ABSTRACT Non‐Hermitian quantum systems exhibiting parity‐time () symmetry can yield real eigenvalues under specific parameter regimes, expanding traditional ideas of Hermitian operators in quantum mechanics. This concept has catalyzed the development of experimental platforms, particularly in electronics and optics, where pseudo‐Hermitian principles enable useful implementations providing insight into their behaviors. Among these, active LCR circuit dimers have emerged as powerful tools to test ‐symmetry breaking, mode coalescence, and nonreciprocal signal dynamics. This work presents a systematic design methodology for constructing circuit topologies that mimic quantum Hamiltonians (both Hermitian and non‐Hermitian) via a decomplexification framework. The proposed approach accommodates a range of and anti‐ configurations through a flexible coupled oscillator network, offering practical utility in signal processing, metamaterials, and coherent amplification devices.
ABSTRACT Non‐Hermitian quantum systems exhibiting parity‐time () symmetry can yield real eigenvalues under specific parameter regimes, expanding traditional ideas of Hermitian operators in quantum mechanics. This concept has catalyzed the development of experimental platforms, particularly in electronics and optics, where pseudo‐Hermitian principles enable useful implementations providing insight into their behaviors. Among these, active LCR circuit dimers have emerged as powerful tools to test ‐symmetry breaking, mode coalescence, and nonreciprocal signal dynamics. This work presents a systematic design methodology for constructing circuit topologies that mimic quantum Hamiltonians (both Hermitian and non‐Hermitian) via a decomplexification framework. The proposed approach accommodates a range of and anti‐ configurations through a flexible coupled oscillator network, offering practical utility in signal processing, metamaterials, and coherent amplification devices.
PT-symmetric electronics
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.
Engineering quantum bath networks through non-Hermitian subsystem Hamiltonians has recently emerged as a promising strategy for qubit cooling, state stabilization, and fault-tolerant quantum computation. However, scaling these systems while maintaining precise control over their complex interconnections, especially in the optical domain, poses significant challenges in both theoretical modeling and physical implementation. In this work, drawing on principles from quantum and mathematical physics, we introduce a systematic framework for constructing non-Hermitian subsystems within entirely Hermitian photonic platforms. In particular, controlled exponential decay without actual absorption loss is realized in finite 1-D waveguide chains through discrete-to-continuum coupling and Lanczos transformations. Using this new methodology, we implement parity-time symmetric quantum systems and experimentally demonstrate that these artificial bath environments accurately replicate the dynamics of non-Hermitian arrangements in both single- and multi-photon excitation regimes. Since the non-Hermitian subsystem response deterministically arises from an artificially built Hermitian bath, the quantum evolution can be monitored via post-selection in this fully conservative configuration. This approach bridges the gap between theoretical models and experimental realizations, thus paving the way for exploiting quantum bath engineering in advanced information processing and emerging quantum technologies.
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. PACS numbers: 11.30.Er, 05.60.-k, 45.05.+x 1.
A Hamiltonian with Parity-Time (PT) symmetry can have fully real eigenvalues within its PT-symmetric regime. This is a special case in non-Hermitian quantum mechanics and has been widely used in open-system physics research. A pair of electromagnetically coupled parallel RLC resonant circuits, when incorporating a pair of equal-magnitude positive and negative resistances with equivalent gain (dissipation) strength, can form a PT-symmetric non-Hermitian system. This paper presents a teaching-oriented design and practical exploration of PT-symmetric physics research based on RLC resonant circuits. It also offers experimental studies on multilevel phase transitions resulting from the combination of PT symmetry and RLC resonance, enhancing the understanding of their characteristics.
The traditional framework of quantum mechanics and many classical wave phenomena is underpinned by Hermitian operators, which guarantee real eigenvalues corresponding to observable quantities and orthogonal eigenvectors. However, a growing number of physical systems exhibit non-reciprocal interactions, leading to Hamiltonians or system matrices that are inherently non-Hermitian. This paper delves into the spectral theory of such non-reciprocal systems, exploring the unique mathematical and physical characteristics that emerge when the constraint of Hermiticity is relaxed. We discuss phenomena like complex energy eigenvalues, exceptional points where both eigenvalues and eigenvectors coalesce, and the breakdown of standard perturbation theory. The implications of non-Hermitian spectral properties extend to diverse fields, including parity-time (PT) symmetric photonics, active matter, open quantum systems, and even classical wave propagation in active or lossy media. By extending spectral analysis beyond the Hermitian paradigm, we aim to provide a comprehensive overview of the current understanding, challenges, and future directions in characterizing the dynamics and phases of non-reciprocal systems. This exploration is crucial for advancing both fundamental theoretical understanding and practical applications in emerging technologies that leverage tailored non-reciprocity.
The non-Hermitian models, which are symmetric under parity ( P ) and time-reversal ( T ) operators, are the cornerstone for the fabrication of new ultra-sensitive optoelectronic devices. However, providing the gain in such systems usually demands precise control of nonlinear processes, limiting their application. In this paper, to bypass this obstacle, we introduce a class of time-dependent non-Hermitian Hamiltonians (not necessarily Floquet) that can describe a two-level system with temporally modulated on-site potential and couplings. We show that implementing an appropriate non-Unitary gauge transformation converts the original system to an effective one with a balanced gain and loss. This will allow us to derive the evolution of states analytically. Our proposed class of Hamiltonians can be employed in different platforms such as electronic circuits, acoustics, and photonics to design structures with hidden PT -symmetry potentially without imaginary onsite amplification and absorption mechanism to obtain an exceptional point.