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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 thespontaneous emission noise $\beta$-factor tends to zero. We provideexperimental evidence of mesoscopic limit cycles $-$with $\sim 10^3$intracavity photons$-$ through photon statistics measurements. We first showthat the order parameter quantifying the limit cycle amplitude can bereconstructed from the mode intensity statistics. As a main result we observe amaximum of the averaged amplitude at the mode switching, accounting for limitcycle oscillations. We finally relate this maximum to a dip of modecross-correlations, reaching a minimum of $g_{ij}^{(2)}=2/3$, which we show tobe a mesoscopic limit. Coupled nanolasers are thus an appealing testbed for theinvestigation of spontaneous breaking of time-translation symmetry in presenceof strong quantum fluctuations.

Mesoscopic limit cycles in coupled nanolasers