Quantum beats and superradiant effects in the spontaneous emission from two nonidentical atoms

The problem considered is that of the spontaneous emission from two nonidentical two-level atoms coupled to a continuum of quantized electromagnetic modes. The atoms are separated by distances comparable to the resonant wavelength and have different transition frequencies and natural linewidths. Correlation functions and radiation rates are expressed in terms of expectation values of time-dependent atomic operators. The radiation pattern, total radiation rate and spectral distribution of radiation are obtained with the initial conditions that only one atom is excited and that the system is fully inverted. We find that the radiation pattern and total radiation rate show quantum beats when initially only one atom is excited. Moreover, the total radiation rate for strong interatomic interaction becomes greater than its initial value at the beginning of the emission process. This “superradiant” property is absent for two identical atoms. For initially fully inverted system, the radiation pattern and total radiation rate decay monotonically in time. Some weak beats can appear for drastically different atoms. The spectrum of radiation calculated for the case of strong interatomic interaction, i.e., for separations much smaller than the resonant wavelength shows two peaks, located at frequency ±Ω12, contrary to the case of identical atoms, when the spectrum consists of only one peak located at the frequency +Ω12.