Anomalous echoes in quantum systems

M. Aihara, Humio Inaba

An analytical study of the photon echoes associated with the three-level system interacting resonantly with optical pulses possessing two different frequencies is performed. It is predicted that photon echoes arise at anomalous times corresponding to the correlation between the inhomogeneous broadenings for the different spectral lines as well as at the normal time expected in a simple two-level system. This new effect is caused by the coupling of the two resonant transitions through the common energy level. Furthermore, if the particle does not have inversion symmetry, the echoes with the sum or difference frequency of the exciting optical pulses can be observed in such a system. The quantitative analysis is also given for intensities, direction of propagation and polarizations of the anomalous echoes which depend upon the exciting pulses with different frequency.

R. Sankaranarayanan, Jane H. Sheeba, M. Lakshmanan

Ignacio García-Mata, Diego A. Wisniacki

The Loschmidt echo (LE) is a measure of the stability and reversibility of quantum evolution under perturbations of the Hamiltonian. One of the expected and most relevant characteristics of this quantity for chaotic systems is an exponential decay with a perturbation-independent decay rate given by the classical Lyapunov exponent. However, a non-uniform decay—instead of the Lyapunov regime—has been reported in several systems. In this work, we find an analytical semiclassical expression for the averaged fidelity amplitude that can be directly related to the anomalous—unexpected—behaviour of the LE.

Pavel Karhan

Giovanni Costa

Jincheng Zhang

Quantum Momentum-Echo Spectroscopy (QMES) introduces a novel theoretical framework designed to probe hidden quantum dynamical memories through the delayed re-emergence of momentum responses in quantum systems. By defining the momentum echo response via a specialized linear response integral incorporating a momentum memory kernel, K_P(t - t'), and analyzing system behavior under impulsive short-pulse excitations of the form F(t) = F_0 * delta(t), QMES identifies anomalous momentum responses, Delta p(t_E) different from 0, at characteristic echo times t = t_E. This approach isolates the momentum channel to reveal microscopic scattering and non-Markovian memory mechanisms, clearly distinguishing itself from conventional state-history or multi-pulse causal echo methodologies.