The photon blockade is an effect that causes the light at the output of an atom-cavity system to become antibunched when irradiated by coherent light. A straightforward application would be the single photon router [1], which transmits a single photon in a two-photon pulse, reflecting the other one. We show that the efficiency of this process is inherently limited due to the time-energy uncertainty principle. The maximum obtainable efficiency is calculated to be ~65%, and the corresponding optimal pulse width is shown to be of the order of the system decay time. This bound applies to any photon-blockade setup, ranging from the traditional one in the strong coupling regime [2] to the more recent turnstile effect in the bad-cavity limit [3]. We conclude that any photon blockade effect based on a setup that can be approximated by a two-level system, has limited applicability as a single photon router.

[1] T. Aoki et al., Phys. Rev. Lett. 102, 083601 (2009)

[2] K. M. Birnbaum et al., Nature 436, 87–90 (2005) 

[3] B. Dayan et al., Science 319, 1062–1065 (2008)