$\mathcal{PT}$-symmetric electronics

Abstract

We show both theoretically and experimentally that a pair of inductively coupled active LRC circuits (dimer), one with amplification and another with an equivalent amount of attenuation, display all the features which characterize a wide class of non-Hermitian systems which commute with the joint parity-time PT operator: typical normal modes, temporal evolution, and scattering processes. Utilizing a Liouvilian formulation, we can define an underlying PT -symmetric Hamiltonian, which provides important insight for understanding the behavior of the system. When the PT -dimer is coupled to transmission lines, the resulting scattering signal reveals novel features which reflect the PT -symmetry of the scattering target. Specifically we show that the device can show two different behaviors simultaneously, an amplifier or an absorber, depending on the direction and phase relation of the interrogating waves. Having an exact theory, and due to its relative experimental simplicity, PT -symmetric electronics offers new insights into the properties of PT -symmetric systems which are at the forefront of the research in mathematical physics and related fields.

PT-Symmetric Acoustics

“…In the broken phase (red curve), the second components of the eigenvectors are purely imaginary, and under conjugation, one of the components transforms into the other. It should be pointed out that the unusual scattering properties of the PT -symmetric medium have also been demonstrated in optics and electronics, both in theories and experiments [41,42,44,45].…”

Spectra, current flow, and wave-function morphology in a modelPT-symmetric quantum dot with external interactions

“…Dynamical transitions with the Hamiltonian in Eq. (18) have been studied in, e.g., [45,46] and used in [42,43] to interpret the experimental data. In [45,46] the number of channels is K = 1, and it has been shown that the transition really can be regarded as a second-order phase transition in the sense of thermodynamics in the limit N → ∞.…”

“…EPs of this kind may be studied experimentally, and there is a rapidly increasing number of studies related to fundamental science and technology. For example, there are studies with pump-induced lasers [7,8], microwave cavities and wires [9][10][11][12][13][14][15][16][17], LRC circuits [18], exciton-polariton billiards [19], and more [20,21].…”

A versatile all-optical parity-time signal processing device using a Bragg grating induced using positive and negative Kerr-nonlinearity

“…The stable operating conditions are determined by the amount of gain and loss in the grating, whereby if the magnitudes of the gain and loss are equal, and 2 exceed a certain critical amount, the grating operation becomes unstable (Chong et al 2011;Nixon et al 2012). This critical amount of gain/loss is commonly referred to as the Lasing and Coherent Perfect Absorber (CPAL) point (Chong et al 2011;Phang et al 2013b;Schindler et al 2012), and operation above this point yields an exponential energy growth. In a linear PT grating structure, the CPAL occurs when the trajectories of a pole and a zero of the scattering matrix S coincide on the real frequency axis in the complex frequency plane (Chong et al 2011).…”