Dissipative Level Research Articles

Level Attraction due to Dissipative Phonon–Phonon Coupling in an Opto-Mechano-Fluidic Resonator

Dissipative couplings between solid-cavity optomechanical oscillators provide an underlying mechanism for many physical phenomena, such as level attraction, non-Hermitian parity-time-symmetric, and topological energy transfer with exceptional points (EPs). Until now, cavity optomechanical mode couplings on different phases of material have not been demonstrated. Here, we report the experimental demonstration of optomechanical mode dissipative coupling, mediated by high-quality-factor photon whispering-gallery modes, between a solid surface wave mode (SWM) and a liquid radial breathing mode (RBM), both of which coexist in an optofluidic microbubble resonator consisting of silica layer and liquid metal core. The resonant frequencies of solid-SWM and liquid-RBM depend mainly on the physical parameters of the silica and liquid metal, respectively. These physical parameters are all related to the microcavity temperature, which can be electrically controlled by wiring the liquid metal to a circuit. The dissipative level attraction between the solid-SWM and liquid-RBM is achieved by changing the current applied to the liquid metal. Our results open new avenues toward exploring topological energy transfer between solid and liquid materials or ultrasensitive biological sensing around EPs.

Quantized quasinormal-mode theory of coupled lossy and amplifying resonators

In the presence of arbitrary three-dimensional linear media with material loss and amplification, we present an electromagnetic field quantization scheme for quasinormal modes (QNMs), extending previous work for lossy media [Franke et al., Phys. Rev. Lett. 122, 213901 (2019)]. Applying a symmetrization transformation, we show two fundamentally different ways for constructing a QNM photon Fock space, including (i) where there is a separate operator basis for both gain and loss, and (ii) where the loss and gain degrees of freedom are combined into a single basis. These QNM operator bases are subsequently used to derive the associated QNM master equations, including the interaction with a quantum emitter, modelled as a quantized two-level system (TLS). We then compare the two different quantization approaches, and also show how commonly used phenomenological methods to quantize light in gain-loss resonators are corrected by several important aspects, such as a loss-induced and gain-induced intermode coupling, which appears through the rigorous treatment of loss and amplification on a dissipative mode level. For specific resonator designs, modelled in a fully consistent way with the classical Maxwell equations with open boundary conditions, we then present numerical results for the quantum parameters and observables of a TLS weakly interacting with the medium-assisted field in a gain-loss microdisk resonator system, and discuss the validity of the different quantization approaches for several gain-loss parameter regimes.

Coherent Coupling of Two Remote Magnonic Resonators Mediated by Superconducting Circuits.

We demonstrate microwave-mediated distant magnon-magnon coupling on a superconducting circuit platform, incorporating chip-mounted single-crystal Y_{3}Fe_{5}O_{12} (YIG) spheres. Coherent level repulsion and dissipative level attraction between the magnon modes of the two YIG spheres are demonstrated. The former is mediated by cavity photons of a superconducting resonator, and the latter is mediated by propagating photons of a coplanar waveguide. Our results open new avenues toward exploring integrated hybrid magnonic networks for coherent information processing on a quantum-compatible superconducting platform.

Conductance of a dissipative quantum dot: Nonequilibrium crossover near a non-Fermi-liquid quantum critical point

We find the nonlinear conductance of a dissipative resonant level in the nonequilibrium steady state near its quantum critical point. The system consists of a spin-polarized quantum dot connected to two resistive leads that provide ohmic dissipation. We focus on the crossover from the strong-coupling, non-Fermi-liquid regime to the weak-coupling, Fermi-liquid ground state, a crossover driven by the instability of the quantum critical point to hybridization asymmetry or detuning of the level in the dot. We show that the crossover properties are given by tunneling through an effective single barrier described by the boundary sine-Gordon model. The nonlinear conductance is then obtained from thermodynamic Bethe ansatz results in the literature, which were developed to treat tunneling in a Luttinger liquid. The current-voltage characteristics are thus found for any value of the resistance of the leads. For the special case of lead resistance equal to the quantum resistance, we find mappings onto, first, the two-channel Kondo model and, second, an effectively noninteracting model from which the nonlinear conductance is found analytically. A key feature of the general crossover function is that the nonequilibrium crossover driven by applied bias is different from the crossover driven by temperature -- we find that the nonequilibrium crossover is substantially sharper. Finally, we compare to experimental results for both the bias and temperature crossovers: the agreement is excellent.

Nonequilibrium quantum critical steady state: Transport through a dissipative resonant level

Nonequilibrium properties of correlated quantum matter are being intensively investigated because of the rich interplay between external driving and the many-body correlations. Of particular interest is the nonequilibrium behavior near a quantum critical point (QCP), where the system is delicately balanced between different ground states. We present both an analytical calculation of the nonequilibrium steady-state current in a critical system and experimental results to which the theory is compared. The system is a quantum dot coupled to resistive leads: a spinless resonant level interacting with an Ohmic dissipative environment. A two-channel Kondo-like QCP occurs when the level is on resonance and symmetrically coupled to the leads, conditions achieved by fine tuning using electrostatic gates. We calculate and measure the nonlinear current as a function of bias (I−V curve) at the critical values of the gate voltages corresponding to the QCP. The quantitative agreement between the experimental data and the theory, with no fitting parameter, is excellent. As our system is fully accessible to both theory and experiment, it provides an ideal setting for addressing nonequilibrium phenomena in correlated quantum matter.Received 16 October 2020Revised 16 January 2021Accepted 21 January 2021DOI:https://doi.org/10.1103/PhysRevResearch.3.013136Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.Published by the American Physical SocietyPhysics Subject Headings (PhySH)Research AreasCoulomb blockadeQuantum criticalityTransport phenomenaPhysical SystemsNanotubesQuantum dotsCondensed Matter, Materials & Applied PhysicsGeneral Physics

Distinguishing between topological and quasi Majorana zero modes with a dissipative resonant level

Distinguishing between topological Majorana zero modes and quasi Majorana modes -- trivial low energy Andreev bound states -- is an important step towards realizing topological hybrid nanowire devices. We propose that this distinction can be made by connecting a hybrid nanowire to a dissipative resonant level realized by a quantum dot weakly coupled to high resistance leads. We show that the qualitative temperature scaling of the width of the resonant level zero bias conductance peak provides a signature unique to true Majorana zero modes. The degeneracy induced by a true Majorana zero mode is further shown to stabilize this conductance peak against particle-hole asymmetry.

Finite-time dynamic output-feedback dissipative control for singular uncertainty T–S fuzzy systems with actuator saturation and output constraints

This paper studies the problem of finite-time dynamic output-feedback control for singular uncertainty T–S time-varying delay fuzzy systems with actuator saturation and output constraints. Through a dynamic parallel distributed compensator, the (U,V,R)−α− dissipative output-feedback fuzzy controller is designed. Furthermore, by employing reciprocally convex approach and a new lemma, the sufficient conditions are obtained to guarantee that the systems are finite-time bounded subject to (U,V,R)−α− dissipative performance level. Then, the desired fuzzy state-feedback controller and dynamic output feedback controller are derived by solving the linear matrix inequalities (LMIs). Finally, the feasibility and effectiveness of the proposed method can be validated by some simulations.

Dissipative-based non-fragile filtering for fuzzy networked control systems with switching communication channels

The problem of finite-time dissipative-based non-fragile filter design for a class of discrete-time nonlinear networked control systems subject to randomly occurring parameter uncertainties, external disturbances as well as packet dropouts due to unreliable communication channels and networked induced time-varying delay is discussed. The randomly occurring uncertainties are assumed to satisfy Bernoulli distribution and the considered stochastic variables are mutually independent. Multiple communication channel scenario is taken into account to enhance the data transmission performance and the channel switching phenomena is governed by a Markov chain. The intention here is to design a dissipative-based non-fragile filter for the filtering error system such that it is stochastically finite-time bounded and attains a prescribed dissipative performance attenuation level. Lyapunov stability theory and linear matrix inequality approach are exploited to develop a set of sufficient criterion for the existence of the desired filter. Finally, the filter design framework is applied to the truck-trailer model to demonstrate its effectiveness.

A method of adaptively adjusting dissipation for the simulation of separated flow

Separate flow is a typical complex turbulent phenomenon. The full development of small-scaled structures is of great importance for accurate numerical simulation. However, these small-scaled structures can be easily damped by the inherent dissipation of numerical method. Therefore, based on the 5th-order dissipative compact scheme (DCS), we propose an adaptive dissipative compact scheme (ADCS), which can adjust the numerical dissipation with self-adaptive capability by incorporating a flow related adjusting parameter. Combining with the delay detached eddy simulation (DDES), the ADCS can reduce the influence of numerical dissipation in LES region to enhance the ability to discern small-scaled structures, and restore the normal dissipation level in the RANS region to keep numerical stability. In the process of numerical simulation, firstly, the approximate dispersion relation (ADR) is obtained, it shows that the ADCS method can effectively reduce the influence of dissipation in the high wave number region, without contaminating the dispersive performance, which is conducive to enhancing the resolution of turbulent structures. Secondly, the advection of vortical structure is simulated. Compared with DCS, the ADCS can reach the theoretical accuracy in an efficient way and acquire more advanced resolution of vortical structure even on a relatively coarse mesh scale, which proves that the ADCS reduces the negative influence of dissipation on vortical structure. The third case is the decay of isotropic turbulence. The energy spectral curves stay close to the reference before cut-off number, showing that more small-scaled structures can be distinguished by the ADCS method, and most of the vortical dominated regions are solved at a near-minimum level. The forth case is the plate channel turbulent flow. Both of DCS method and ADCS method give acceptable results. The ADCS method is performed with optimal dissipation in the near-wall region and reduces the dissipative level in the vortex dominated region, and it is also exhibited that the ADCS method can maintain the stability for flow with high gradient and avoid divergence. Finally, the sub-critical <i>Re</i> = 3900circular cylinder is simulated, and the fully separate flow is developed in the wake. The turbulent fluctuation near the wall is sensitive to the effect of numerical dissipation. The contour of flow field shows that the ADCS method obtains more small-scale structures. As for the pressure coefficient and mean velocity, the ADCS method shows an acceptable accuracy. Considering the Reynolds stress profile, which can be easily affected by the dissipation, the ADCS exhibits more accurate results than the traditional DCS method. Generally, the ADCS method can reduce the influence of dissipation and is beneficial to acquiring more accurate results in separate flow.

Asynchronous dissipative filtering for Markov jump discrete-time systems subject to randomly occurring distributed delays

This work investigates the issue of the dissipativity-based asynchronous filtering for Markov jump discrete-time systems subject to mixed time delays. Different from the existing results on this topic, a kind of distributed time delay is fully considered, which randomly occurs. The aim of this paper is to determine the parameters of the designed asynchronous filter. By utilizing the convex optimization technique and stochastic analysis theory, some new sufficient conditions with less conservatism are established, which ensure the resulting error system is stochastically stable with the extended dissipative performance level. The superiority and availability of the developed approach are finally verified by some comparison examples.

Robust H∞ Filtering of Nonhomogeneous Markovian Jump Delay Systems via N‐Step‐Ahead Lyapunov‐Krasovskii Functional Approach

In this paper, we study the robust H∞ filtering problem for a class of nonhomogeneous Markovian jump delay systems (NMJDSs) with an N‐step‐ahead Lyapunov‐Krasovskii functional (NALKF) approach. The N‐step‐ahead approach is utilized to reduce the conservatism of robust H∞ filtering. We aim to design filters such that, for all possible time‐varying transition probabilities and all admissible parameter uncertainties and time‐delays, the filtering error system is mean‐square stable with a smaller estimated error and a lower dissipative level. In terms of linear matrix inequalities, sufficient conditions for the solvability of the addressed problem are developed via a moving horizon method. An illustrative example is included to elucidate advantages of the developed results and the practical potential of NALKF approach for NMJDSs.

Finite-Time Nonfragile Dissipative Filter Design for Wireless Networked Systems with Sensor Failures

In this study, the problem of finite-time nonfragile dissipative-based filter design for wireless sensor networks that is described by discrete-time systems with time-varying delay is investigated. Specifically, to reduce the energy consumption of wireless sensor networks, it is assumed that the signal is not transmitted at each instant and the transmission process is stochastic. By constructing a suitable Lyapunov-Krasovskii functional and employing discrete-time Jensen’s inequality, a new set of sufficient conditions is established in terms of linear matrix inequalities such that the augmented filtering system is stochastically finite-time bounded with a prescribed dissipative performance level. Meanwhile, the desired dissipative-based filter gain matrices can be determined by solving an optimization problem. Finally, two numerical examples are provided to illustrate the effectiveness and the less conservatism of the proposed filter design technique.

Finite-time dissipative control for singular discrete-time Markovian jump systems with actuator saturation and partly unknown transition rates

Abstract In this work, the finite-time dissipative control problem is considered for singular discrete-time Markovian jumping systems with actuator saturation and partly unknown transition rates. By constructing a proper Lyapunov–Krasonski functional and the method of linear matrix inequalities (LMIs), sufficient conditions that ensure the systems singular stochastic finite-time stability and singular stochastic finite-time dissipative are obtained. Then, the state feedback controllers are designed, and in order to get the optimal values of the dissipative level, the results are extended to LMI convex optimization problems. Finally, numerical examples are given to illustrate the validity of the proposed methods.

Dissipative Landau-Zener level crossing subject to continuous measurement: Excitation despite decay

The Landau-Zener formula provides an analytical expression for the final excitation of a quantum system after passage of an avoided crossing of two energy levels. If the two levels correspond to a ground state, and to an excited state which is subject to radiative decay, the probability of exciting the system by adiabatic passage of the level crossing is reduced. In this article we use a stochastic master equation to study the level crossing dynamics when the system is subject to continuous probing of the emitted radiation. The measurement backaction on the system associated with the fluctuating homodyne detection record alters the level crossing dynamics, leading to significant excitation in spite of decay and imperfect transfer.

Tunable quantum phase transitions in a resonant level coupled to two dissipative baths

We study tunneling through a resonant level connected to two dissipative bosonic baths: one is the resistive environment of the source and drain leads, while the second comes from coupling to potential fluctuations on a resistive gate. We show that several quantum phase transitions (QPT) occur in such a model, transitions which emulate those found in interacting systems such as Luttinger liquids or Kondo systems. We first use bosonization to map this dissipative resonant level model to a resonant level in a Luttinger liquid, one with, curiously, two interaction parameters. Drawing on methods for analyzing Luttinger liquids at both weak and strong coupling, we obtain the phase diagram. For strong dissipation, a Berezinsky-Kosterlitz-Thouless QPT separates strong-coupling and weak-coupling (charge localized) phases. In the source-drain symmetric case, all relevant backscattering processes disappear at strong coupling, leading to perfect transmission at zero temperature. In fact, a QPT occurs as a function of the coupling asymmetry or energy of the resonant level: the two phases are (i) the system is cut into two disconnected pieces (zero transmission), or (ii) the system is a single connected piece with perfect transmission, except for a disconnected fractional degree of freedom. The latter arises from the competition between the two fermionic leads (source and drain), as in the two-channel Kondo effect.

Nonequilibrium quantum transport through a dissipative resonant level

The resonant-level model represents a paradigmatic quantum system which serves as a basis for many other quantum impurity models. We provide a comprehensive analysis of the nonequilibrium transport near a quantum phase transition in a spinless dissipative resonant-level model, extending earlier work [Phys. Rev. Lett 102, 216803 (2009)]. A detailed derivation of a rigorous mapping of our system onto an effective Kondo model is presented. A controlled energy-dependent renormalization-group approach is applied to compute the nonequilibrium current in the presence of a finite bias voltage $V$. In the linear-response regime $V\ensuremath{\rightarrow}0$, the system exhibits as a function of the dissipative strength a localized-delocalized quantum transition of the Kosterlitz-Thouless (KT) type. We address fundamental issues of the nonequilibrium transport near the quantum phase transition: Does the bias voltage play the same role as temperature to smear out the transition? What is the scaling of the nonequilibrium conductance near the transition? At finite temperatures, we show that the conductance follows the equilibrium scaling for $V<T$, while it obeys a distinct nonequilibrium profile for $V>T$. We furthermore provide different signatures of the transition in the finite-frequency current noise and ac conductance via a recently developed functional renormalization group (FRG) approach. The generalization of our analysis to nonequilibrium transport through a resonant level coupled to two chiral Luttinger liquid leads, generated by fractional quantum Hall edge states, is discussed. Our work on the dissipative resonant level has direct relevance to experiments on a quantum dot coupled to a resistive environment, such as H. Mebrahtu et al., [Nature (London) 488, 61 (2012)].

Analogue of the Quantum Hanle Effect and Polarization Conversion in Non-Hermitian Plasmonic Metamaterials

The Hanle effect, one of the first manifestations of quantum theory introducing the concept of coherent superposition between pure states, plays a key role in numerous aspects of science varying from applicative spectroscopy to fundamental astrophysical investigations. Optical analogues of quantum effects help to achieve deeper understanding of quantum phenomena and, in turn, to develop cross-disciplinary approaches to realizations of new applications in photonics. Here we show that metallic nanostructures can be designed to exhibit a plasmonic analogue of the quantum Hanle effect and the associated polarization rotation. In the original Hanle effect, time-reversal symmetry is broken by a static magnetic field. We achieve this by introducing dissipative level crossing of localized surface plasmons due to nonuniform losses, designed using a non-Hermitian formulation of quantum mechanics. Such artificial plasmonic "atoms" have been shown to exhibit strong circular birefringence and circular dichroism which depends on the value of loss or gain in the metal-dielectric nanostructure.

Nonequilibrium Transport at a Dissipative Quantum Phase Transition

We investigate the nonequilibrium transport near a quantum phase transition in a generic and relatively simple model, the dissipative resonant level model, that has many applications for nanosystems. We formulate a rigorous mapping and apply a controlled frequency-dependent renormalization group approach to compute the nonequilibrium current in the presence of a finite bias voltage V and a finite temperature T. For V-->0, we find that the conductance has its well-known equilibrium form, while it displays a distinct nonequilibrium profile at finite voltage.

Kelvin-Helmholtz driven propeller in AE Aquarii: A unified model for thermal and non-thermal flares

In this paper, an attempt is made to integrate the propeller ejection of material by the fast rotating white dwarf in AE Aquarii with the highly transient thermal and non-thermal emission in a single unifying model. It has been shown that the violent interaction between the fast rotating magnetosphere and a clumpy fragmented stream, in AE Aquarii specifically, may result in the growth of unstable modes of the Kelvin‐Helmholtz instability and associated turbulence over length scales comparable to the stream radius on time-scales τ K−H ∼ t dyn (∼ 600 s). For all conversion efficiencies of magnetohydrodynamic (MHD) power to mechanical energy � 0.1, these instabilities result in the effective azimuthal acceleration of the gas parcels to the escape velocity over time-scales t acc 1000 s (∼t dyn). Further, it has been shown that the turbulence in the flow will cascade down to the dissipative level over time-scales τ cas ∼ 3h . If released through dissipative shocks, this reservoir can drive a luminosity of L ∼ 10 33 erg s −1 , which can significantly contribute to the total emission when blobs collide in the exit stream, resulting in shock heating and associated flares. During the propeller process, particles can also be accelerated to high energies, which may be the driving mechanism behind the non-thermal radio to mid-infrared emission. The confluence of these ejected magnetized clouds may result in radio remnant surrounding AE Aquarii, which is optically thin between frequencies ν 100 MHz‐1 GHz.

Fractal modelling of turbulent mixing

The aim of this work is to propose a new model for turbulent flows, called the fractal model (FM), applicable both in a Reynolds averaged Navier–Stokes (RANS) and a large-eddy simulation (LES) formulation, with the ultimate goal of applying it to simulate turbulent combustion irrelevant of its mode (premixed or non-premixed). The model is able to turn itself off in the laminar zones of the flow, and in particular near walls. It is based on the fractal theory. It describes the physics of the smaller spatial scales and therefore represents a small-scales model. FM describes the physics of the small scales of turbulence based on the phenomenological concept of vortex cascade and on the self-similar behaviour of turbulence in the inertial range. Such a model is used in each cell of a numerical calculation. A characteristic length Δ is associated to each cell, and the local energy u 3 Δ/Δ is distributed over a certain number of eddies, which depends on the local Reynolds number Re Δ. Each vortex of the cascade generates N c vortices; the recursive process of vortex generation terminates at the dissipative scale level, i.e. when the eddy Reynolds number is equal to one. FM is also able to estimate the volume fraction occupied by the dissipative fine structures of turbulence; this quantity is critical in reactive turbulent flows. The physics of small scales is summarized by a turbulent ‘viscosity’ μt, to be added to the molecular one. μt is zero where the flow is laminar and, in particular, goes to zero at solid walls. Assuming μt to be isotropic, FM is applicable in a RANS formulation (IFM, isotropic fractal model). The model can be extended to the anisotropic case (AFM, anisotropic fractal model) and therefore used to close the transport equations in an LES approach. In the present paper, the model (IFM) is used in a RANS approach and is validated through a test case studied experimentally by Johnson and Bennett, and numerically (with LES) by Akselvoll and Moin. The results obtained are in good agreement both with the experimental and the numerical ones. Other tests are being performed.