We consider the dynamics of single photons in a nonlinear optical cavity. When the Kerr nonlinearities of atomic dark resonances are utilized, the cavity mode is well described by a spin- $1/2$ Hamiltonian. We show that it is possible to achieve coherent control of the cavity-mode wave function using $\ensuremath{\pi}$ pulses for single photons that switch the state of the cavity with very high accuracy. The underlying physics is best understood as the nonlinearity induced anticorrelation between single-photon injection/emission events, which we refer to as photon blockade. We also propose a method which uses these strong dispersive interactions to realize a single-photon turnstile device.