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.

17 pages, 7 figures

References in corpus (11)

• Making Sense of Non-Hermitian Hamiltonians
• Coherent Perfect Absorbers: Time-reversed Lasers
• PT-symmetry breaking and laser-absorber modes in optical scattering systems
• Unidirectional Nonlinear PT-symmetric Optical Structures
• Faster than Hermitian Quantum Mechanics
• Exponentially Fragile PT-Symmetry in Lattices with Localized Eigenmodes
• Mean-field dynamics of a non-Hermitian Bose-Hubbard dimer
• PT-Symmetric Wave Chaos
• Experimental observation of the dual behavior of $\mathcal{P}\mathcal{T}$-symmetric scattering
• Bypassing the bandwidth theorem with PT symmetry
• Bifurcations in Resonance Widths of an Open Bose-Hubbard Dimer

Cited by in corpus (112)

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• Parametric amplification and bidirectional invisibility in PT-symmetric time-Floquet systems
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• Tunneling of Obliquely-Incident Waves through PT-Symmetric Epsilon-Near-Zero Bi-Layers
• PT Symmetric Aubry-Andre Model
• Breaking of PT-symmetry in bounded and unbounded scattering systems
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• $\mathcal{P}\mathcal{T}$-Symmetry-Induced Wave Confinement and Guiding in Epsilon-Near-Zero Metamaterials
• Hermitian four-well potential as a realization of a PT-symmetric system
• Parity-time symmetry in optical microcavity systems
• Non-Hermiticity Induced Flat Band
• Nearby states in non-Hermitian quantum systems
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• Random Matrix Theory Approach to Chaotic Coherent Perfect Absorbers
• Perfect Absorption in Complex Scattering Systems with or without Hidden Symmetries
• Antiferromagnetism emerging in a ferromagnet with gain
• Permanent Rabi oscillations in coupled exciton-photon systems with PT-symmetry
• Steering magnonic dynamics and permeability at exceptional points in a parity-time symmetric waveguide
• Frequency-stable robust wireless power transfer based on high-order pseudo-Hermitian physics
• Giant Non-reciprocity Near Exceptional Point Degeneracies
• Linear response theory of open systems with exceptional points
• PT-Symmetric Dimer of Coupled Nonlinear Oscillators
• On the integrability of PT-symmetric dimers
• Environmentally-induced exceptional points in elastodynamics
• Coupling approach for the realization of a $\mathcal{P}\mathcal{T}$-symmetric potential for a Bose-Einstein condensate in a double well
• Scattering by finite periodic $\mathcal{P}\mathcal{T}$-symmetric structures
• Non-Hermitian phase transition and eigenstate localization induced by asymmetric coupling
• Distribution of zeros of the S-matrix of chaotic cavities with localized losses and Coherent Perfect Absorption: non-perturbative results
• Response strengths of open systems at exceptional points
• Revisiting the PT-symmetric Trimer: Bifurcations, Ghost States and Associated Dynamics
• Towards a Broad-Band Coherent Perfect Absorption in systems without Scale-Invariance
• Tilted optical lattices with defects as realizations of PT symmetry in Bose-Einstein condensates
• Non-self-adjoint hamiltonians defined by Riesz bases
• Statistical PT-symmetric lasing in an optical fiber network
• Type II Perfect Absorption and Amplification Modes with Controllable Bandwidth in PT-Symmetric/Traditional Bragg Grating Combined Structures
• Revisiting the optical $PT$-symmetric dimer
• PT Meets Supersymmetry and Nonlinearity: An Analytically Tractable Case Example
• Generalized bulk-boundary correspondence in periodically driven non-Hermitian systems
• Coupling-independent, Real-time Wireless Resistive Sensing through Nonlinear PT-symmetry
• Wavepacket Self-imaging and Giant Recombinations via Stable Bloch-Zener Oscillations in Photonic Lattices with Local $\mathcal{P}\mathcal{T}$-Symmetry
• Interaction of sine-Gordon kinks and breathers with a $\mathcal{P}\mathcal{T}$-symmetric defect
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• Wireless Real-Time Capacitance Readout Based on Perturbed Nonlinear Parity-Time Symmetry
• Emitter and absorber assembly for multiple self-dual operation and directional transparency
• Realizing PT-symmetric BEC subsystems in closed hermitian systems
• PT-symmetric phase in kagome photonic lattices
• CPA-laser effect and exceptional points in PT-symmetric multilayer structures
• Anti-parity-time symmetry hidden in a damping linear resonator
• Observation of size-dependent boundary effects in non-Hermitian electric circuits
• Solitary waves of a PT-symmetric Nonlinear Dirac equation
• Conserved quantities, exceptional points, and antilinear symmetries in non-Hermitian systems
• Scattering of gap solitons by PT-symmetric defects
• Nonorthogonality constraints in open quantum and wave systems
• Controlling the nonclassical properties of a hybrid Cooper pair box system and an intensity dependent nanomechanical resonator
• Bifurcations and exceptional points in a PT-symmetric dipolar Bose-Einstein condensate
• Novel PT-invariant Solutions For a Large Number of Real Nonlinear Equations
• Floquet Perfect Absorbers based on Periodically Driven Targets
• Enhanced Frequency Conversion in Parity-Time Symmetry Line
• PT-symmetry Management in Oligomer Systems
• Compact Localized States in Engineered Flat-Band $\mathcal{P}\mathcal{T}$ Metamaterials
• Generalized Dimers and their Stokes-variable Dynamics
• Solitary waves in the Nonlinear Dirac Equation
• Universal Route for the Emergence of Exceptional Points in PT-Symmetric Metamaterials with Unfolding Spectral Symmetries
• Pseudo-invariant approach for a particle in a complex time-dependent linear potential
• Resonant interaction of ${\varphi }^4$ kink with spatially periodic $\mathcal{P}\mathcal{T}$-symmetric perturbation
• Realization of $\mathcal{P}\mathcal{T}$-symmetric and $\mathcal{P}\mathcal{T}$-symmetry broken states in static optical lattice potentials
• Eigenstates Transition Without Undergoing an Adiabatic Process
• Theory and Numerical Modelling of Parity-Time Symmetric Structures in Photonics: Introduction and Grating Structures in One Dimension
• Variational Approach to studying solitary waves in the nonlinear Schrodinger equation with Complex Potentials
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• Solitons in a chain of charge-parity-symmetric dimers
• All-optical $\mathcal{P}\mathcal{T}$-symmetric amplitude to phase modulator
• Photon propagation through linearly active dimers
• Localizing EP sets in dissipative systems and the self-stability of bicycles
• Emergence of Exceptional Points in Periodic Metastructures with Hidden PT-symmetric Defects
• Stable solitons in a nearly PT-symmetric ferromagnet with spin-transfer torque
• Scattering of the asymmetric ${\varphi }^6$ kinks from a $\mathcal{P}\mathcal{T}$-symmetric perturbation: Creation of multiple pairs of kink-antikink from phonons
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• Stability and response of trapped solitary wave solutions of coupled nonlinear Schrödinger equations in an external, $\mathcal{P}\mathcal{T}$- and supersymmetric potential
• Integrability and trajectory confinement in $\mathcal{P}\mathcal{T}$-symmetric waveguide arrays
• The Effect of non-Hermiticity on Adiabatic Elimination
• Spectral Singularities with Directional Sensitivity
• Balanced gain and loss in spatially extended non-$\mathcal{P}\mathcal{T}$-symmetric multi-well potentials
• Higher-order exceptional points in composite non-Hermitian systems
• Krein signature for instability of $\mathcal{P}\mathcal{T}$-symmetric states
• Delocalization of interacting directed polymers on a periodic substrate: Localization length and critical exponents from non-Hermitian spectra
• Stability of exact solutions of the nonlinear Schroedinger equation in an external potential having supersymmetry and parity-time symmetry
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• On the Pauli group on 2-qubits in dynamical systems with pseudofermions
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