Regular Article

Observation of two 𝓟𝓣 transitions in an electric circuit with balanced gain and loss^★

¹ School of Physics and Astronomy, Sun Yat-sen University, Zhuhai, Guangdong 519082, P.R. China
² Department of Physics, Indiana University Purdue University Indianapolis (IUPUI), Indianapolis, IN 46202, USA
³ School of Electronics and Information Technology, Sun Yat-sen University, Guangzhou, Guangdong 510006, P.R. China

^a e-mail: yojoglek@iupui.edu
^b e-mail: wangzix@mail.sysu.edu.cn
^c e-mail: lijiam29@mail.sysu.edu.cn
^d e-mail: luole5@mail.sysu.edu.cn

Received: 2 March 2020
Received in final form: 3 June 2020
Published online: 4 August 2020

Abstract

We investigate 𝓟𝓣-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, 𝓟𝓣-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 𝓟𝓣 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, 𝓟𝓣-symmetric electronics are ideally suited for classical simulations of non-Hermitian systems.