Resonant interactions among two-dimensional nonlinear localized waves and lump molecules for the(2+1)-dimensional elliptic Toda equation

The(2+1)-dimensional elliptic Toda equation is a high-dimensional generalization of the Toda lattice and a semidiscrete Kadomtsev–Petviashvili I equation.This paper focuses on investigating the resonant interactions between two breathers,a breather/lump and line solitons as well as lump molecules for the(2+1)-dimensional elliptic Toda equation.Based on the N-soliton solution,we obtain the hybrid solutions consisting of line solitons,breathers and lumps.Through the asymptotic analysis of these hybrid solutions,we derive the phase shifts of the breather,lump and line solitons before and after the interaction between a breather/lump and line solitons.By making the phase shifts infinite,we obtain the resonant solution of two breathers and the resonant solutions of a breather/lump and line solitons.Through the asymptotic analysis of these resonant solutions,we demonstrate that the resonant interactions exhibit the fusion,fission,time-localized breather and rogue lump phenomena.Utilizing the velocity resonance method,we obtain lump–soliton,lump–breather,lump–soliton–breather and lump–breather–breather molecules.The above works have not been reported in the(2+1)-dimensional discrete nonlinear wave equations.

Nonclassical properties in the resonant interaction of a three level ∧-type atom with two-mode field in coherent state

In this paper, we study the nonclassical properties of the electromagnetic field resulting from the interaction of a three-level ∧-type atom with a two-mode field initially in the coherent state, such as squeezing properties and sub-Poisson statistics. We show that the squeezing can be enhanced by selective atomic measurement.

Position-dependent property of resonant dipole-dipole interaction mediated by localized surface plasmon of an Ag nanosphere

We use the photon Green-function method to study the quantum resonant dipole-dipole interaction（RDDI） induced by an Ag nanosphere（ANP）.As the distance between the two dipoles increases,the RDDI becomes weaker,which is accompanied by the influence of the higher-order mode of the ANP on RDDI declining more quickly than that of the dipole mode.Across a broad frequency range（above 0.05 eV）,the transfer rate of the RDDI is nearly constant since the two dipoles are fixed at the proper position.In addition,this phenomenon still exists for slightly different radius of the ANPs.We find that the frequency corresponding to the maximum transfer rate of RDDI exhibits a monotonic decrease by moving away one dipole as the other dipole and the ANP are kept fixed.In addition,the radius of ANP has little effect on this.When the two dipoles are far from the ANP,the maximum transfer rate of the RDDI takes place at the frequency of the dipole mode.In contrast,when the two dipoles are close to the ANP,the higher-order modes come into effect and they will play a leading role in the RDDI if they match the transition frequency of the dipole.Our results may be used in a biological detector and have a certain guiding significance for further application.

Preparation of Entangled Atomic States Through Resonant Atom-Field Interaction

一个计划被建议因为二原子的格言联盟者的产生纠缠了状态，多原子格言联盟者纠缠了 W 班的状态。计划与一个单个模式的洞基于原子的同时的反响的相互作用删除。它不要求相互作用时间的精确调整。需要完成产生的时间不与原子的数字增加。

Teleportation of N-qubit W State without Bell-State Measurement via Selective Resonant Interaction in Cavity QED

We present a scheme in which the N-atom W state is teleported by employing the selective interactionof a cavity field with a driven three-level atom in the A configuration and detecting a single atom in one of the groundstates.The long-lived W state is teleported from atom A to atom B when the atoms B and A are sent through acavity successively and atom A is then detected.The advantage is that the present one does not involve the Bell-statemeasurement and is robust against the atomic spontaneous emission.

INTERNAL WAVE EIGENMODES AND THEIR WEAK NONLINEAR RESONANT INTERACTION IN A NONLINEARLY STRATIFIED FLUID- A PRELIMINARY THEORETICAL AND EXPERIMENTAL STUDY

A preliminary theoretical and experimental study was conducted on internal wave modes and their weak nonlinear resonant interaction in a nonlinearly stratified fluid . An asymptotical solution of the modes and a dispersion relation of internal waves in a stratified fluid with density profile similar to that in our experiment were obtained theoretically . The resonant-interaction mechanism to 2nd order approximation is also discussed . The resonant interaction of the 3rd and 4th mode internal waves excited by the unstable 1st mode wave is analyzed on the basis of data obtained by conductivity probes. The resonant-interaction condition, , is examined . It is shown that the resonant instability increases with pycnocline thickness and wave maker driving frequency .

Generation of various multiatom entangled graph states via resonant interactions

In this paper, a scheme for generating various multiatom entangled graph states via resonant interactions is proposed. We investigate the generation of various four-atom graph states first in the ideal case and then in the case in which the cavity decay and atomic spontaneous emission are taken into consideration in the process of interaction. More importantly, we improve the possible distortion of the graph states coming from cavity decay and atomic spontaneous emission by performing appropriate unitary transforms on atoms. The generation of multiatom entangled graph states is very important for constructing quantum one-way computer in a fault-tolerant manner. The resonant interaction time is very short, which is important in the sense of decoherence. Our scheme is easy and feasible within the reach of current experimental technology.

Generation of any superposition of coherent states along a straight line via resonant atom-cavity interaction

This paper proposes a scheme for generating arbitrary superpositions of several coherent states along a straight line for a cavity mode. In the scheme, several atoms are sent through a cavity initially in a strong coherent state. The superposition of several coherent states with desired coefficients may be generated if each atom is detected in the excited state after it exits the cavity. The scheme is based on resonant atom-cavity interaction and no classical field is required during and after the atom cavity interaction. Thus, the scheme is very simple and the interaction time is very short, which is important in view of decoherence.

Preparation of steady-state entanglement via a laser-excited resonant interaction

In this paper we propose a scheme in which two-mode entanglement in a steady state is produced by using two lasers to resonantly drive a single four-level atom embedded inside a two-mode optical cavity. In this scheme, atomic coherence induced by a classical laser plays an important role in the process of preparing the entangled state. With the coupling of a strong control field, direct two-photon transition is generated and the relatively weak pump field induces the parametric interaction between two photons, which makes them entangle with each other. By numerical calculation, we find that the degree of entanglement depends strongly on the Rabi frequencies of the classical laser fields and the cavity losses.

INTERNAL RESONANT INTERACTIONS OF THREE FREE SURFACE-WAVES IN A CIRCULAR CYLINDRICAL BASIN

The basic equations of free capillary_gravity surface_waves in a circular cylindrical basin were derived from Luke's principle. Taking Galerkin's expansion of the velocity potential and the free surface elevation, the second_order perturbation equations were derived by use of expansion of multiple scale. The nonlinear interactions with the second order internal resonance of three free surface_waves were discussed based on the above. The results include:derivation of the couple equations of resonant interactions among three waves and the conservation laws; analysis of the positions of equilibrium points in phase plane; study of the resonant parameters and the non_resonant parameters respectively in all kinds of circumstances; derivation of the stationary solutions of the second_order interaction equations corresponding to different parameters and analysis of the stability property of the solutions; discussion of the effective solutions only in the limited time range. The analysis makes it clear that the energy transformation mode among three waves differs because of the different initial conditions under nontrivial circumstance. The energy may either exchange among three waves periodically or damp or increase in single waves.

Generation of entangled coherent states for two cavity modes via resonant interaction with a V-type three-level atom

This paper proposes a scheme for the generation of entangled coherent states for two cavity modes. In the scheme a V-type three-level atom is sent through a two-mode cavity filled with a coherent field. After the atom cavity interaction and detection of the atomic state the cavity modes may evolve to a superposition of two-mode coherent states. As the scheme is based on resonant atom-cavity interaction, the required interaction time is short, which is important in view of the decoherence. Moreover, additional classical pulses are unnecessary before and after the atom-cavlty interaction.

Implementation of n-qubit Deutsch-Jozsa algorithm using resonant interaction in cavity QED

We propose a scheme to implement the n-qubit Deutsch-Jozsa algorithm based on resonant interaction between the atoms and a single-mode cavity. In the scheme, the resonant transitions between two ground states and one excited state of an atom are changed alternately by adjusting the cavity frequency appropriately, and the operations required to complete the algorithm can be significantly simplified following the increment of the number of qubits. The implementation of the scheme in experiment would show the full power of quantum algorithm and would be significative and important for more complicated quantum algorithm in cavity quantum electrodynamics.

Transferring Three-Dimensional Quantum States and Implementing a Quantum Phase Gate Based on Resonant Interaction between Distant Atoms

We propose a more efficient and reliable scheme for transferring quantum states between distant atoms than previous schemes based on resonant atom-cavity interaction.In addition,our system can also be used to implement a controlled phase gate with high fidelity.

An Alternative Scheme to Generate Arbitrary Anticorrelated States of a Two-Mode Field via A-type Atom Resonant Interaction with a Two-Mode Cavity Field

<Abstract>An alternative scheme is presented to generate arbitrary anticorrelated states of a two-mode field.In the scheme,a sequence of A-type three-level atoms are orderly sent across the cavity to interact with the cavity field initially in the two-mode vacuum state.The detection of all the atoms in the ground state collapses the two-mode field to the desired state.In this way,we can prepare the anticorrelated states of a two-mode field.

Topographicaly Forced Thre-Wave Quasi-Resonant and Non-Resonant Interactions among Barotropic Rossby Waves on an Infinite Beta-Plane

In this paper, we first apply the assumption h=εh' of topographic variation ( h is the nondimensional topographic height and is a small parameter) to obtain nonlinear equations describing three-wave quasi-resonant and non-resonant interactions among Rossby waves for zonal wavenumbers 1—3 over a wavenumber-two bottom topography (WTBT). Some numerical calculations are made with the fourth-order Rung-Kutta Scheme. It is found that for the case without topographic forcing, the period of three-wave quasi-resonance (TWQR) is found to be independent of the zonal basic westerly wind, but dependent on the meridional wavenum ber and the initial amplitudes. For the fixed initial data, when the frequency mismatch is smaller and the meridional wavelength is moderate, its period will belong to the 30-60-day period band. However, when the wavenumber-two topography is included, the periods of the forced quasi-resonant Rossby waves are also found to be strongly dependent on the setting of the zonal basic westerly wind. Under the same conditions, only when the zonal basic westerly wind reaches a moderate extent, intraseasonal oscillations in the 30-60-day period band can be found for zonal wavenumbers 1-3. On the other hand, if three Rossby waves considered have the same meridional wavenumber, three-wave non-resonant interaction over a WTBT can occur in this case.When the WTBT vanishes, the amplitudes of these Rossby waves are conserved. But in the presence of a WTBT, the three Rossby waves oscillate with the identical period.The period, over a moderate range of the zonal basic westerly wind, is in the intraseasonal, 30-60-day range.

Approximate Toffoli Gate Originated from a Single Resonant Interaction of Cavity Dissipation and Atomic Spontaneous Emission

我们建议一个潜在地实际的计划在洞模式腐烂和原子自发的排放在被考虑的消散的洞证完由一个单个反响的相互作用实现一扇近似 three-qubit Toffoli 门。计划不要求控制的 two-qubit -- 不门但是使用一扇 three-qubit 阶段门和二扇 Hadamard 门，在近似阶段门能被仅仅和洞模式的原子的一个单个消散的反响的相互作用实现的地方。讨论为优点和我们的计划的试验性的可行性被做。

Generating Even-Photon State via Resonant Interaction Between Ladder-Type Three-Level Atoms with a Single-Mode Field

一个计划被介绍基于在梯子类型之间的反响的相互作用产生平光子的状态有一块单个模式的地的三水平的原子。在计划，合适准备的梯子类型的一个序列三水平的原子是有序的通过一个单个模式的洞送了开始。处于扎根的状态的所有原子的察觉折叠洞到需要的状态。计划与洞基于原子的反响的相互作用，并且因此，要求的相互作用时间能极大地被弄短。鉴于 decoherence，这是重要的。

Preparation of Multicomponent Schroedinger Cat States Through Resonant Atom-Field Interaction

A simple method is presented for generating multicomponent Schroedinger cat states through resonant atomfield interactions. In the scheme n two-level atoms, initially in ground states, are sent through a resonant cavity filled with a strong coherent field sequentially. Then state-selective measurements are performed on the atoms. The detections of the atoms in ground states collapse the cavity field onto a superposition of 2^n coherent states. This is the first way for producing superpositions of many coherent states through resonant atom-field interaction.

SHORT-AND RESONANT-RANGE INTERACTIONS BETWEEN SCALES IN TURBULENCE AND THEIR APPLICATIONS

Interactions between different scales in turbulence were studied starting from the incompressible Navier-Stokes equations. The integral and differential formulae of the short-range viscous stresses, which express the short-range interactions between contiguous scales in turbulence,were given. A concept of the resonant-range interactions between extreme contiguous scales was introduced and the differential formula of the resonant-range viscous stresses was obtained. The short- and resonant-range viscous stresses were applied to deduce the large-eddy simulation (LES) equations as well as the multiscale equations, which are approximately closed and do not contain any empirical constants or relations. The properties and advantages of using the multiscale equations to compute turbulent flows were discussed. The short-range character of the interactions between the scales in turbulence means that the multiscale simulation is a very valuable technique for the calculation of turbulent flows. A few numerical examples were also given.