Echo responses of an ensemble of cold atoms in optical lattices

The dynamics of an ultracold dilute boson gas in an optical lattice is described in the framework of the Bose-Hubbard model in which the parameters of the system are controlled by light. Within this model, an ensemble of Bose-Einstein condensates trapped in cells of a double optical lattice generates an echo response in the quantum-mechanical probability current. The echo signal is excited by biharmonic radiation pulses under two-photon (Raman) resonance conditions. The time profile of the echo signal and the role played by the inhomogeneous broadening and the interaction of atoms in the formation of the boson echo are discussed.