Population density gratings produced by a pair of nonharmonic unipolar rectangular attosecond pulses in a resonant medium

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.

Electromagnetically induced gratings created by extremely short non-overlapping pulses of light in a three-level resonant medium

“…The interaction of a three-level medium with the pulse driving field can be described by the following system of equations, which includes the system of equations for the three-level density matrix elements coupled to the 1D wave equation for the electric field strength. This system is written without both the slowly varying envelope and the rotating wave approximations [49,64]:…”

“…Another possible application of ultra-short [36][37][38][39] and extremely short pulses [40][41][42][43][44][45][46][47][48][49][50][51] is the creation and control of electromagnetically induced atomic population gratings (EMIGs). In conventional approaches, such EMIGs are created by the superposition of two coherent monochromatic laser beams in the medium by the formation of the interference pattern [52].…”

“…The interference of the polarization waves of the medium that generated each previous pulse with the subsequent pulses is the physical mechanism for the generation of such gratings [40][41][42][43][44][45][46][47][48][49][50][51]. In the case of half-cycle pulses, when their direct interference is impossible, when the amplitude of the pulses is small, their effect on quantum systems can be described in terms of interference of pulse areas [17,47,49]. In this case, it can be said that the creation of gratings by half-cycle pulses is due to the interference of the electrical areas of the pulses.…”

“…The possibility of guidance and ultra-fast control of such EMIGs by means of single-cycle and half-cycle pulses has been theoretically studied in the works [17,[40][41][42][43][44][45][46][47][48][49][50][51]. However, these studies have been carried out in a variety of approximations.…”

“…For the consideration of additional levels of the medium, an approximate solution of the time-dependent Schrödinger equation (TDSE) was used in the approximation of a small amplitude of the field excitation and approximation of sudden perturbations was also used [21,43,44,49]. In [48] numerical solution of TDSE was used to study gratings.…”