Controllable photon echo phase induced by modulated pulses and chirped beat detection

In this paper, we propose a scheme for photon echo chirped detection process composed of additional modulation pulses to obtain controllable geometric phase. The geometric phases are observed and measured by a beat signal between the photon echo field and the chirped field. The chirped detection model reveals that the period of the beat signal increases as the chirped rate and delay time increase. Additionally, a two-fold relationship between the modulation phase and the echo shift phase is obtained. The numerical simulations accord with the theoretical results obtained by the finite difference time domain (FDTD) method.