Weak Coupling Case Research Articles

Frozen Quantum Coherence for a Central Two-Qubit System in a Spin-Chain Environment**Supported by the National Natural Science Foundation of China under Grant No 11404246, and the Shandong Provincial Natural Science Foundation under Grant No ZR2017MF040.

We investigate the dynamics of coherence for a central two-qubit system coupled to an XY spin chain with the Dzyaloshinsky–Moriya interaction. It is found that a sudden transition of coherence exists near the critical point in the weak-coupling case, and an oscillatory envelope appears in the strong-coupling case. In both cases the freezing phenomenon of coherence can be found.

On finite-time consensus objectives in time-varying interconnected discrete linear dynamic systems under internal and external delays

This article formulates the properties of achievable consensus of linear interconnected discrete systems with multiple internal and external point delays. The formulation is stated in an algebraic generic context as the ability of achievement of (a non-necessarily zero) finite-time common error between the various subsystems. The consensus signals are generically defined so that they can be, in general, distinct of the output or state components. However, the consensus signals of all the interconnected subsystems have the same dimension for coherency reasons. A particular attention is paid to the case of weak interconnection couplings in both the open-loop case and the closed-loop one under, in general, linear output feedback. Some further extensions are given related to consensus over intervals and related to consensus of positive interconnected systems.

Effect of Electron–Phonon Interaction on the Conductivity and Work Function of Epitaxial Graphene

In the context of the cluster model of epitaxial graphene, the condition for a stepwise change in the charge of carbon atoms under the action of graphene–substrate electron–phonon interaction and an external electric field is derived. Such charge transfer brings about corresponding steps of the static conductivity and work function of epitaxial graphene. Numerical estimates for the case of weak coupling of quasi-free graphene with metal and semiconductor substrates are given.

Anomalous zero-temperature magnetopolaronic blockade of resonant electron tunneling in Majorana-resonant-level single-electron transistor

The magnetopolaronic generalization of a Majorana-resonant-level (MRL) model is considered for a single-level vibrating quantum dot coupled to two half-infinite $g=1/2$ Tomonaga-Luttinger liquid (TLL) leads. A qualitatively new non-trivial formula for the effective transmission coefficient and differential conductance for resonant magnetopolaron-assisted tunneling is obtained under the assumption about a fermion-boson factorization of corresponding averages. This approach is valid for the case of weak magnetopolaronic coupling in a system. Surprisingly, it is found that despite a supposed weakness of interaction between fermionic and bosonic subsystems in that case, a strongly correlated electron transport in the system reveals features of strong (and, hence, anomalous) magnetopolaronic blockade at zero temperature if the energy of a vibrational quantum is the smallest (but nonzero) energy parameter in the system. Such an effect should be referred to as magnetic phase-coherent magnetopolaron-assisted resonant tunneling of Andreev type, that originates from a special, Majorana-like, symmetry of magnetopolaron-coupled tunnel Hamiltonian. The effect predicted in this paper can be used as an experimental fingerprint of Majorana-resonant level situation in single-electron transistors as well as for detection of ultra-slow zero-point oscillations of suspended carbon nanotubes in the Majorana-resonant level regime of electron tunneling through corresponding single-electron transistors.

Topological invariant for two-dimensional open systems

We study the topology of two-dimensional open systems in terms of the Green's function. The Ishikawa-Matsuyama formula for the integer topological invariant is applied in open systems, which indicates the number difference of gapless edge bands arising from the poles and zeros of the Green's function. Meanwhile, we define another topological invariant via the single-particle density matrix, which works for general gapped systems and is equivalent to the former for the case of weak coupling to an environment. We also discuss two applications. For time-reversal-invariant insulators, the ${Z}_{2}$ index can be expressed by the invariant of each spin subsystem. As a second application, we consider the proximity effect when an ordinary insulator is coupled to a topological insulator.

Cavity-QED interactions of two correlated atoms

We consider the resonant van der Waals (vdW) interaction between two correlated identical two-level atoms (at least one of which being excited) within the framework of macroscopic cavity quantum electrodynamics in linear, dispersing and absorbing media. The interaction of both atoms with the body-assisted electromagnetic field of the cavity is assumed to be strong. Our time-independent evaluation is based on an extended Jaynes–Cummings model. For a system prepared in a superposition of its dressed states, we derive the general form of the vdW forces, using a Lorentzian single-mode approximation. We demonstrate the applicability of this approach by considering the case of a planar cavity and showing the position dependence of Rabi oscillations. We also show that in the limiting case of weak coupling, our results reproduce the perturbative ones for the case where the field is initially in vacuum state while the atomic state is in a superposition of two correlated states sharing one excitation.

Ground state of spin-orbit coupled rotating two-component Bose-Einstein condensate in gradient magnetic field

Two-component Bose-Einstein condensate offers an ideal platform for investigating many intriguing topological defects due to the interplay between intraspecies and interspecies interactions. The recent realization of spin-orbit coupling in two-component Bose-Einstein condensate, owing to coupling between the spin and the centre-of-mass motion of the atom, provides possibly new opportunities to search for novel quantum states. In particular, the gradient magnetic field in the Bose-Einstein condensate has brought a new way to create topologically nontrivial structures including Dirac monopoles and quantum knots. Previous studies of the gradient magnetic field effect in the Bose-Einstein condensate mainly focused on the three-component case. However, it remains unclear how the gradient magnetic field affects the ground state configuration in the rotating two-component Bose-Einstein condensate with spin-orbit coupling. In this work, by using quasi two-dimensional Gross-Pitaevskii equations, we study the ground state structure of a rotating two-component Bose-Einstein condensate with spin-orbit coupling and gradient magnetic field. We concentrate on the effects of the spin-orbit coupling and the gradient magnetic field on the ground state. The numerical results show that increasing the strength of the spin-orbit coupling can induce a phase transition from skyrmion lattice to skyrmion chain in the presence of the gradient magnetic field. Unlike the study of skyrmion in rotating two-component Bose-Einstein condensate with only spin-orbit coupling, the skyrmion chain can occur under the isotropic spin-orbit coupling when the gradient magnetic field is considered. It is worth noting that the skyrmion chain here is arrayed along the diagonal direction. Next we examine the effect of the gradient magnetic field on spin-orbit coupled two-component Bose-Einstein condensate. For the case of weak spin-orbit coupling and the slow rotation, a phase transition from a single plane-wave to half-skyrmion is found through increasing magnetic field gradient strength. For the case of strong spin-orbit coupling and the fast rotation, the nature of the ground state is shown to support the formation of a hidden vortex as the gradient magnetic field is enhanced. These hidden vortices have no visible cores in density distributions but have phase singularities in phase distributions, which are arrayed along the diagonal direction. This result confirms a new method of creating the hidden vortices in the two-component Bose-Einstein condensate. These topological structures can be detected by using the time-of-flight absorption imaging technique. Our results illustrate that the gradient magnetic field not only provides an opportunity to explore the exotic topological structures in spin-orbit coupled spinor Bose-Einstein condensate, but also is crucial for realizing the phase transitions among different ground states. This work paves the way for the future exploring of topological defect and the corresponding dynamical stability in quantum systems subjected to a gradient magnetic field.

Влияние электрон-фононного взаимодействия на проводимость и работу выхода эпитаксиального графена

AbstractIn the context of the cluster model of epitaxial graphene, the condition for a stepwise change in the charge of carbon atoms under the action of graphene–substrate electron–phonon interaction and an external electric field is derived. Such charge transfer brings about corresponding steps of the static conductivity and work function of epitaxial graphene. Numerical estimates for the case of weak coupling of quasi-free graphene with metal and semiconductor substrates are given.

Understanding the Different Exciton–Plasmon Coupling Regimes in Two-Dimensional Semiconductors Coupled with Plasmonic Lattices: A Combined Experimental and Unified Equation of Motion Approach

We study exciton–plasmon coupling in two-dimensional semiconductors coupled with Ag plasmonic lattices via angle-resolved reflectance spectroscopy and by solving the equations of motion (EOM) in a coupled oscillator model accounting for all the resonances of the system. Five resonances are considered in the EOM model: semiconductor A and B excitons, localized surface plasmon resonances (LSPRs) of plasmonic nanostructures, and the lattice diffraction modes of the plasmonic array. We investigated the exciton–plasmon coupling in different 2D semiconductors and plasmonic lattice geometries, including monolayer MoS2 and WS2 coupled with Ag nanodisk and bowtie arrays and examined the dispersion and line shape evolution in the coupled systems via the EOM model with different exciton–plasmon coupling parameters. The EOM approach provides a unified description of the exciton–plasmon interaction in the weak, intermediate, and strong coupling cases with correctly explaining the dispersion and lineshapes of the complex system. This study provides a much deeper understanding of light–matter interactions in multilevel systems in general and will be useful to instruct the design of novel two-dimensional exciton–plasmonic devices for a variety of optoelectronic applications with precisely tailored responses.

The quantum Zeno and anti-Zeno effects with strong system-environment coupling

To date, studies of the quantum Zeno and anti-Zeno effects focus on quantum systems that are weakly interacting with their environment. In this paper, we investigate what happens to a quantum system under the action of repeated measurements if the quantum system is strongly interacting with its environment. We consider as the quantum system a single two-level system coupled strongly to a collection of harmonic oscillators. A so-called polaron transformation is then used to make the problem in the strong system-environment coupling regime tractable. We find that the strong coupling case exhibits quantitative and qualitative differences as compared with the weak coupling case. In particular, the effective decay rate does not depend linearly on the spectral density of the environment. This then means that, in the strong coupling regime that we investigate, increasing the system-environment coupling strength can actually decrease the effective decay rate. We also consider a collection of two-level atoms coupled strongly with a common environment. In this case, we find that there are further differences between the weak and strong coupling cases since the two-level atoms can now indirectly interact with one another due to the common environment.

A new symmetrical quasi-classical model for electronically non-adiabatic processes: Application to the case of weak non-adiabatic coupling

Previous work has shown how a symmetrical quasi-classical (SQC) windowing procedure can be used to quantize the initial and final electronic degrees of freedom in the Meyer-Miller (MM) classical vibronic (i.e, nuclear + electronic) Hamiltonian, and that the approach provides a very good description of electronically non-adiabatic processes within a standard classical molecular dynamics framework for a number of benchmark problems. This paper explores application of the SQC/MM approach to the case of very weak non-adiabatic coupling between the electronic states, showing (as anticipated) how the standard SQC/MM approach used to date fails in this limit, and then devises a new SQC windowing scheme to deal with it. Application of this new SQC model to a variety of realistic benchmark systems shows that the new model not only treats the weak coupling case extremely well, but it is also seen to describe the "normal" regime (of electronic transition probabilities ≳ 0.1) even more accurately than the previous "standard" model.

Synthetic dimensions in the strong-coupling limit: Supersolids and pair superfluids

We study the many-body phases of bosonic atoms with $N$ internal states confined to a 1D optical lattice under the influence of a synthetic magnetic field and strong repulsive interactions. The $N$ internal states of the atoms are coupled via Raman transitions creating the synthetic magnetic field in the space of internal spin states corresponding to recent experimental realisations. We focus on the case of strong $\mbox{SU}(N)$ invariant local density-density interactions in which each site of the 1D lattice is at most singly occupied, and strong Raman coupling, in distinction to previous work which has focused on the weak Raman coupling case. This allows us to keep only a single state per site and derive a low energy effective spin $1/2$ model. The effective model contains first-order nearest neighbour tunnelling terms, and second-order nearest neighbour interactions and correlated next-nearest neighbour tunnelling terms. By adjusting the flux $\phi$ one can tune the relative importance of first-order and second-order terms in the effective Hamiltonian. In particular, first-order terms can be set to zero, realising a novel model with dominant second-order terms. We show that the resulting competition between density-dependent tunnelling and repulsive density-density interaction leads to an interesting phase diagram including a phase with long-ranged pair-superfluid correlations. The method can be straightforwardly extended to higher dimensions and lattices of arbitrary geometry including geometrically frustrated lattices where the interplay of frustration, interactions and kinetic terms is expected to lead to even richer physics.

Quantum states of dark solitons in the 1D Bose gas

We present a series of quantum states that are characterized by dark solitons of the nonlinear Schrödinger equation (i.e. the Gross–Pitaevskii equation) for the one-dimensional Bose gas interacting through the repulsive delta-function potentials. The classical solutions satisfy the periodic boundary conditions and we simply call them classical dark solitons. Through exact solutions we show corresponding aspects between the states and the solitons in the weak coupling case: the quantum and classical density profiles completely overlap with each other not only at an initial time but also at later times over a long period of time, and they move together with the same speed in time; the matrix element of the bosonic field operator between the quantum states has exactly the same profiles of the square amplitude and the phase as the classical complex scalar field of a classical dark soliton not only at the initial time but also at later times, and the corresponding profiles move together for a long period of time. We suggest that the corresponding properties hold rigorously in the weak coupling limit. Furthermore, we argue that the lifetime of the dark soliton-like density profile in the quantum state becomes infinitely long as the coupling constant approaches zero, by comparing it with the quantum speed limit time. Thus, we call the quantum states quantum dark soliton states.

Analysis of Mutually Injection-Locked Oscillators for Differential Resonant Sensing

The potential benefits of oscillator synchronization are receiving increased interest in the resonant MEMS community, for clocking or sensing applications. In this paper, we explore the possibilities of differential resonant sensing applications based on the phase-difference between two injection-locked resonators, strongly coupled through an electronic mixer. A general model of such oscillators is established, and their static and dynamic performance is determined. The design space offered by the mixing scheme is then investigated at the system-level, in the weak and strong coupling cases. The practical implementation of the corresponding architectures in the context of a MEMS application is discussed. The theoretical results are supported by simulations and experimental data.

A variational formulation for vibro-acoustic analysis of a panel backed by an irregularly-bounded cavity

A weak form variational based method is developed to study the vibro-acoustic responses of coupled structural-acoustic system consisting of an irregular acoustic cavity with general wall impedance and a flexible panel subjected to arbitrary edge-supporting conditions. The structural and acoustical models of the coupled system are formulated on the basis of a modified variational method combined with multi-segment partitioning strategy. Meanwhile, the continuity constraints on the sub-segment interfaces are further incorporated into the system stiffness matrix by means of least-squares weighted residual method. Orthogonal polynomials, such as Chebyshev polynomials of the first kind, are employed as the wholly admissible unknown displacement and sound pressure field variables functions for separate components without meshing, and hence mapping the irregular physical domain into a square spectral domain is necessary. The effects of weighted parameter together with the number of truncated polynomial terms and divided partitions on the accuracy of present theoretical solutions are investigated. It is observed that applying this methodology, accurate and efficient predictions can be obtained for various types of coupled panel-cavity problems; and in weak or strong coupling cases for a panel surrounded by a light or heavy fluid, the inherent principle of velocity continuity on the panel-cavity contacting interface can all be handled satisfactorily. Key parametric studies concerning the influences of the geometrical properties as well as impedance boundary are performed. Finally, by performing the vibro-acoustic analyses of 3D car-like coupled miniature, we demonstrate that the present method seems to be an excellent way to obtain accurate mid-frequency solution with an acceptable CPU time.

Decoherence of a quantum system coupled to an XY spin chain: Role of the initial state of the spin chain

We study the decoherence of a coupled quantum system consisting of a central spin and its correlated environment described by a general XY spin-chain model. We make it clear that the evolution of the coherence factor sensitively depends on the initial state of the environment spin-chain. Specially, the dynamical evolution of the coherence factor of the central spin is numerically and analytically investigated in both weak and strong coupling cases with initial state set as the ground state of the initial Hamiltonian HE(λi) at time t=0 which may be different from the evolving Hamiltonian HE(λe) for time t> 0, as well as set as the thermal equilibrium state. In both weak and strong coupling cases, we show that the evolution of the coherence factor with initial state being the ground state of the initial Hamiltonian can be approximated by a Gaussian. Particularly, in the strong coupling regime the coherence factor oscillates rapidly under a Gaussian envelope. The width of the Gaussian decay (envelope) is presented in detail.

Ground-state phase diagram of the quantum Rabi model

The Rabi model plays a fundamental role in understanding light-matter interaction. It reduces to the Jaynes-Cummings model via the rotating-wave approximation, which is applicable only to the cases of near resonance and weak coupling. However, recent experimental breakthroughs in upgrading light-matter coupling order require understanding the physics of the full quantum Rabi model (QRM). Despite the fact that its integrability and energy spectra have been exactly obtained, the challenge to formulate an exact wavefunction in a general case still hinders physical exploration of the QRM. Here we unveil a ground-state phase diagram of the QRM, consisting of a quadpolaron and a bipolaron as well as their changeover in the weak-, strong- and intermediate-coupling regimes, respectively. An unexpected overweighted antipolaron is revealed in the quadpolaron state, and a hidden scaling behavior relevant to symmetry breaking is found in the bipolaron state. An experimentally accessible parameter is proposed to test these states, which might provide novel insights into the nature of the light-matter interaction for all regimes of the coupling strengths.

Coupling analysis of linear vibration energy harvesting systems

This paper has disclosed the relationship of vibration energy harvester performance with dimensionless force factor. Numerical ranges of the dimensionless force factor have been defined for cases of weak, moderate and strong coupling. The relationships of coupling loss factor, dimensionless force factor, critical coupling strength, coupling quotient, electro-mechanical coupling factor, damping loss factor and modal densities have been established in linear vibration energy harvester systems. The new contribution of this paper is to determine a frequency range where the vibration energy harvesting systems are in a weak coupling and the statistical energy analysis is applicable.

Protecting remote atomic entanglement against spontaneous emission by separated photonic pulses

We study the entanglement dynamics between two spatially separated atoms trapped in two separate optical cavities. Based on cavity-assisted interactions between the atoms and separated photonic pulses, we propose a scheme for the implemention of a controlled-phase-flip gate (CPF gate) between each of the atoms and the photonic pulse to protect the remote atomic quantum entanglement against the decaying caused by spontaneous emission. What we need to do is to shoot the horizontally polarized photons onto the cavity mirror successively, plus a train of Hadamard operations on the atoms, and no measurement is needed here. It is shown that the quantum entanglement of the two remote atoms can be protected effectively in this way. We also extend our scheme to the case of weak coupling and low Q cavity cases. The simplicity of the current scheme may warrant its experimental realization.

Recurrence Time in the Quantum Dynamics of the 1D Bose Gas

Recurrence time is evaluated for some initial quantum states in the one-dimensional Bose gas with repulsive short-range interactions. In the relatively strong and weak coupling cases some different types of initial states show almost complete recurrence and the estimates of recurrence time are proportional to some powers of the system size at least in some range of the system size. They are much longer than in the case of free particles such as 100 times. In the free-bosonic and free-fermionic regimes we evaluate the recurrence time rigorously, which is proportional to the square of the system size. The estimate of recurrence time is given by the order of ten milliseconds in the corresponding experimental systems of cold atoms trapped in one dimension of ten micrometers in length. It is much shorter than the estimate in a generic quantum many-body system, which may be as long as the age of the universe.