavelength of the resonant transition of the medium, whose parameters can be controlled, for example, by the amplitude of the incident pulses, is shown. It has been suggested that it is possible to create an EMIG of a predetermined non-harmonic shape only in the general case of using unipolar pulses. Keywords: attosecond pulses, unipolar pulses, rectangular pulses, electromagnetically induced gratings, polarization waves, light-induced microresonators.
The coherent interaction of extremely short light pulses with a resonant medium can result in the formation of population difference gratings. Such gratings have been created by pulses that are π/2 or smaller. This paper demonstrates that a microcavity with Bragg-like mirrors can be formed by colliding two single-cycle attosecond self-induced transparency pulses in the center of a two-level medium. The parameters of this structure can be quickly adjusted by increasing the number of collisions, which showcases the ability to control the dynamic properties of the medium on a sub-cycle time scale by using attosecond pulses.