2-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 trap's radio frequency (rf) electric quadrupole field. One signature of superradiance is a deviation of the two-ion average upper state decay rate <(gamma)over bar> from the one-ion value gamma. A master equation is derived, giving a fractional change in the upper state lifetime gamma/<(gamma)over bar>-1 = sinkR/2kR [J(0)(2)(z)-2J(1)(2)(z)+...]cos Phi, where k=2 pi/lambda,lambda is the emission wavelength, R is the ion-ion distance, J(n)(z) is a Bessel function of integer order n, and z = ka, a is the ion amplitude of motion, and Phi is the two-ion relative phase due to the preparation. In the Lamb-Dicke regime, a < lambda, J(0)(2)(z)approximate to 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.