Classical mechanics in non-commutative phase space

In this paper the laws of motion of classical particles have been investigated in a non-commutative phase space.The corresponding non-commutative relations contain not only spatial non-commutativity but also momentum non-commutativity.First,new Poisson brackets have been defined in non-commutative phase space.They contain corrections due to the non-commutativity of coordinates and momenta.On the basis of this new Poisson brackets,a new modified second law of Newton has been obtained.For two cases,the free particle and the harmonic oscillator,the equations of motion are derived on basis of the modified second law of Newton and the linear transformation (Phys.Rev.D,2005,72:025010).The consistency between both methods is demonstrated.It is shown that a free particle in commutative space is not a free particle with zero-acceleration in the non-commutative phase space.but it remains a free particle with zero-acceleration in non-commutative space if only the coordinates are non-commutative.     

Classical mechanics in non-commutative phase space

In this paper the laws of motion of classical particles have been investigated in a non-commutative phase space. The corresponding non-commutative relations contain not only spatial non-commutativity but also momentum non-commutativity. First, new Poisson brackets have been defined in non-commutative phase space. They contain corrections due to the non-commutativity of coordinates and momenta. On the basis of this new Poisson brackets, a new modified second law of Newton has been obtained. For two cases, the free particle and the harmonic oscillator, the equations of motion are derived on basis of the modified second law of Newton and the linear transformation (Phys. Rev. D, 2005, 72: 025010). The consistency between both methods is demonstrated. It is shown that a free particle in commutative space is not a free particle with zero-acceleration in the non-commutative phase space, but it remains a free particle with zero-acceleration in non-commutative space if only the coordinates are non-commutative.     

Classical mechanics in phase space revisited

A Bose type of classical Hamilton algebra, i.e., the algebra of the canonical formalism of classical mechanics, is represented on a linear space of functions of phase space variables. The symplectic metric of the phase space and possible algorithms of classical mechanics (which include the standard one) are derived. It is shown that to each of the classical algorithms there is a corresponding one in the phase space formulation of quantum mechanics.     

Resolving power of phase annular and annulus apertures illuminated by partially coherent light

A more suitable criterion has been used in assessing the limit of resolution of phase annular and annulus apertures, operating in partially coherent light. In order to show the variation of the limit of resolution with the degree of coherence, the results of some specific examples have been presented graphically.     

Controlling phase space caustics in the semiclassical coherent state propagator

The semiclassical formula for the quantum propagator in the coherent state representation is not free from the problem of caustics. These are singular points along the complex classical trajectories specified by z′, z″ and T where the usual quadratic approximation fails, leading to divergences in the semiclassical formula. In this paper, we derive third order approximations for this propagator that remain finite in the vicinity of caustics. We use Maslov’s method and the dual representation proposed in Phys. Rev. Lett. 95, 050405 (2005) to derive uniform, regular and transitional semiclassical approximations for coherent state propagator in systems with two degrees of freedom.     

Generalized phase space method in spin systems-spin coherent state representation

A generalized phase space method for spin operators is developed. With the use of a spin coherent state representation, mapping rules from spin operators onto ac-number space are established; simple formulas to calculate the mappedc-number functions are also derived. A product theorem, which gives a way of mapping a product of operators, is obtained in an intuitive form. This can be advantageously used to transform a Liouville equation into ac-number equation. As an illustrative example, the method is applied to the Heisenberg model of a magnet.     

Amplification of nonclassical light in phase space

Journal of the Korean Physical Society - The scale transformation acting on P-functions associated with density operators of light is introduced as an amplification process for single-mode...     

相干态在参数量子相空间的两维正态分布

把量子力学与数理统计的正态分布联系起来进行初步的尝试.用数理统计的观点和有序算符内的积分技术研究相干态,指出在依赖一个实参数k的量子化方案中,相干态|z??z|在相空间呈现出以(q,p)为随机变量的两维正态分布,z=(q+ip)/√2.两个随机变量的相关系数为ik.在k=±1的参数相空间中,|z??z|分别表现出P排序(P在Q左)和Q排序的形式(Q在P左),而在k=0的参数相空间中,|z??z|表现出Weyl排序的形式.在P排序和Q排序的情况下,量子算符|z??z||z=(q+ip)/√2的经典对应函数中随机变量(q,p)是关联的,只有在Weyl对应时,随机变量(q,p)是独立的.也就是说,算符的Weyl排序有利于其经典对应的随机变量解脱关联.     

Super-sensitive phase estimation with coherent boosted light using parity measurements

We consider a passive and active hybrid interferometer for phase estimation, which can reach the sub-shot-noise limit in phase sensitivity with only the cheapest coherent sources. This scheme is formed by adding an optical parametric amplifier before a Mach-Zehnder interferometer. It is shown that our hybrid protocol can obtain a better quantum Cramer-Rao bound than the pure active(e.g., SU(1,1)) interferometer, and this precision can be reached by implementing the parity measurements. Furthermore, we also draw a detailed comparison between our scheme and the scheme suggested by Caves[Phys. Rev. D 23 1693(1981)], and it is found that the optimal phase sensitivity gain obtained in our scheme is always larger than that in Caves' scheme.     

Vibrational anharmonicities revealed by coherent two-dimensional infrared spectroscopy

Two-dimensional infrared photon echo spectroscopy has been used to describe the anharmonic nuclear potential of two coupled molecular vibrations. The two-dimensional spectrum shows diagonal and off-diagonal features, each composed of two peaks. The splitting between these peaks is directly related to the anharmonicity, while the relative amplitude of the diagonal and off-diagonal features describes the projection angle between interacting dipoles.     

Quantum coherent versus classical coherent light

The paper shows that the Wigner distribution function of quantum optical coherent states, or of a superposition of such states, can be produced and measured with a classical optical set-up using classical coherent light fields. This measurement cannot be done directly in quantum optics since the quantum phase space variables correspond to non-commuting operators. As an example, the Wigner distribution function of Schrödinger cat states of light has been measured. It is also shown that the possibility of measuring the Wigner distribution function of quantum coherent states with classical coherent fields is unique in the sense that it cannot be extended to other quantum states, not even to the incoherent limit of the superposition of coherent states.     

Mean-square coherent light

Mean-square coherent light is defined as light that is able to interfere with fringes of unit visibility when its electromagnetic field is multiplied by appropriate nonsingular deterministic Jones matrices. It includes light that satisfies the factorization condition at order one and partially polarized light that leads to interference fringes of unit visibility. A necessary and sufficient experimentally measurable condition to determine if two electromagnetic fields are mean-square coherent is established. Furthermore, different properties of partially polarized mean-square coherent light are discussed, such as its relation to the factorization condition and its evolution with propagation.     

Direct phase control method for binary phase-shift keying space coherent laser communication

An optical phase locking method based on direct phase control is proposed. The core of this method is to synchronize the carrier by directly changing the phase of the local beam. The corresponding experimental device and the supporting algorithm were configured to verify the feasibility of this method. Phase locking can be completed without cycle skipping, and the acquisition time is 530 ns. Without an optical preamplifier, a sensitivity of-34.4 d Bm is obtained, and the bit error rate is10^...     

Performance of phase compensated coherent free space optical communications through non-Kolmogorov turbulence

The bit-error-rate (BER) performance of coherent free-space optical (FSO) links employing phase compensation techniques is investigated in weak non-Kolmogorov turbulence. Assuming that the amplitude fading and phase fluctuation follow lognormal model and Gaussian distribution respectively and using the expression of non-Kolmogorov turbulence in terms of Zernike polynomials, the signal-to-noise ratio (SNR) at the coherent receiver is analyzed and as a special case, a new closed-form expression using chi-square distribution is obtained. Thus, the influence of different compensation modes and normalized receiver diameter on BER performance is evaluated and an optimum normalized receiver diameter is suggested to achieve the minimum BER. Moreover, the impact of outer scale L₀ and the exponent value α in non-Kolmogorov spectrum is studied with the optimum diameter, which reveals that the BER has an obvious decrease with larger values of L₀ and α.     

Holography,coherent light amplification and optical phase conjugation with photorefractive materials

This paper presents a review of photorefractive effects in electro-optic materials and their applications. Materials properties giving rise to increased photo-sensitivities are discussed and compared with experimental data for a series of newer materials. The formation of volume holograms in these crystals, and accompanying optical effects such as beam coupling and phase conjugation, are discussed. Theoretical results derived from charge transport parameters are compared with our original data obtained in “dynamic holography” experiments with Bi₁₂GeO₂₀, Bi₁₂SiO ₂₀ and KNbO₃:Fe²⁺. The optimum parameters for applications such as volume hologram storage, coherent light amplification, optical phase conjugation etc. have been determined, and possible applications are discussed.     

Tunable coherent light sources

The physical principles of tunable sources of coherent light are briefly described. Characteristic data and the present stage of development are reviewed.     

Charge density wave dislocation as revealed by coherent x-ray diffraction

Coherent x-ray diffraction experiments have been performed on high quality crystals of the charge density wave (CDW) system K0.3MoO3. The satellite reflections associated with the CDW have been measured as a function of the 20-microm-diameter beam position. For some positions, regular fringes have been observed. We show that this observation is consistent with the presence of a single CDW dislocation. Beyond charge density wave systems, this experiment shows that coherent x-ray diffraction is a suitable tool to probe topological defects embedded in the bulk.     

Classical theory of non-degenerate sum-frequency generation by coherent nonlinear optical mixing of coherent and chaotic radiations

Classical solution of coherent nonlinear optical sum-frequency generation process based on the averaging of stochastic quantities over the initial photocount distributions in sub-frequency radiations is presented in this paper. The evolution of second-order light statistics in sum-frequency generation with coherent and chaotic input radiations is calculated for arbitrary values of the time or space parameter.The author would like to thank Dr. M. Krková from the Computer Centre of Palacky University for performing the numerical calculations.