Exceptional points in coupled dissipative dynamical systems

Energetic Cost for Speedy Synchronization in Non-Hermitian Quantum Dynamics

Quantum synchronization is crucial for understanding complex dynamics and holds potential applications in quantum computing and communication. Therefore, assessing the thermodynamic resources required for finite-time synchronization in continuous-variable systems is a critical challenge. In the present work, we find these resources to be extensive for large systems. We also bound the speed of quantum and classical synchronization in coupled damped oscillators with non-Hermitian anti-PT-symmetric interactions, and show that the speed of synchronization is limited by the interaction strength relative to the damping. Compared to the classical limit, we find that quantum synchronization is slowed by the noncommutativity of the Hermitian and anti-Hermitian terms. Our general results could be tested experimentally, and we suggest an implementation in photonic systems.

Non-hermiticity in spintronics: oscillation death in coupled spintronic nano-oscillators through emerging exceptional points

The emergence of exceptional points (EPs) in the parameter space of a non-hermitian (2D) eigenvalue problem has long been interest in mathematical physics, however, only in the last decade entered the scope of experiments. In coupled systems, EPs give rise to unique physical phenomena, and enable the development of highly sensitive sensors. Here, we demonstrate at room temperature the emergence of EPs in coupled spintronic nanoscale oscillators and exploit the system's non-hermiticity. We observe amplitude death of self-oscillations and other complex dynamics, and develop a linearized non-hermitian model of the coupled spintronic system, which describes the main experimental features. The room temperature operation, and CMOS compatibility of our spintronic nanoscale oscillators means that they are ready to be employed in a variety of applications, such as field, current or rotation sensors, radiofrequeny and wireless devices, and in dedicated neuromorphic computing hardware. Furthermore, their unique and versatile properties, notably their large nonlinear behavior, open up unprecedented perspectives in experiments as well as in theory on the physics of exceptional points expanding to strongly nonlinear systems.

Chiral exceptional point in transformation cavity

Unlike the ideal circular whispering gallery cavities, those without mirror symmetry intrinsically support resonant modes exhibiting chirality which indicates an imbalance between clockwise and counterclockwise wave components. In extreme cases, nearly degenerate pairs of copropagating modes can be found around the chiral exceptional points (EPs) in parameter spaces. The chiral EPs have been studied in various schemes; however, most attention has been focused on the cases with piecewise constant or periodic refractive index profiles. In this Letter, we report the formation of a chiral EP in a gradient-index cavity designed by conformal transformation optics. Here, the mirror symmetry of the cavity is broken solely by its gradient index profile, and the parameter space is constructed with coordinate transformation parameters. We unveil the chirality, nonorthogonality, and complex-square-root topology near the chiral EP, which can be explained by the non-Hermitian model Hamiltonian.

Effect of parameter mismatch and dissipative coupling on amplitude death regime in a coupled nonlinear aeroelastic system

Amplitude death (AD) has been recently identified as a phenomenon that can be exploited to stop unwanted large amplitude oscillations arising from instabilities in engineering systems. These oscillations are a consequence of the occurrence of dynamic instability, for example, the flutter instability, which results in the manifestation of sustained limit cycle oscillations. Recent studies have demonstrated amplitude death in coupled aeroelastic systems with identical parameters using suitable reactive coupling. Deriving impetus from the same, the dynamical signatures of coupled non-identical aeroelastic systems under a variety of coupling characteristics are investigated in the present study. The coupling characteristics between the individual airfoils here are assumed to possess both reactive and dissipative terms and are represented via a linear torsional spring and a damper, respectively. Explicit parameter mismatch is introduced via the use of different structural parameters such as frequency ratio and air-mass ratio for the individual airfoils. We demonstrate that a nonlinear coupled aeroelastic system with parameter mismatch and combined coupling characteristics gives rise to broader regimes of AD in aeroelastic systems. Specifically, the possibility of encountering large amplitude oscillations, usually found with pure reactive coupling can be avoided by adding a dissipative coupling term. On introducing dissipative coupling, the regime of AD was found to increase substantially, for both identical and non-identical scenarios, which in turn aids in serving as an effective tool to be developed further toward the application of flutter instability suppression.

Rayleigh scatterer-induced steady exceptional points of stable-island modes in a deformed optical microdisk

A formation of second-order non-Hermitian degeneracies, called exceptional points (EPs), in a chaotic oval-shaped dielectric microdisk is studied. Different symmetric optical modes localized on a stable period-3 orbit coalesce to form chiral EPs. Unlike a circular microdisk perturbed by two scatterers (CTS), our proposed system requires only one scatterer to build chiral EPs. The scatterer positions for counterpropagating EP modes are far distant from one another and almost steady against varying scatterer sizes in contrast to the CTS case. Our results can contribute to establishing a more solid platform for EP-based-device applications with flexibility and easy feasibility in obtaining EPs.

Oscillation death in coupled counter-rotating identical nonlinear oscillators

We study oscillatory and oscillation suppressed phases in coupled counter-rotating nonlinear oscillators. We demonstrate the existence of limit cycle, amplitude death, and oscillation death, and also clarify the Hopf, pitchfork, and infinite period bifurcations between them. Especially, the oscillation death is a new type of oscillation suppressions of which the inhomogeneous steady states are neutrally stable. We discuss the robust neutral stability of the oscillation death in non-conservative systems via the anti-parity-time-symmetric phase transitions at exceptional points in terms of non-Hermitian systems.

Reconfiguration of quantum states in [Formula: see text]-symmetric quasi-one-dimensional lattices

We demonstrate mesoscopic transport through quantum states in quasi-1D lattices maintaining the combination of parity and time-reversal symmetries by controlling energy gain and loss. We investigate the phase diagram of the non-Hermitian system where transitions take place between unbroken and broken [Formula: see text]-symmetric phases via exceptional points. Quantum transport in the lattice is measured only in the unbroken phases in the energy band-but not in the broken phases. The broken phase allows for spontaneous symmetry-broken states where the cross-stitch lattice is separated into two identical single lattices corresponding to conditionally degenerate eigenstates. These degeneracies show a lift-up in the complex energy plane, caused by the non-Hermiticity with [Formula: see text]-symmetry.

Amplitude death in a ring of nonidentical nonlinear oscillators with unidirectional coupling

We study the collective behaviors in a ring of coupled nonidentical nonlinear oscillators with unidirectional coupling, of which natural frequencies are distributed in a random way. We find the amplitude death phenomena in the case of unidirectional couplings and discuss the differences between the cases of bidirectional and unidirectional couplings. There are three main differences; there exists neither partial amplitude death nor local clustering behavior but an oblique line structure which represents directional signal flow on the spatio-temporal patterns in the unidirectional coupling case. The unidirectional coupling has the advantage of easily obtaining global amplitude death in a ring of coupled oscillators with randomly distributed natural frequency. Finally, we explain the results using the eigenvalue analysis of the Jacobian matrix at the origin and also discuss the transition of dynamical behavior coming from connection structure as the coupling strength increases.