Two-ion superradiance theory

A superradiance theory is developed for two identical hydrogenic ions (four states each) in a microtrap, as in recent experiments. The ions oscillate (micromotion) due to the traps radio frequency (rf) electric quadrupole field. One signature of superradiance is a deviation of the two-ion average upper state decay rate from the one-ion value. A master equation is derived, giving a fractional change in the upper state lifetime /-1=sinkR/2kR [J02(z)-2J12(z)+...] cos, where k=2/, is the emission wavelength, R is the ion-ion distance, Jn(z) is a Bessel function of integer order n, and z=ka, a is the ion amplitude of motion, and is the two-ion relative phase due to the preparation. In the Lamb-Dicke regime, a<, J02(z)1 and thus superradiance is not influenced significantly by ion motion. This damped sinusoid is diluted by the factor of 1/2 due to destructive interference. Superradiance vanishes in the absence of coherent preparation, e.g., with inversion, as indicated by the time evolution of the two-ion dipole correlation function. Fringes and a beat at the rf are predicted in forward scattering, the most elementary form of optical free induction decay. © 1995 The American Physical Society.