Integrable models of the dynamics of longitudinal-transverse acoustic pulses in a paramagnetic crystal

Abstract

We study the interaction between longitudinal-transverse acoustic pulses and a system of paramagnetic impurities with the effective spin S = 1 in a statically deformed crystal. We show that the dynamics of a pulse propagating at an arbitrary angle to the static-deformation direction and of the effective spins satisfy the modified reduced Maxwell-Bloch equations and, if the spectrum of the acoustic pulse overlaps the quantum transitions between spin sublevels, the modified sine-Gordon equation. These equations generalize the well-known models in the theory of the inverse scattering method and in the theory of self-induced transparency and also belong to the class of integrable equations. Analyzing soliton solutions shows that the pulse-medium interaction reveals some qualitatively new features in these models compared with the cases of purely transverse or purely longitudinal acoustic fields.

Nonlinear transparency regimes for three-component acoustic pulses in a system of electron and nuclear spins

“…The equations appearing in this case are threecomponent generalizations of the SIT and SG equations to the case of a Stark medium. They can also be integrable in the ISM framework as in the case of one-and two-component pulses in Stark media [16], [25].…”

“…Conditions (25) imply a relation between the solutions: if ϕ = (ϕ 1 , ϕ 2 ) T is the solution of system (23) with the spectral parameter μ, then the column vector C 2 ϕ * = (ϕ * 2 , −ϕ * 1 ) T is the solution of the same system with λ = −μ * .…”

“…(12) and (13), the sign of the component Ω z is such that the transition frequency decreases dynamically during the pulse propagation. Such an asymmetry for the components shifting quantum levels is common for optical and acoustic Stark media and occurs for both the one-component( [12], [15], [24]) and the two-component ( [13], [16], [25], [26]) pulses even in the cases where the corresponding equations have no integral similar to (20). …”

Self-induced acoustic transparency of three-component longitudinal-transverse pulses

“…Since the 2000s, studies of self induced acoustic transparency for longitudinal-transverse pulses were reported [32][33][34][35][36][37][38][39], where it is assumed that the veloci ties of longitudinal and transverse sounds are equal to each other. This assumption seems idealistic, but ensured the efficient interaction between the corre sponding components of hypersound.…”