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Optics and Spectroscopy

Population Gratings Created by a Pair of Unipolar Attosecond Pulses in a Three-Level Atomic Medium

Rostislav M. Arkhipov

Published Nov 1, 2020• 9 citations
Publisher

Abstract

Abstract The possibility of inducing population gratings in a three-level resonant medium using a pair of unipolar attosecond pulses that do not overlap in the medium has been studied theoretically. It has been shown that the results of the approximate solution of the Schrödinger equation agree with the results of the numerical solution of the system of equations for the density matrix of a three-level medium whose parameters are close to the parameters of atomic vapors of rubidium.

DOI
10.1134/s0030400x2011003x

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Abstract The possibility of inducing population gratings in a three-level resonant medium using a pair of unipolar attosecond pulses that do not overlap in the medium has been studied theoretically. It has been shown that the results of the approximate solution of the Schrödinger equation agree with the results of the numerical solution of the system of equations for the density matrix of a three-level medium whose parameters are close to the parameters of atomic vapors of rubidium.
Abstract Recently, the possibility of obtaining non-harmonic unipolar electromagnetic pulses with a specific electric field strength’s dependence on time (e.g. a rectangular pulse) has been actively discussed in optics. Unipolar pulses have a nonzero electric area and a wide spectrum: from zero frequency up to the visible region. This could open up wide application of such pulses, for example, for faster and more efficient control of the quantum systems’ properties with a high temporal resolution compared to conventional bipolar multicycle pulses. In this paper, based on an approximate solution of the time dependent Schrödinger equation and a numerical solution of the equation system for the density matrix, we show the possibility of creating electromagnetically induced population density gratings in an atomic medium using a pair of unipolar rectangular attosecond light pulses that do not overlap in the medium. The formation of such gratings can be explained on the basis of the concept of ‘interference’ of electric pulse areas, recently introduced into optics.
Abstract The possibility of selective population of the energy levels of quantum systems using a single unipolar subcycle pulse and a pair of pulses has been studied. The possibility of selective population of quantum levels has been clearly illustrated based on the numerical solution of a system of equations for the density matrix of a three-level medium that interacts with a pair of subcycle attosecond and terahertz pulses. The possibility of creating a population inversion in a three-level medium using a pair of such pulses has been shown. The dynamics of population gratings in a three-level medium exposed to the action of a pair of Gaussian pulses of large amplitude on the system is studied. Whereas the shape of the gratings in a weak field is harmonic, according to analytical calculations performed by the perturbation theory, in the case of a strong field, the spatial profile of the gratings may differ from the sinusoidal profile and may have a complex structure of peaks.
Abstract We study the possibility of creating gratings of populations in a gas of hydrogen atoms using a pair of UV attosecond pulses that do not overlap in the medium. In this case, the central frequency of the pulses can either coincide with the frequency of the 1–2 resonant transition from the ground state to the first excited state (the main line of the Lyman series), or be detuned from it. The values of numerically calculated quantities agree with those obtained analytically from the solution of an approximate Schrödinger equation in perturbation theory. We show that, upon resonant excitation, the greatest creation efficiency of gratings is achieved with increasing pulse duration. In the case of nonresonant excitation, on the contrary, the system is excited more efficiently by short quasi-unipolar subcycle pulses than by bipolar multicycle once. The obtained results can be applied to coherent excitation of a single atom (thin layer) using a pair of UV pulses. We show that the modulation depth of gratings can be controlled by changing the carrier envelope phase (CEP) of UV attosecond pulses.
Abstract In a fixed spectral range, single- and half-cycle electromagnetic pulses have the shortest duration. Half-cycle pulses are promising tools for ultrafast control of quantum systems. Previously, the possibility of using a sequence of single- and half-cycle attosecond pulses to generate and ultrafast control light-induced population difference gratings has been demonstrated. However, such studies have been carried out using different approximations, such as the sudden perturbation theory and the two-level model for the resonant medium. In this paper, based on the numerical solution of constitutive equations for elements of the density matrix and wave equation it is shown that it is possible to generate and control population gratings in a three-level medium without using the approximation of sudden perturbations used in previous studies. It is shown that taking into account the additional level of the medium does not lead to a violation of the effect of generating such gratings. This extends the applicability of previous results.
Attosecond pulses can be used to create and control coherence in resonant media, since their duration is shorter than the population relaxation times T1 and medium polarization T2. Previously, the possibility of creating and ultrafast control of electromagnetically induced gratings (EMIG) of atomic populations in a resonant medium was shown using a sequence of extremely short light pulses, when the pulses coherently interact with the medium and do not simultaneously overlap in the medium. These studies were carried out in various approximations, when a finite number of energy levels of the medium is taken into account, or when the pulse amplitude is small. In this paper, based on a direct numerical solution of the time dependent Schredinger equation without the indicated approximations, we study the possibility of ultrafast coherent control of populations and the creation of an EMIG by a pair of attosecond pulses in a multilevel resonant medium with a low density of particles. The medium is modeled using a one-dimensional rectangular potential well with infinitely high walls. The studies performed show the possibility of ultrafast coherent control of the properties of resonant media based on quantum wells using attosecond pulses. Keywords: electromagnetically induced gratings, coherent interaction, extremely short pulses, unipolar pulses, attosecond pulses, medium coherence.