Single-shot measurement of quantum optical phase

Although the canonical phase of light, which is defined as the complement of photon number, has been described theoretically by a variety of distinct approaches, there have been no methods proposed for its measurement. Indeed doubts have been expressed about whether or not it is measurable. Here we show how it is possible, at least in principle, to perform a single-shot measurement of canonical phase using beam splitters, mirrors, phase shifters and photodetectors.Comment: This paper was published in PRL in 2002 but, at the time, was not placed on the archive. It is included now to make accessing this paper easie

The fundamental cycle of concept construction underlying various theoretical frameworks

In this paper, the development of mathematical concepts over time is considered. Particular reference is given to the shifting of attention from step-by-step procedures that are performed in time, to symbolism that can be manipulated as mental entities on paper and in the mind. The development is analysed using different theoretical perspectives, including the SOLO model and various theories of concept construction to reveal a fundamental cycle underlying the building of concepts that features widely in different ways of thinking that occurs throughout mathematical learning

Growth, yield and Fusarium wilt resistance of six FHIA tetraploid bananas (Musa spp.) grown in the Australian subtropics

Six tetraploid hybrids from Fundación Hondureña de Investigación Agrícola (FHIA) were evaluated in Australia over a five year period. They included three AAAA hybrids (FHIA-02, FHIA-17 and FHIA-23) and three AAAB hybrids (FHIA-01, FHIA-18 and SH-3640.10) and they were compared with industry standards, ‘Williams’ (AAA, Cavendish subgroup) and ‘Lady Finger’ (AAB, Pome subgroup). They were screened for their resistance to Fusarium wilt race 1 and subtropical race 4 caused by the pathogen Fusarium oxysporum f.sp. cubense and they were also grown for several cycles on farms not infested with Fusarium wilt to record their agronomic characteristics. The AAAB hybrids, all derived from female parent ‘Prata Anã’ (AAB, Pome subgroup) were the most resistant to both races of Fusarium wilt and were very productive in the subtropics. They were significantly more productive than ‘Lady Finger’, which was susceptible to both races of Fusarium wilt. The AAAA hybrids, with the exception of FHIA-02 which was very susceptible to Fusarium wilt and displayed the poorest agronomic traits of the six hybrids, produced bunch weights as good as Cavendish but were significantly slower to cycle. FHIA-17 and FHIA-23, both derived from the female parent ‘Highgate’ (AAA, Gros Michel subgroup), were also significantly more resistant to Fusarium wilt than ‘Gros Michel’, while FHIA-17 demonstrated a level of resistance similar to ‘Williams’ and FHIA-23 was intermediate between ‘Lady Finger’ and ‘Williams

Creation of macroscopic quantum superposition states by a measurement

We propose a novel protocol for the creation of macroscopic quantum superposition (MQS) states based on a measurement of a non-monotonous function of a quantum collective variable. The main advantage of this protocol is that it does not require switching on and off nonlinear interactions in the system. We predict this protocol to allow the creation of multiatom MQS by measuring the number of atoms coherently outcoupled from a two-component (spinor) Bose-Einstein condensate.Comment: 4 pages (revtex4), 2 figure

Measuring the elements of the optical density matrix

Most methods for experimentally reconstructing the quantum state of light involve determining a quasiprobability distribution such as the Wigner function. In this paper we present a scheme for measuring individual density matrix elements in the photon number state representation. Remarkably, the scheme is simple, involving two beam splitters and a reference field in a coherent state.Comment: 6 pages and 1 figur

Genetic Variation Among Vegetative Compatibility Groups of Fusarium oxysporum f. sp. cubense Analyzed by DNA Fingerprinting

Genetic variation within a worldwide collection of 208 isolates of Fu-sarium oxysporum f. sp. cubense, representing physiological races 1, 2, 3, and 4 and the 20 reported vegetative compatibility groups (VCGs), was analyzed using modified DNA amplification fingerprinting. Also characterized were 133 isolates that did not belong to any of the reported VCGs of F. oxysporum f. sp. cubense including race 3 isolates from a Heliconia species and isolates from a symptomatic wild banana species growing in the jungle in peninsular Malaysia. The DNA fingerprint patterns were generally VCG specific, irrespective of geographic or host origin. A total of 33 different genotypes were identified within F. oxysporum f. sp. cu-bense; 19 genotypes were distinguished among the isolates that belonged to the 20 reported VCGs, and 14 new genotypes were identified among the isolates that did not belong to any of the existing VCGs. DNA fingerprinting analysis also allowed differentiation of nine clonal lineages within F. oxysporum f. sp. cubense. Five of these lineages each contained numerous closely related VCGs and genotypes, and the remaining four lineages each contained a single genotype. The genetic diversity and geographic distribution of several of these lineages of F. oxysporum f. sp. cubense suggests that they have coevolved with edible bananas and their wild diploid progenitors in Asia. DNA fingerprinting analysis of isolates from the wild pathosystem provides further evidence for the coevolution hypothesis. The genetic isolation and limited geographic distribution of four of the lineages of F. oxysporum f. sp. cubense suggests that the pathogen has also arisen independently, both within and outside of the center of origin of the host

Generation of arbitrary quantum states of traveling fields

We show that any single-mode quantum state can be generated from the vacuum by alternate application of the coherent displacement operator and the creation operator. We propose an experimental implementation of the scheme for traveling optical fields, which is based on field mixings and conditional measurements in a beam splitter array, and calculate the probability of state generation.Comment: 1 Table and 2 Postscript figures, using Latex; modifications and changes in Figure 2, Table 1 and Eqs. 11-13,17,18,2

Quantum jumps in hydrogen-like systems

In this paper it is shown that the Lyman-$\alpha$ transition of a single hydrogen-like system driven by a laser exhibits macroscopic dark periods, provided there exists an additional constant electric field. We describe the photon-counting process under the condition that the polarization of the laser coincides with the direction of the constant electric field. The theoretical results are given for the example of $^4{He}^+$. We show that the emission behavior depends sensitively on the Lamb shift (W.E. Lamb, R.C. Retherford, Phys. Rev. 72, 241 (1947)) between the $2s_{1/2}$ and $2p_{1/2}$ energy levels. A possibly realizable measurement of the mean duration of the dark periods should give quantitative information about the above energy difference by using the proposed photon-counting process.Comment: 7 pages RevTeX + 2 figures Phys. Rev A accepte