Strong Squeezing of Duffing Oscillator in a Highly Dissipative Optomechanical Cavity System

In the conventional scheme of generating strong mechanical squeezing by the joint effect between mechanical parametric amplification and sideband cooling, the resolved sideband condition is required so as to overcome the quantum backaction heating. In the unresolved sideband regime, to suppress the quantum backaction, a χ⁽²⁾ nonlinear medium is introduced to the cavity. The result shows that the quantum backaction heating effect caused by unwanted counter-rotating term can be completely removed. Hence, the strong mechanical squeezing can be obtained even for the system far from the resolved-sideband regime.     

Dicke超辐射系统多光子过程中光场的压缩效应

本文利用微扰技术研究了与Ｄｉｃｋｅ模型中Ｎ个两能级原子系统通过多光子过程相互作用的相干态场的时间演化．研究表明，若多光子Ｄｉｃｋｅ模型中的Ｎ个两能级原子初始时皆处于去激发状态，则在短时近似下光场可存在二阶压缩效应．     

Information Entropy Squeezing for a Atom in Mode-Mode Competition System

The entropy squeezing properties for a two-level atom interacting with a two-mode field via two different competing transitions are investigated from a quantum information point of view. The influences of the initial state of the system and the relative coupling strength between the atom and the field on the atomic information entropy squeezing are discussed. Our results show that the squeezed direction and the frequency of the information entropy squeezing can be controlled by choosing the phase of the atom dipole and the relative competing strength of atom-field, respectively. We find that, under the same condition, no atomic variance squeezing is predicted from the HUR while optimal entropy squeezing is obtained from the EUR, so the quantum information entropy is a remarkable precision measure for the atomic squeezing in the considered system.     

非线性应变波耦合组的指数吸引子

本文研究了一在应变波耦合组所生成的半群性质,通过算子解和构造进紧不变集,得到了该耦合组的紧的指数吸引子。     

二维广义Ginzburg-Landau方程的指数吸引子

在文[1]的基础上，得到了二维广义的Ginzburg－Landau方程的指数吸引子的存在性．     

广义Kuramoto—Sivashinsky型方程的惯性流形

本文及续文对一类广义Kuramoto-Sivashinsky型方程证明了惯性流形的存在性，并对其维数作了估计同时研究该方程的不变锥性质（ICP）和轨线的强挤压性（SSP）。     

混合态的不确定关系与压缩效应

在关于混合态的海森堡不确定关系的基础上，研究了纯态和混合态的最小不确定性和压缩效应.虽然最小不确定态必定是纯态，但在某些并非最小不确定态的纯态或混合态中，依然可 以实现力学量不确定度的压缩.还给出了普通统计学的不确定关系，它们不涉及量子相干性却与量子力学的海森堡不确定关系具有相似的数学结构.     

与q形变玻色算符逆算符相关的相干态及其量子统计性质

讨论了ｑ形变玻色算符的广义逆算符作用于ｑ－相干态所得到的两类量子态的数学及量子统计性质。结果表明，ｑ－相干态的光子激发态不存在压缩但呈现反聚束效应，而ｑ－相干态的光子湮灭态却存在压缩但不呈现反聚束效应。     

New 3-mode bosonic operator realization of SU（2） Lie algebra： From the point of view of squeezing

We consider the quantum mechanical SU(2) transformation e2λ JzJ± e-2λJz= e±2λJ± as if the meaning of squeezing with e±2λbeing squeezing parameter. By studying SU(2) operators(J±,Jz) from the point of view of squeezing we find that(J±,Jz) can also be realized in terms of 3-mode bosonic operators. Employing this realization, we find the natural representation(the eigenvectors of J+ or J-) of the 3-mode squeezing operator e2λ Jz. The idea of considering quantum SU(2) transformation as if squeezing is liable for us to obtain the new bosonic operator realization of SU(2) and new squeezing operators.     

A Class of k-Quantum Nonlinear Coherent States and Some of Their Properties

A class of k-quantum nonlinear coherent states, i.e., the k eigenstates of the powers B ^k (k 3) of the annihilation operator of f-oscillators, is obtained and its completeness is investigated. An alternative method to construct them is proposed. We introduce a new kind of higher-order squeezing and sub-Poissonian distribution. The quantum statistical properties of the k states are studied. The result shows that all of the eigenstates can be generated by a linear superposition of k Roy-type nonlinear coherent states. These states may form a complete Hilbert space, and the M-th order [M = (n + 1/2)k; n = 0,1, ...] squeezing effects exist in all of the k states when k is even. There is the sub-Poissonian distribution in all of the states.