Loss of synchonization. As the coupling is reduced, either by increasing

*d* or by detuning the characteristic beating times of the two oscillators, synchronization is lost due to thermal noise. (

*A*) Heat map showing the histogram of the synchronization order parameter

*Q* as a function of distance, and thus at varying coupling strength. A strong antiphase correlation (

*Q* ≃ 0.8) can be seen in both experiments (

*Top*) and numerical simulation (

*Bottom*).

*Q* < 1 is principally determined by a time delay Δ

*t* which results from correlated fluctuations. As

*d* increases, synchronization is lost via the process shown in (

*B*). (

*B*) The switch time difference

is plotted as a function of the period index (each panel is obtained a distance

*d*, as labeled). At small

*d* this quantity fluctuates around the locked state, while phase-slips and drift emerge as the coupling weakens. (

*Bottom*) Noise level in flat regions is plotted and shows a linear increase with

*d*, up to a level that is comparable to the half-period of the motion (solid line). This is the process by which synchronization is lost in this system. (

*C*) (

*Top*) and (

*Middle*) Histogram of

*Q* at varying ratio of the stiffness for the two traps, and thus of the intrinsic frequency of the two oscillators. Maximal antiphase correlation is observed for oscillators of equal intrinsic frequency. (

*Bottom*) Loss of synchrony (defined by a threshold at

*Q* = 0.6) at different coupling strengths. The numerical data (black circles) provides a measure of the Arnold tongues for this system and are compatible with the experimental observations at

*d* = 10 μm. Error bar is the uncertainty in the trap stiffness ratio.

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