Coherent Control and Creation of Population Gratings for a Pair of Attosecond Pulses in a Resonant Medium Based on One-Dimensional Rectangular Quantum Wells
Rostislav M. Arkhipov, P. Belov, Mikhail V. Arkhipov, A. V. Pakhomov, N. N. Rosanov
Abstract 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 Schrödinger 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.
Abstract 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 Schrödinger 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.
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.
Attosecond pulses can be used to create and control coherence in resonant media, since their duration is shorter than the population relaxation times T_1 and medium polarization T_2. 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 Schrödinger 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.
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.
Abstract 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.
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 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.