增加光子对和减少光子对相干态的统计性质

引入增加光子对相干态|ζ,q;m >_a=a^+m|ζ,q >和减少光子对相干态|ζ,q;-m >_b=b^m|ζ,q >,研究了这些态所描写的光场的统计性质。结果显示当在对相干态的a模增加光子时,两模的平均光子数均增加,亚泊松分布性质增强;当在对相干态的b模取走光子时,b模的平均光子数减少,而a模的平均光子数却增加;b模的亚泊松分布性质减弱,而a模的亚泊松分布性质却增强。我们还计算了场模间的相关度和场模的压缩。     

k光子Jaynes-Cummings模型光场的熵压缩

研究了k光子Jaynes-Cummings模型光场的熵压缩，讨论了光子数k和原子的初始状态对光场熵压缩的影响.结果表明，随光子数k的增大，光场的位置熵压缩愈趋明显，动量熵压缩量减小；当k≥3时，位置熵始终是被压缩的.原子的初态对光场的熵压缩也有一定的影响.     

增加光子奇偶q相干态的高阶压缩效应

通过数值计算研究了增加光子奇q相干态a_q^+m|α>_q^o和增加光子偶q相干态a_q^+m|α>_q^e的高阶压缩效应.结果表明:当q较小时,态a_q^+m|α>_q^o和a_q^+m|α>_q^e都能呈现出强烈的奇次方阶压缩效应,但无偶次方阶压缩效应,而且奇次方阶压缩随m的增大而增强.当m=0时a_q^+m|α>_q^o和a_q^+m|α>_q^e为光场振幅偶次幂的最小测不准态,但当m≠0时它们不是光场振幅偶次幂的最小测不准态.     

叠加激发双模压缩真空态的量子统计特性(英文)

从激发双模压缩真空态a^+mb^+m|ξ>出发构造了叠加态|Ψ>,研究了|Ψ>的量子统计特性.结果表明:在一定的条件下,随着相位差的变化,叠加态|Ψ>的平均光子数出现类似于Rabi振荡的崩塌与复原现象,而且与单个激发双模压缩真空态a^+mb^+m|ξ>相比,在叠加态|Ψ>中光场的相位压缩和亚泊松光子统计特性都得到了加强.     

增加光子位移福克态的量子统计性质

引入了增加光子位移福克态 a^+m| α,n〉,其中 | α,n〉是位移福克态,m是整数.用数值计算的方法研究了这种态的量子统计性质.结果表明,在位移福克态上增加光子后可以使原有的光场呈现较强的压缩,并能使光场的亚泊松特性得到明显增强.     

双模SU(2)相干态场与一个Λ型三能级原子共振相互作用的光场非经典性质

采用全量子理论和数值计算方法, 研究了初始处于SU(2)相干态的双模腔场与一个Λ型三能级原子共振相互作用的光场非经典性质,讨论了在没有对原子进行态选择测量、 直接对原子进行态选择测量和应用经典微波场并对原子进行态选择测量的三种情况下,两个腔模总光子数、配分参量和耦合系数对光场非经典性质的影响.结果表明,增加两个腔模的总光子数M或对原子进行态选择测量,双模差压缩明显增强;减小配分参量和应用经典场并对原子进行态选择测量,a模光子的亚Poisson统计分布的平均程度变浅,而b模变深;两模间的反相关特征保持不变,增加M或直接对原子进行态选择测量,反相关平均程度变浅;直接对原子进行态选择测量,违背Cauchy-Schwartz不等式.     

光子消灭算符高次幂本征态的振幅N次方压缩

本文研究了光子消灭算符高次幂a^k(k≥3)的k个正交归一本征态的振幅N次方压缩特性,结果表明,当k为偶数时,这些本征态均可存在振幅N次方(N=(m+1/2)k,m=0,1,2,…)压缩。     

第I种非对称三态叠加多模叠加态光场的高次和压缩——第一正交分量的N次方H压缩效应

构造了第孙中禹种强度不等的非对称三态叠加多模叠加态光场|ψ₁^(ABC)〉_q.利用多模压缩态理论研究了态|ψ₁^(ABC)〉_q第一正交分量高次和压缩.结果发现:①当构成态|ψ₁^(ABC)〉_q的三个多模相干态光场的强度不相等时,在一定条件下,态|ψ₁^(ABC)〉_q的第一正交分量可出现任意幂次的高次和压缩.②当上述的三个多模相干态光场强度相等时,态|ψ₁^(ABC)〉_q的第一正交分量的高次和压缩现象消失.在这种情况下,态|ψ₁^(ABC)〉_q的第一正交分量恒处于NH最小测不准态.     

由多模奇偶相干态组成的第种四态叠加多模叠加态光场的等阶N次方Y压缩

本文根据量子力学中的线性叠加原理,构造了由多模复共轭奇相干态与多模复共轭偶相干态所组成的第Ⅱ种四态叠加多模叠加态光场|Ψ_o,e⁽⁴⁾Ⅱ>_q.利用多模压缩态理论,研究了态|Ψ_o,e⁽⁴⁾Ⅱ>_q的等阶N次方Y压缩特性.结果发现:1)多模叠加态光场|Ψ_o,e⁽⁴⁾Ⅱ>_q中,压缩阶数N为偶数时,只存在等阶N-Y最小测不准态;2)多模叠加态光场|Ψ_o,e⁽⁴⁾Ⅱ>_q,在压缩阶数为奇数时,随着腔模总数q、态间相位差(θ_e-θ_o)、各模初相位φ_j以及态的几率幅值r_e和r_o及平均光子数R_j²等取不同的组合定值时,可呈现以下几种状态:①等阶N-Y最小测不准态、②“半相干态”、③“半压缩态”;3)本文构造的多模叠加态|Ψ_o,e⁽⁴⁾Ⅱ>_q与文献17、18研究的多模叠加态|Ψ_o,e⁽⁴⁾Ⅰ>_q在相同的条件下呈现出完全相同的压缩特性,故态|Ψ_o,e⁽⁴⁾Ⅱ>_q与态|Ψ_o,e⁽⁴⁾Ⅰ>_q之间存在着“压缩简并”现象.     

与Λ型三能级原子非共振相互作用的SU(1,1)场的性质

导出了介质中双模SU(1,1)相干态场与Λ型三能级原子非共振相互作用系统的态函数,研究了场模失谐量、克尔介质以及原子初态对场的互关联函数和Mandel Q参量的影响.结果表明:失谐量将削弱光场两模的关联性,并影响场模光子数的统计分布;当SU(1,1)场两模间的光子数之差增大时,失谐量对它们产生的影响变得更弱,此时克尔效应的影响变得明显,它使两模的关联性和光子数的统计分布趋于稳定.     

压缩态光场在双光子吸收介质中的演化

采用生成函数方法,由光场密度算符主方程,求得光场压缩度s,二阶相干度g^(x)和光子统计分布的严格解析表达式,同时讨论它们随标度时间τ的演化。计算表明,在双光子吸收过程中,虽然压缩度s逐渐减弱,但相当长的时间内光场仍呈现压缩特性;该过程有利于呈现和增强光子反聚束效应和光子亚泊松分布特性;光子分布的振荡特征维持较短一段时间后很快消失。 关键词：     

THE LOOP PHASE-FACTOR APPROACH TO GAUGE FIELDS

The gauge field theory is formulated via loop phase factors with a fixed point O as their initial and final point. Let G be the gauge group. When the base space is the Minkowski space E₄, we introduce a set of standard paths Ox （for example, the set of line segments Ox）, where x is arbitrary. The phase factor for the infinitesimal loop Oxx+dxO corresponds to an element in the Lie algebra g and can be expressed as a g-valued differential form k（x, dx） which satisfies the following conditions of consistency （a） k（O, dx）=0, （b） k（x, v）=0, where v is the tangential vector of Ox at x. It is shown that an equivalent class of gauge fields is determined by k（x, dx） or （ad a） k（x, dx） where a is a fixed element of G. Hence if we adopt k（x, dx） for the fundamental physical quantity of a gauge field then a great part of gauge indefiniteness is eliminated. Moreover if the phase factors Φ_xo for standard paths Ox are given then the phase factors for differential arcs x x+dx are easily calculated, and hence a gauge field in the equivalent class is extracted. We call the set of phase factors for standard paths a gauge and k（x, dx） may be interpretated as the gauge potential under a special gauge under which Φ_xo=the unit element of G.The method is useful in considering the equivalence problem and the spacetime symmetry of gauge fields. For example, it is quite easy to determine all spherically symmetric gauge fields if they are free of singularities. By using the method it can also be proved that if two gauge fields have the same gauge and the same field strength then their gauge potentials are equal to each other. Consequently, under a given gauge in the above sense the field strength determines the gauge potential completely.For a general base manifold M_n, every equivalent class of gauge fields over M_n can be defined by loop phase factors also. In this case, M_n is expressed as the sum of a set of neighborhoods each of which is homeomorphic to the Euclidean space. The standard paths are constructed according a certain rule, the phase factors for standard differential loops are also introduced. The transition functions and gauge potentials of a gauge field in the given equivalent class are derived as the phase factors for some finite loops and standard differential loops respectively. Further it is remarkable that a global gauge field is determined completely by the field strength and some discrete loop factors, if the phase factors for the standard paths are gwen.In mathematical terminology principal G-bundle structure as well as a connection in it is determined by the holonomic mapping which maps the set of loops through a fixed point into the group G, provided the mapping is differentible in a certain.The author is very grateful to Prof. Yang Chen Ning for many helpful discussions.     

The photon statistics of multiphoton lasers with single photon losses

We investigate the photon statistics of a single-modem-photon laser in a generalized Scully-Lamb laser model. The solution for the stationary state is obtained by recursion although detailed balance is not available form2. The threshold condition is gained from a discussion of the photon distribution in the stationary state. At threshold we find no amplitude stabilization and somewhat above it there is bistability form2 giving rise to enhanced fluctuations. Increasing the pumping the bistability more and more disappears and the photon statistics become similar to the ones of a usual laser.     

Stability of One-Electron Molecules in the Brown–Ravenhall Model

In appropriate units, the Brown-Ravenhall Hamiltonian for a system of 1 electron relativistic molecules with K fixed nuclei having charge and position Zk, R_k, k=1,2, ?,Kk=1,2, \ldots,K, is of the form \bB_1,K = L₊ ( D₀ + aV_c) L₊ \bB_{1,K}= \Lambda_+ \bigl( D_0 + \alpha V_c\bigr) \Lambda_+ , where v₊ is the projection onto the positive spectral subspace of the free Dirac operator D₀ and V_c = - ?_k=1^K \fracaZ_k\lmod \bx-R_k \rmod + ?_{k < l,  k,l=1}^K \fracaZ_k Z_l\lmod R_k-R_l \rmod V_c= - \sum_{k=1}^K \frac{\alpha Z_k}{\lmod \bx-R_k \rmod} + \sum_{kZ_k ￡ aZ_c = \frac2p/2 + 2/ p\alpha Z_k \leq \alpha Z_c = \frac{2}{\pi /2 + 2/ \pi}, k=1,2, ?,Kk=1,2, \ldots,K, and a ￡ \frac2 p(p²+4)(2+?{1+ p/2})\alpha \leq \frac{2 \pi}{(\pi^2+4)(2+\sqrt{1+ \pi /2})}, \ \bB_1,K 3 \operatornameconst \cdotp K\bB_{1,K} \geq \operatorname{const} \cdotp K.     

Antibunching,sub-poissonian photon statistics and finite bandwidth effects in resonance fluorescence

It is demonstrated that, although the fluorescent photons from a driven two-level atom always exhibit antibunching, they need not obey sub-poissonian statistics. The maximum sub-poissonian excursion of the normalized second factorial moment (〈(Δn)²〉 ? 〈n〉)/〈n〉 occurs in the transient regime where it can approach the value -1. Effect s of finite bandwidth of excitation on photon statistics are also investigated and it is shown that the photon number distribution may be narrower with finite bandwidth excitation than with coherent excitation.     

FINE STRUCTURES OF INCLUSIVE SPECTRA(Ⅰ)——SUM RULES AND THE GENERALIZATION OF FEYNMAN-YANG SCALING

Important implications of the fine structure of inclusive spectra(to be calledinclusive and semi-inclusive spectra of nearby particles,which represent the local dis-tributions of nearby particles in three-dimensional phase space with rapidity y and transverse momenta P_⊥x, P_⊥z as independent coordinates are explained,and some basicfeatures of the fine stucture are found,namely,sum rules and the generalized formof the Feynman-Yang scaling.One of the sum rules,for example,is:where f_(1;k) denotes the normalized invariant inclusive cross section of k closely neigh-boring particles.It follows that the inclusive the spectra of nearby particles arequalitatively different from the usual ones.The generalized form of the Feynman-Yang scaling for the case of k closelyneighboring particles,for example,is:f_(1;k)(s,x₁,P_⊥1,…x_k,P_⊥k⁾∞,（s→∞,x₁≤x₂≤…≤x_k）.where‘∞’denotes‘approaches a definite limit’.For k=2,the existing experimentaldata for the rapidity gap-length distributions show that for FNAL energies,f_(1,k） isalready close to its limiting form.The inclusive（semi-inclusive）spectra of nearbyparticles way be able to reflect effectively short-range correlation effects.     

Uniaxial Strain Effects on Optical Properties of c-plane Wurtzite GaN

We investigate the uniaxial strain effect in the e-plane on optical properties of wurtzite GaN based on k.p theory, the spin-orbit interactions are also taken into account. The energy dispersions show that the uniaxial strain in the c-plane gives an anisotropic energy splitting in the kx - ky plane, which can reduce the density of states. The uniaxial strain also results in giant in-plane optical polarization anisotropy, hence causes the threshold carrier density reduced. We clarify the relations between the uniaxial strain and the optical polarization properties. As a result, it is suggested that the compressive uniaxial strain perpendicular to the laser cavity direction in the c-plane is one of the preferable approaches for the efficient improvement of GaN-based laser performance.     

Connection Considerations of Gravitational Field in Finsler Spaces

Some alternative connection structures of the Finslerian gravitational field are considered by modifying the independent variables (x,y) (x: point and y: vector) in various ways. For example, (x ^k ,y ⁱ ) (k,i = 1,2,3,4) are changed to (x ^k ,y ⁰) (y ⁰: scalar) or (x ⁰,y ⁱ ) (x ⁰: time axis); (x ^k ,y ⁱ ) are generalized to (x ^k ,y ⁱ ,p _i ) (p _i : covector dual to y ⁱ ) or (x ^k ,y ⁱ ,q _a ) (q _a : covector different from p _i ); (x ^k ,y ⁱ ) are further generalized to (x ^k ,y ^(a)i ) (a = 1,2,…,m), (y ^(a): (a)th vector), etc.