  Two coupled semiconductor nanolasers exhibit a mode switching transition,
theoretically characterized by limit cycle $-$or mode-beating$-$ oscillations.
Their decay rate is vanishingly small in the thermodynamic limit, i.e. when the
spontaneous emission noise $\beta$-factor tends to zero. We provide
experimental evidence of mesoscopic limit cycles $-$with $\sim 10^3$
intracavity photons$-$ through photon statistics measurements. We first show
that the order parameter quantifying the limit cycle amplitude can be
reconstructed from the mode intensity statistics. As a main result we observe a
maximum of the averaged amplitude at the mode switching, accounting for limit
cycle oscillations. We finally relate this maximum to a dip of mode
cross-correlations, reaching a minimum of $g_{ij}^{(2)}=2/3$, which we show to
be a mesoscopic limit. Coupled nanolasers are thus an appealing testbed for the
investigation of spontaneous breaking of time-translation symmetry in presence
of strong quantum fluctuations.
