Effectiveness of Locking a Stimulated Photon Echo in a Three-Level System, Depending on the Mutual Orientation of Standing Waves of Nonresonant Laser Pulses

Abstract

We consider the effectiveness of locking the stimulated photon echo response in a three-level system, depending on the mutual orientation of external nonresonant electromagnetic standing waves. We show that the effect of locking the stimulated photon echo response depends on the "non-equidistance" parameter for the spectrum of the system. Keywords: stimulated photon echo, three-level system, information ″locking,″ nonresonant electromagnetic standing waves.Introduction. Photon echo is widely used in optical spectroscopy, and also in optical memory devices and processors [1], for operation of which we need an effi cient mechanism for erasing information. In [2,3], it is shown that the effect of locking the stimulated photon echo (SPE) signals is promising for solving such problems. The effect of locking a long-lived photon echo was predicted theoretically and confi rmed experimentally for an LaF 3 Pr 3+ crystal (the transition 3 H 4 -3 P 0 , λ = 477.7 nm) when an inhomogeneous electric fi eld is applied between the fi rst and second laser pulses [2]. In [3][4][5], the effect of locking information in SPE responses and its application in optical memory systems, echo processors, and multichannel recording of information were considered, as well as the effectiveness of suppressing the SPE response for different schemes for application of spatially inhomogeneous electric fi elds to a resonant medium. Such an effect can be achieved by exposure to nonresonant laser pulses with spatial inhomogeneity or standing-wave pulses, where the spatial inhomogeneity is connected with the electric fi eld distribution in the antinodes of the standing waves. In [6], we considered the effectiveness of locking a long-lived photon echo as a function of the mutual orientation of standing waves of nonresonant laser pulses in a two-level system, and showed that "locking" information in the SPE response is observed even at angles <0.1°.In this paper, we consider the effectiveness of locking the SPE response in a three-level system for a mutual orientation of external nonresonant electromagnetic standing waves.Basic Equations. Let us consider the excitation scheme for an SPE in a three-level system. Let the object pulse be the fi rst exciting laser pulse, the temporal shape of which we represent as a step (Fig. 1). Between the fi rst and second laser pulses and after the third readout pulse, the three-level system is exposed to nonresonant standing waves SW1 and SW2. The pulse SW1 is oriented along the z axis; SW2 is oriented along the z′ axis, making an angle β to the z axis.In order to look for the evolution operator for the system when it is excited by a resonant laser pulse of duration Δt η at the instant of time t η , we use the results of [7]. Knowing the evolution operator, we can determine the density matrix after action of the η-th laser pulse