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

Wang, Tishuo; Fang, Jianxiong; Xie, Zhongyi; Dong, Nenghao; Joglekar, Yogesh N.; Wang, Zixin; Li, Jiaming; Luo, Le

doi:10.1140/epjd/e2020-10131-7

Cited by 22 publications

(14 citation statements)

References 32 publications

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“…We start with the review of an electrical PT -symmetric dimer [18,19,30,31]. Let us consider two identical LC circuits, with effective, parallel resistors ±R respectively, that are connected with a coupling inductor L c as shown in Fig.…”

Section: Coupled Lc Circuits With Pt Symmetrymentioning

confidence: 99%

“…The transition from a PT -symmetric region (real spectrum) to the PT -symmetry broken region (complex conjugate spectrum) across the EP has been extensively studied in classical wave systems where both gain and loss are readily implemented. Realizations include coupled optical waveguides [13], fiber loops [14], microring resonators [15], acoustic setups [16], coupled mechanical oscillators [17], and coupled electrical circuits [18,19]. Due to quantum fluctuations associated with a linear gain [20], balanced gain and loss configurations are not possible at a quantum level [21].…”

Section: Introductionmentioning

confidence: 99%

“…Formally, this is to be achieved by making either the gain-loss or the Hermitian part of the Hamiltonian dependent on the history of the system. We use coupled, active and lossy LC circuits as the model [18,19,30], because resistive and inductive elements with memory, i.e. memristors and meminductors, are well understood.…”

Section: Introductionmentioning

confidence: 99%

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Parity-time symmetric systems with memory

Cochran,

Saxena,

Joglekar

2020

Preprint

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Classical open systems with balanced gain and loss, i.e. parity-time (PT ) symmetric systems, have attracted tremendous attention over the past decade. Their exotic properties arise from exceptional point (EP) degeneracies of non-Hermitian Hamiltonians that govern their dynamics. In recent years, increasingly sophisticated models of PT -symmetric systems with time-periodic (Floquet) driving, time-periodic gain and loss, and time-delayed coupling have been investigated, and such systems have been realized across numerous platforms comprising optics, acoustics, mechanical oscillators, optomechanics, and electrical circuits. Here, we introduce a PT -symmetric (balanced gain and loss) system with memory, and investigate its dynamics analytically and numerically. Our model consists of two coupled LC oscillators with positive and negative resistance, respectively. We introduce memory by replacing either the resistor with a memristor, or the coupling inductor with a meminductor, and investigate the circuit energy dynamics as characterized by PT -symmetric or PT -symmetry broken phases. Due to the resulting nonlinearity, we find that energy dynamics depend on the sign and strength of initial voltages and currents, as well as the distribution of initial circuit energy across its different components. Surprisingly, at strong inputs, the system exhibits selforganized Floquet dynamics, including PT -symmetry broken phase at vanishingly small dissipation strength. Our results indicate that PT -symmetric systems with memory show a rich landscape.

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Section: Coupled Lc Circuits With Pt Symmetrymentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Parity-time symmetric systems with memory

Cochran,

Saxena,

Joglekar

2020

Preprint

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“…The latter was engendered by the observation that imaginary potentials represent gain or loss [8][9][10], and therefore, PT -symmetric, non-Hermitian Hamiltonians faithfully describe open, classical systems with balanced gain and loss. Over the past decade, classical PT -symmetric systems have been investigated in coupled waveguides [11], fiber loops [12], optical resonators [13,14], acoustics [15], mechanical oscillators [16], and electrical circuits [17,18].…”

Section: Introductionmentioning

confidence: 99%

Maximal quantum entanglement at exceptional points via unitary and thermal dynamics

Kumar,

Murch,

Joglekar

2021

Preprint

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Minimal, open quantum systems that are governed by non-Hermitian Hamiltonians have been realized across multiple platforms in the past two years. Here we investigate the dynamics of open systems with Hermitian or anti-Hermitian Hamiltonians, both of which can be implemented in such platforms. For a single system subject to unitary and thermal dynamics in a periodic manner, we show that the corresponding Floquet Hamiltonian has a rich phase diagram with numerous exceptional-point (EP) degeneracy contours. This protocol can be used to realize a quantum Hatano-Nelson model that is characterized by asymmetric tunneling. For one unitary and one thermal qubit, we show that the concurrence is maximized at the EP that is controlled by the strength of Hermitian coupling between them. Surprisingly, the entropy of each qubit is also maximized at the EP. Our results point to the multifarious phenomenology of systems undergoing unitary and thermal dynamics.

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“…Since the seminal work of Bender and coworkers [1,2], the field of non-Hermitian Hamiltonians with parity-time (PT ) symmetry has diversified and matured over the past two decades [3][4][5][6]. PT -symmetric Hamiltonians represent open classical systems with balanced gain and loss [7], and have been experimentally realized in diverse platforms comprising optics [8][9][10][11][12], electrical circuits [13][14][15], mechanical oscillators [16], acoustics [17], and viscous fluids [18]. Post-selection over no-quantum-jump trajectories has further enabled their realizations in minimal quantum systems such as an NV center [19], a superconducting qubit [20], ultracold atoms [21], or correlated photons [22].…”

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confidence: 99%