Displacement Echoes: Classical Decay and Quantum Freeze

Abstract

Motivated by neutron scattering experiments, we investigate the decay of the fidelity with which a wave packet is reconstructed by a perfect time-reversal operation performed after a phase-space displacement. In the semiclassical limit, we show that the decay rate is generically given by the Lyapunov exponent of the classical dynamics. For small displacements, we additionally show that, following a short-time Lyapunov decay, the decay freezes well above the ergodic value because of quantum effects. Our analytical results are corroborated by numerical simulations.

Atom interferometry using wave packets with constant spatial displacements

“…In the future, such a system could study the quantum stability of wave packets due to displaced potentials [19] by deliberately introducing time-dependent variations in the potential along the waveguide direction [20,21]. Instead of measuring the mixed-state correlation functions, a fidelity-type measurement [19] can be performed with sub-recoil cooled atoms occupying a single matter-wave state, where velocityselective beam-splitting schemes can be applied [22,23].…”

“…Instead of measuring the mixed-state correlation functions, a fidelity-type measurement [19] can be performed with sub-recoil cooled atoms occupying a single matter-wave state, where velocityselective beam-splitting schemes can be applied [22,23].…”

“…The correlation functions are directly analogous to the neutron-scattering correlation function discussed in Ref. [19], where momentum displacements were considered. Notice that if the uniform atomic sample has a spatial extension L δx and with thermal velocity u δp/m, the original and shifted density matrix are approximately the same, and the correlation functions are approximately independent of δx m or δp m .…”

Relation of exact Gaussian basis methods to the dephasing representation: Theory and application to time-resolved electronic spectra

“…22 The fidelity amplitude was also used as a measure of the dynamical importance of diabatic, 23 nonadiabatic, 20 or spin-orbit couplings, 21 and of the accuracy of quantum molecular dynamics on an approximate potential energy surface. 24 In practical calculations, correlation function (7) is usually approximated, and DR provides an efficient semiclassical approximation.…”

“…14,15,18,19 Although the original formulation of the DR pertains to a single electronic potential energy surface, a generalization to multiple surfaces exists. 20,21 The DR has many other applications: e.g., in inelastic neutron scattering, 22 as a measure of the dynamical importance of diabatic, 23 nonadiabatic, 20 or spin-orbit couplings, 21 and as a measure of the accuracy of quantum molecular dynamics on an approximate potential energy surface. 24 In the field of quantum chaos, DR successfully describes the local density of states and transition from the Fermi-Golden-Rule to the Lyapunov regime of fidelity decay.…”