Observation of two ð"Ÿð"£ transitions in an electric circuit with balanced gain and loss

We investigate ð"Ÿð"£-symmetry breaking transitions in a dimer comprising two LC oscillators, one with loss and the second with gain. The electric energy of this four-mode model oscillates between the two LC circuits, and between capacitive and inductive energy within each LC circuit. Its dynamics are described by a non-Hermitian, ð"Ÿð"£-symmetric Hamiltonian with three different phases separated by two exceptional points. We systematically measure the eigenfrequencies of energy dynamics across the three regions as a function of gain-loss strength. In addition to observe the well-studied ð"Ÿð"£ transition for oscillations across the two LC circuits, at higher gain-loss strength, transition within each LC circuit is also observed. With their extraordinary tuning ability, ð"Ÿð"£-symmetric electronics are ideally suited for classical simulations of non-Hermitian systems.