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Description
Synchronization describes an interesting dynamical process of coupled oscillators.
Particularly, it refers to oscillators oscillating at the same frequency despite their
natural frequency difference. Besides, for a coupled two-oscillator system, its
hybridized eigenmodes can be mapped onto the Bloch Sphere.
We experimentally studied the relationship between synchronization and
hybridized modes on the Bloch sphere through dissipatively coupled two electric
oscillators. The circuit consists of two parallel LC oscillators with identical
linewidth, connected by a coupling resistor. Utilizing adjustable components
enables great tunability of the system. The setup also allows us to perform
comprehensive spectral and time-domain analyses on the essential consequences
of dissipative coupling.
We observed anti-parity-time-symmetry preservation/breaking, exceptional points,
trajectories of eigenmodes on the surface of the Bloch sphere, and the
synchronization zone accompanied by characteristic phase difference between two
oscillating waveforms. As a result, we confirm that the exceptional points enclose
the synchronization zone and the equator states on the Bloch sphere are nothing
more than a later twin.
