A bacterial colony may develop a small number of cells genetically identical to, but phenotypically different from, other normally growing bacteria. These so-called persister cells keep themselves in a dormant state and thus are insensitive to antibiotic treatment, resulting in serious problems of drug resistance. In this paper, we proposed a novel strategy to 'kill' persister cells by triggering them to switch, in a fast and synchronized way, into normally growing cells that are susceptible to antibiotics. The strategy is based on resonant activation (RA), a well-studied phenomenon in physics where the internal noise of a system can constructively facilitate fast and synchronized barrier crossings. Through stochastic Gilliespie simulation with a generic toggle switch model, we demonstrated that RA exists in the phenotypic switching of a single bacterium. Further, by coupling single cell level and population level simulations, we showed that with RA, one can greatly reduce the time and total amount of antibiotics needed to sterilize a bacterial population. We suggest that resonant activation is a general phenomenon in phenotypic transition, and can find other applications such as cancer therapy.