Study of Multiple Quantum Beats in Atomic Wavepackets

A theoretical model consisting of 5 energy levels in coupled four-wave mixing processes was proposed to analyze the coherent characteristics of atomic wavepackets using perturbative theory. The equations of motions of the density matrix were derived and the third-order density matrix elements were presented. Under the condition that the duration of laser pulses is sufficiently short, the system response was treated as impulse response. Moreover, in the lowest order perturbation theory, the third-order nonlinear polarization was obtained using rotating-wave approximation. The results show that multiple quantum beats are embedded in the coupled four-wave mixing signals, and coherent dynamics of wavepackets can be retrieved from the quantum beat dynamics.