Test of the linearity of quantum mechanics by rf spectroscopy of the ${}_{}{}^9{}_{}{}^{}\mathrm{Be}_{}^{+}{}_{}{}^{}$ ground state

A hyperfine transition in the ground state of ${}_{}{}^9{}_{}{}^{}\mathrm{Be}_{}^{+}{}_{}{}^{}$ was used to test a nonlinear generalization of quantum mechanics recently formulated by Weinberg. We searched for a dependence of the frequency of a coherent superposition of two hyperfine states on the populations of the states. We are able to set a limit of 4×${10}^{\mathrm{-}27}$ on the fraction of binding energy per nucleon of the ${}_{}{}^9{}_{}{}^{}\mathrm{Be}_{}^{+}{}_{}{}^{}$ nucleus that could be due to nonlinear corrections to quantum mechanics.