Phase Fluctuations of s-Wave Superconductors on a Lattice

Based on an attractive U Hubbard model on a lattice with up to second neighbor hopping we derive an effective Hamiltonian for phase fluctuations. The superconducting gap is assumed to have s-wave symmetry. The effective Hamiltonian we finally arrive at is of the extended XY type. While it correctly reduces to a simple XY in the continuum limit, in the general case, it contains higher neighbor interaction in spin space. An important feature of our Hamiltonian is that it gives a much larger fluctuation region between the Berezinskii–Kosterlitz–Thouless transition temperature identified with T _c for superconducting and the mean field transition temperature identified with the pseudogap temperature.     

Fluctuations of the Order Parameter''s Phase in Layered Superconductors

The influence of the quantum fluctuations of the order parameter's phase on the critical temperature T _c is studied for a Josephson coupled layered superconductor. Two characteristic critical temperatures exist for a system, namely the superconducting critical temperature T ⁽²⁾ _c for a single layer estimated by the mean-field theory and the transition temperature for the outset or the superconducting phase coherence T* _c . The true critical temperature T _c is shown to vary inside the intervals T* _c T _c T ⁽²⁾ _c . For a strong quantum phase fluctuation limit, the superconducting layers become decoupled.     

Fluctuations of the Order Parameter's Phase in Layered Superconductors

The influence of the quantum fluctuations of the order parameter's phase on the critical temperature T _c is studied for a Josephson coupled layered superconductor. Two characteristic critical temperatures exist for a system, namely the superconducting critical temperature T ⁽²⁾ _c for a single layer estimated by the mean-field theory and the transition temperature for the outset or the superconducting phase coherence T* _c . The true critical temperature T _c is shown to vary inside the intervals T* _c ≤ T _c ≤ T ⁽²⁾ _c . For a strong quantum phase fluctuation limit, the superconducting layers become decoupled.     

Four-mode Squeezing and Applications

Abstract

The interactions among radiation modes in optical fibres and other Kerr media can create correlations among two, four or more distinct field components. These correlations can reduce the noise levels found with various detector schemes. Some interactions produce the correlations required for quantum non-demolition detection.     

Photon Antibunching and Squeezing

The occurrence of photon antibunching and squeezing is strongly connected with nonlinear optical phenomena in general. Recent results are presented for two-atom resonance fluorescence, the anharmonic oscillator, nonlinear propagation of light and higher-harmonic generation.     

Superposition Phases and Squeezing

Abstract

Quadrature variances of a radiation field depend not only on the photon number distribution in the field but also on the relative phases of the photon number probability amplitudes. Two fields with the same photon number distribution can show different degrees of squeezing if photon number states are superposed with different relative phases. It is thus possible, for example, for a radiation field with Poissonian photon statistics to exhibit squeezed quadrature fluctuations. Since different relative superposition phases in general yield different maximum and minimum values of the quadrature variances, measurement of the variances can yield information concerning the relative phases between different number states.     

大气湍流引起的特种激光外差通信系统相位起伏的研究

本文对特种激光外差通信系统接收中频信号相位受大气湍流随机起伏进行了实验测试。实验结果表明:该系统有助于克服大气湍流对接受中频信号相位的随机起伏,由大气湍流带来的随机相位噪声可以不予考虑。     

Squeezing with Rydberg Atoms

Abstract

It is shown that some 17 Rydberg Na atoms initially placed into a coherent atomic state and super-radiating into a low-Q microwave cavity at temperatures T ? 0·4 K will show modest squeezing in the fluorescence field, the squeezing arising from terms oscillating at twice the cavity frequency. It is also shown that similar numbers of Rydberg atoms undergoing resonance fluorescence in a coherent single-mode microwave driving field and without any cavity will show more substantial squeezing in the fluorescence field.     

Squeezing in Multiphoton Absorption

Abstract

The conditions for obtaining squeezing by single-beam multiphoton absorption are examined. For an initial coherent light the amount of squeezing is calculated in the second order of interaction time using the master-equation formalism. A limit formula for the amount of squeezing is found in the case of an initial strong coherent beam. The results are compared with the exact numerical calculations and some remarks are made on the short-time approximation in multiphoton absorption.     

Squeezing in Second-harmonic Generation

Abstract

The production of squeezed states in second-harmonic generation is discussed theoretically from the viewpoint of the structure of the nonlinear medium, phase-matching conditions, and the polarization state of the fields. The nonlinear coupling constants are derived in explicit form for all 102 magnetic symmetry groups for crystalline as well as electrically polarized isotropic media. The phase-matching conditions are discussed in detail. Phase mismatch is shown to accumulate along the optical path, and is calculated in full detail for various media and geometries. We refer to this as the mismatch accumulation effect. General formulae for normally ordered variances of the second-harmonic and fundamental fields are derived by perturbative procedure, and are specified for some special cases of practical interest.     

Superconductivity and Spin Fluctuations

The organizers of the Memorial Session for Herman Rietschel asked that I review some of the history of the interplay of superconductivity and spin fluctuations. Initially, Berk and Schrieffer showed how paramagnon spin fluctuations could suppress superconductivity in nearly-ferromagnetic materials. Following this, Rietschel and various co-workers wrote a number of papers in which they investigated the role of spin fluctuations in reducing the T _c of various electron-phonon superconductors. Paramagnon spin fluctuations are also believed to provide the p-wave pairing mechanism responsible for the superfluid phases of ³ He. More recently, antiferromagnetic spin fluctuations have been proposed as the mechanism for d-wave pairing in the heavy-fermion superconductors and in some organic materials as well as possibly the high-T _c cuprates. Here I will review some of this early history and discuss some of the things we have learned more recently from numerical simulations.     

Squeezing and Sub-poisson Statistics in Three-mode Interactions

Abstract

A unique approach to the photon statistics in nonlinear optical interactions is suggested based on the use of moment equations and generalized superposition of coherent fields and quantum noise. Non-classical features such as squeezing of fluctuations and sub-Poisson statistics are derived for finite interaction times in the three-mode interaction process and limits of the model are provided.     

用闪烁调制理论研究激光大气传输的相位起伏

针对Rytov近似下相位起伏的理论结果与实际情况不符的缺陷,本文提出用Andrews的调制近似理论来研究光波在湍流大气中传输的相位起伏.该方法根据能量守恒的原理,得到了闪烁调制的具体表达式,然后通过功率谱的替换,从闪烁方差得到了上行、下行和水平三种链路的相位起伏的表达式.结果表明,Andrews调制近似其实有很多具体的形式,对于每一种形式,其中的物理量都有不同的物理含义.与Rytov近似下的结果相比,本文的结果将适用于倾斜传输路径和存在闪烁的聚焦和饱和的情况.     

Squeezing Parameters in Two-photon Absorption

A comparison is made between exact numerical results of the squeezing parameters in single-mode two-photon absorption with those predicted by short-time calculations. Numerical calculations lead to much higher squeezing and at longer times than those predicted by short-time calculations. The value of the squeezing parameter in the limit of long times and large initial photon numbers coincides in both calculations, as well as in the limit of long times and small initial photon numbers.     

Squeezing in Correlated Quantum Systems

Abstract

We discuss the connection between quantum correlations and squeezing in simple quantum optical systems. We illustrate this connection by a study of two-mode states of light produced by parametric down-conversion and similar two-photon processes. The intermode correlations in these systems are shown to be responsible for modifications in photon-number sum and difference operators, and for squeezing in the superpositions of the two modes. The disappearance of the diagonal coherent-state quasiprobability function P(α) when non-classical light properties are important is noted, and alternative and better-behaved Wigner functions and coherent-state expectation Q-functions for the two-mode system are developed.     

Phase Diffusion and Suppression of the Supercurrent by Quantum-Mechanical Fluctuations of the Josephson Plasma at Small Superconducting Point Contacts

The RCSJ model of resistively and capacitively shunted Josephson junctions is used to describe superconducting point contacts over a wide range of resistances up to the metallic–tunneling transition. Their small dynamic capacitance of order C = 0.1 fF due to the point-contact geometry results in a huge plasma frequency. The critical current is then strongly suppressed and the contact resistance becomes finite because of quantum-mechanical zero-point fluctuations of the Josephson plasma and the rather large escape rate out of the zero-voltage state due to quantum tunneling. We test the predictions of the RCSJ model on the classical superconductors lead, indium, aluminum, and cadmium.     

Photon Fluctuations and Photographic Noise

Photographic emulsions are found to have experimentally-measured detective quantum efficiencies with peak values of less than 3%. Although such low values have been demonstrated to be not far removed from the highest values attainable with high-latitude on/off detectors of the silver halide type, they have nevertheless given rise to widely conflicting opinions concerning the influence on photographic granularity of the photon fluctuations in the exposure. This is essentially due to the complexity of the photographic process, which obscures the statistical processes which are inherent to the input/output relationship of the photon/grain interaction.

General arguments are developed which indicate the inevitability of a causal relationship between photon noise and granularity. Calculations are made of the quantitative contribution to detector noise from the photon fluctuations for a hypothetical detector having intrinsic properties which approximate to those of practical photographic emulsions.     

Squeezing and Antibunching in Phase-matched Many-atom Resonance Fluorescence

Abstract

We present two approaches to the correlation properties of the fluorescence field emitted by a many-atom source. The first approach is an extension of resonance-fluorescence theory, while the second one is based on scattering theory. Both approaches lead to an understanding of why the ‘anomalous’ correlation properties associated with squeezing and antibunching appear when some phase-matching condition is satisfied and why this condition is the four-wave-mixing one. We show that the effect of atomic motion can be taken into account in the scattering approach and that the many-atom antibunching effect cannot be considered as Doppler-free.