  Classically, the tendency towards spontaneous synchronization is strongest if
the natural frequencies of the self-oscillators are as close as possible. We
show that this wisdom fails in the deep quantum regime, where the uncertainty
of amplitude narrows down to the level of single quanta. Under these
circumstances identical self-oscillators cannot synchronize and detuning their
frequencies can actually help synchronization. The effect can be understood in
a simple picture: Interaction requires an exchange of energy. In the quantum
regime, the possible quanta of energy are discrete. If the extractable energy
of one oscillator does not exactly match the amount the second oscillator may
absorb, interaction, and thereby synchronization is blocked. We demon- strate
this effect, which we coin quantum synchronization blockade, in the minimal
example of two Kerr-type self-oscillators and predict consequences for small
oscillator networks, where synchronization between blocked oscillators can be
mediated via a detuned oscillator. We also propose concrete implementations
with super- conducting circuits and trapped ions. This paves the way for
investigations of new quantum synchronization phenomena in oscillator networks
both theoretically and experimentally.
