Population Gratings Created by a Pair of Unipolar Attosecond Pulses in a Three-Level Atomic Medium
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EMELY STRONG FIELDS AND ULTRASHORT OPTICAL PULSES
Population Gratings Created by a Pair of Unipolar Attosecond Pulses in a Three-Level Atomic Medium R. M. Arkhipov* St. Petersburg State University, St. Petersburg, 199034 Russia *е-mail: [email protected] Received July 8, 2020; revised July 8, 2020; accepted July 20, 2020
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. Keywords: attosecond pulses, light-induced gratings DOI: 10.1134/S0030400X2011003X
INTRODUCTION At present, electromagnetic pulses of attosecond duration (1 as = 10–18 s) have been experimentally obtained in the extreme ultraviolet [1, 2], optical [3– 5], and X-ray spectral ranges [6]. They have already become an important tool of modern physics, since they help to study the motion of electrons in atoms, molecules, and solids, as well as to control this motion [4, 7]. For example, they are used to study the dynamics of bound electrons in atoms [4], in nanoobjects [8], and in tunneling microscopy [9]. Simultaneously, the possibility of obtaining unipolar subcycle pulses in optics [10–12] and their applications to efficiently control the dynamics of quantum systems [13–15], acceleration of charged particles [16], and holographic recording [17] are discussed. The durations of attosecond pulses can be significantly shorter than the inversion and polarization relaxation times of the medium T1 and T2; that is, pulses can coherently interact with matter [18]. Upon coherent interaction of extremely short pulses with a medium, they can rapidly change the populations of atomic levels during times on the order of the pulse duration. In this case, it was shown previously that a sequence of attosecond pulses that do not overlap in a medium can induce population gratings in it and, if a medium is exposed to the action of three or more pulses, it becomes possible to erase these gratings and to multiply their spatial frequencies [19–22]. In the conventional approach, light-induced gratings are created when two long quasi-monochromatic beams overlap in a medium [23]. These gratings find numerous applications in spectroscopy, since the diffraction of probe radiation by them is used, e.g., to study the
properties of substances and to determine their optical characteristics [23]. In the case of long nanosecond pulses, the possibility of creating gratings in a medium using a pair of pulses that do not collide in the medium has been demonstrated experimentally rather long ago, see [24, 25], review [26], and the literature cited therein. Subsequently, this possibility was studied theoretically in a two-level medium in the case of
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