Maximal entanglement from photon-added nonlinear coherent states via unitary beam splitters

In this paper, we construct photon-added f-deformed coherent states （PAf-DCSs） for nonlinear bosonic fields by discussing Klauder＇s minimal set of conditions required to obtain coherent states. Using this set of nonlinear states, we propose a very useful scheme for generating the maximal amount of entanglement via unitary beam splitters for different strength regimes of the input field α, deformation q and excitation number m. Therefore, the possibility to create highly entangled states and to control the entanglement is proposed. Moreover, the condition for a maximal and separable output beam state is obtained. Finally, we examine the statistical properties of the PAf-DCSs through the Mandel parameter and exploit a connection between this quantity and the behavior variation of the output state entanglement. Our result may open new perspectives in different tasks of quantum information processing.

A New Kind of k-Quantum Nonlinear Coherent States： Their Generation and PhysicalMeaning

A new kind of k-quantum nonlinear coherent states,i.e.,the k eigenstates of the k-th power~k (k≥3) of the generalized annihilation operator=1/f() of f-oscillators,are obtained and their properties are discussed.The completeness of the k states is investigated.An alternative method to construct them is proposed.It is shown that these states may form a complete Hilbert space,and all of them can be generated by a linear superposition of k Roy-type nonlinear coherent states.Physically,they can be generated by a linear superposition of the time-dependent Roy-type nonlinear coherent states at different instants.

Algebraic and group treatments to nonlinear displaced number states and their nonclassicality features:A new approach

Recently, nonlinear displaced number states （NDNSs） have been manually introduced, in which the deformation function f（n） has been artificially added to the previously well-known displaced number states （DNSs）. Indeed, just a simple comparison has been performed between the standard coherent state and nonlinear coherent state for the formation of NDNSs. In the present paper, after expressing enough physical motivation of our procedure, four distinct classes of NDNSs are presented by applying algebraic and group treatments. To achieve this purpose, by considering the DNSs and recalling the nonlinear coherent states formalism, the NDNSs are logically defined through an algebraic consideration. In addition, by using a particular class of Gilmore-Perelomov-type of SU（1,1） and a class of SU（2） coherent states, the NDNSs are introduced via group-theoretical approach. Then, in order to examine the nonclassical behavior of these states, sub-Poissonian statistics by evaluating Mandel parameter and Wigner quasi-probability distribution function associated with the obtained NDNSs are discussed, in detail.

Quasiprobability distributions of new kinds of even and odd nonlinear coherent states

Using a numerical computational method, quasiprobability distributions of new kinds of even and odd nonlinear coherent states （EONLCS） are investigated. The results show that the distributions of the new even nonlinear coherent states （NLCS） are distinct from those of the new odd NLCS and imply that the new EONLCS always exhibit some different nonclassical effects. Finally, with the aid of newly introduced intermediate coordinate-momentum representation in quantum optics, the tomograms of the new EONLCS are calculated. This is a new way of obtaining the tomogram function.

Phase Properties of Nonlinear Coherent States

Using the Pegg-Barnett formalism we study the phase probability distributions and the squeezing effects of measured phase operators in the nonlinear coherent states introduced by R.L. de Matos Filho and W. Vogel to describe the center-of mass motion of a trapped ion and the q-coherent states. Moreover, we have obtained the completeness relation of nonlinear coherent states and proved that the q-Fock state \n>(q) introduced in many papers is, in fact, the usual Fock state.

The nonlinear squeezed one-photon states and their nonclassical properties

By virtue of the technique of integration within an ordered product （IWOP） of operators and the properties of the inverses of annihilation and creation operators of f-oscillator, this paper obtains two new types of squeezed operators and f-analogues of squeezed one-photon states, which are quite different from ones constructed by Song and Fan （Phys. Lett. A 294 （2002） 66）. Subsequently, some nonclassical properties of the states are investigated in detail.

Finite-dimensional even and odd nonlinear pair coherent states and their some nonclassical properties

In this paper a new class of finite-dimensional even and odd nonlinear pair coherent states （EONLPCSs）, which can be realized via operating the superposed evolution operators D±（τ） on the state ｜q, 0）, is constructed, then their orthonormalized property, completeness relations and some nonclassical properties are discussed. It is shown that the finite-dimensional EONLPCSs possess normalization and completeness relations. Moreover, the finite-dimensional EONLPCSs exhibit remarkably different sub-Poissonian distributions and phase probability distributions for different values of parameters q, η and ξ.

Statistical Properties of the nonlinear SU（1,1） Coherent States

Using non-Hermitian realizations of SU(1,1) Lie algebra in terms of an f-oscillator, we generalize the notion of nonlinear coherent states to the single-mode and two-mode nonlinear SU(1,1) coherent states. Taking the nonlinearity function , their statistical properties are studied.

Path-Following Control With Obstacle Avoidance of Autonomous Surface Vehicles Subject to Actuator Faults

This paper investigates the path-following control problem with obstacle avoidance of autonomous surface vehicles in the presence of actuator faults,uncertainty and external disturbances.Autonomous surface vehicles inevitably suffer from actuator faults in complex sea environments,which may cause existing obstacle avoidance strategies to fail.To reduce the influence of actuator faults,an improved artificial potential function is constructed by introducing the lower bound of actuator efficiency factors.The nonlinear state observer,which only depends on measurable position information of the autonomous surface vehicle,is used to address uncertainties and external disturbances.By using a backstepping technique and adaptive mechanism,a path-following control strategy with obstacle avoidance and fault tolerance is designed which can ensure that the tracking errors converge to a small neighborhood of zero.Compared with existing results,the proposed control strategy has the capability of obstacle avoidance and fault tolerance simultaneously.Finally,the comparison results through simulations are given to verify the effectiveness of the proposed method.

Active Fault Tolerant Control of a Class of Nonlinear Time-Delay Processes

Based on a nonlinear state predictor (NSP) and a strong tracking filter (STF), a sensor fault tolerant generic model control (FTGMC) approach for a class of nonlinear time-delay processes is proposed. First, the NSP is introduced, and it is used to extend the conventional generic model control (GMC) to nonlinear processes with large input time-delay. Then the STF is adopted to estimate process states and sensor bias, the estimated sensor bias is used to drive a fault detection logic. When a sensor fault is detected, the estimated process states by the STF will be used to construct the process output to form a 'soft sensor', which is then used by the NSP (instead of the real outputs) to provide state predictors. These procedures constitute an active fault tolerant control scheme. Finally, simulation results of a three-tank-system demonstrate the effectiveness of the proposed approach.

Nonlinear health evaluation for lithium-ion battery within full-lifespan

Lithium-ion batteries(LIBs), as the first choice for green batteries, have been widely used in energy storage, electric vehicles, 3C devices, and other related fields, and will have greater application prospects in the future. However, one of the obstacles hindering the future development of battery technology is how to accurately evaluate and monitor battery health, which affects the entire lifespan of battery use. It is not enough to assess battery health comprehensively through the state of health(SoH) alone, especially when nonlinear aging occurs in onboard applications. Here, for the first time, we propose a brand-new health evaluation indicator—state of nonlinear aging(SoNA) to explain the nonlinear aging phenomenon that occurs during the battery use, and also design a knee-point identification method and two SoNA quantitative methods. We apply our health evaluation indicator to build a complete LIB full-lifespan grading evaluation system and a ground-to-cloud service framework, which integrates multi-scenario data collection, multi-dimensional data-based grading evaluation, and cloud management functions. Our works fill the gap in the LIBs’ health evaluation of nonlinear aging, which is of great significance for the health and safety evaluation of LIBs in the field of echelon utilization such as vehicles and energy storage. In addition, this comprehensive evaluation system and service framework are expected to be extended to other battery material systems other than LIBs, yet guiding the design of new energy ecosystem.

ASYMPTOTIC SOLUTION OF A SINGULARLY PERTURBED NONLINEAR STATE REGULATOR PROBLEM

This paper, will seek the optimal control and corresponding trajectories of the singularly perturbed nonlinear state regulator problem. Under appropriate hypotheses. it will be possible to complete an asymptotic solution which is uniformly valid when e→0.

Nonlinear state estimation for fermentation process using cubature Kalman filter to incorporate delayed measurements

State estimation of biological process variables directly influences the performance of on-line monitoring and op- timal control for fermentation process. A novel nonlinear state estimation method for fermentation process is proposed using cubature Kalman filter （CKF） to incorporate delayed measurements. The square-root version of CI（F （SCKF） algorithm is given and the system with delayed measurements is described. On this basis, the sample-state augmentation method for the SCKF algorithm is provided and the implementation of the proposed algorithm is constructed. Then a nonlinear state space model for fermentation process is established and the SCKF algorithm incorporating delayed measurements based on fermentation process model is presented to implement the nonlinear state estimation. Finally, the proposed nonlinear state estimation methodology is applied to the state estimation for penicillin and industrial yeast fermentation processes. The simulation results show that the on-fine state estimation for fermentation process can be achieved by the proposed method with higher esti- mation accuracy and better stability.

The P—representation on Nonlinear Coherent State Basis

Using the technique of integration within an ordered product of nonlinear Bose operators and by composing the nonlinear coherent state's over-completeness relation, we construct the corresponding P-representation theory. The generalized P-representation for some nonlinear Bose operators can be established.

Nonlinear Quantum Optical Springs and Their Nonclassical Properties

The original idea of quantum optical spring arises from the requirement of quantization of the frequency of oscillations in the Hamiltonian of harmonic oscillator. This purpose is achieved by considering a spring whose constant （and so its frequency） depends on the quantum states ofanother system. Recently, it is realized that by the assumption of frequency modulation of ω to ω √1＋ μα＋α the mentioned idea can be established. In the present paper, we generalize the approach of quantum optical spring with particular attention to the dependence or trequency to the intensity of radiation field that naturally observes in the nonlinear coherent states, from which we arrive at a physical system has been called by us as nonlinear quantum optical spring. Then, after the introduction of the generalized tlamiltonian of nonlinear quantum optical spring and it＇s solution, we will investigate the nonclassical properties of the obtained states. Specially, typical collapse and revival in the distribution functions and squeezing parameters, as particular quantum features, will be revealed.

Nonlinear Tripartite Entangled State Representation and Related Generalized Wigner Function

We construct the nonlinear tripartite entangled state representation and the related generalized Wigner operator. Then we discussed the Wigner functions of the nonlinear tripartite entangled state and the three-mode nonlinear squeezed vacuum state, and obtained the classical Weyl corresponding function of the three-mode nonlinear squeezed state.

Bose Description of Pauli Spin Operators and Related Coherent States

Using both the fermionic-kike and the bosonic-like properties of the Paulispin operators σ_+, σ_-, and σ_z we discuss the derivation of Bose description of the Pauli spinoperators originally proposed by Shigefumi Naka, and deduce another new bosonic representation ofPauli operators. The related coherent states, which are nonlinear coherent state and coherent spinstates for two spins, respectively, are constructed.

Wave functions of a new kind of nonlinear single-mode squeezed state

We explore the theoretical possibility of extending the usual squeezed state to those produced by nonlinear singlemode squeezing operators. We derive the wave functions of exp[-（ig/2）（（1-X2）1/2P ＋ P（1-X2）1/2）]｜0 in the coordinate representation. A new operator＇s disentangling formula is derived as a by-product.

Tripartite Nonlinear Entangled State Representations in Quantum Mechanics

Based on the technique of integral within an ordered product of nonlinear bosonic operators we construct a kind of tripartite nonlinear entangled states, which can make up a complete set. As its application, we also derive nonlinear 3-mode charge-related entangled state. The essential point for constructing these states lies in choosing the appropriate charge operator.

New Tripartite Nonlinear Entangled State Representation in Quantum Mechanics

Based on the technique of integral within an ordered product of nonlinear bosonic operators,we constructa new kind of tripartite nonlinear entangled state |α,γ〉_λ in 3-mode Fock space,which can make up a complete set.Wealso simply discuss its properties and application.