Interferometry based on the quantum Kibble-Zurek mechanism
Han-Chuan Kou, Peng Li · Physical review. B./Physical review. B · 2022
We propose an interferometry within the framework of the quantum Kibble-Zurek mechanism by exemplifying two prototypical quench protocols, namely, the round-trip and quarter-turn ones, on the transverse Ising and quantum $XY$ chains. Each protocol contains two linear ramps that drive the system across quantum critical point twice. The two linear ramps arouse two respective nonadiabatic critical dynamics that are well described by the quantum Kibble-Zurek mechanism. However, in combination, the two critical dynamics can interfere with each other deeply. As an effect of the interference, the dynamical phase is exposed in the final excitation probability, which leads to a quantum coherent many-body oscillation in the density of defects with predictable characteristic period. Thus, such an interference is available for direct experimental observations. In the quantum $XY$ model, we show that an interference can also arise from the interplay between two different critical dynamics derived from a critical point and a tricritical point. Furthermore, we demonstrate a phenomenon of multiple length scales in the defect-defect correlator, which is due to the interplay between the interference and the quantum dephasing of excited quasiparticle modes. It turns out that the dephased result relies on how the diagonal and off-diagonal lengths are modulated by the controllable parameters in a quench protocol.