Observation of Berry’s Geometric Phase by Neutron Interferometry

On the 25th anniversary of Berry’s historic papers on the geometric phase, I discuss here our neutron interferometry experiment in which this phase is clearly separated from the dynamical phase. The connection of this experiment to the observation of the sign reversal of the wave function of a fermion during a 2π precession in a magnetic field by three groups independently in 1975 is discussed.     

Phase-shift algorithm for white-light interferometry insensitive to linear errors in phase shift

White-light interference has changes in fringe contrast. When phase-shift techniques are applied to white-light interference, the phase-shift algorithm which can extract the phase accurately under the contrast changes is required. There is often another requirement that the phase shift between frames should not be restricted to π/2. Computer simulations show that the well-known algorithms have non-negligible errors under both requirements. To find an algorithm which will satisfy the requirements, I extract individual terms (I _j ∓ I _k ) in an algorithmic equation by considering symmetry of light intensity against phase, where I _j is light intensity just after the j-th phase shift. Using computer simulations, I search for appropriate coefficients by which the terms are multiplied in the equation, finally finding an algorithm which satisfies both the requirements with the phase shift used.     

A phase unwrapping technique for object relief determination

Phase shifting methods are widely used in photomechanics to analyse fringe patterns obtained from interferometry, moiré, etc. The phase is determined by modulo 2π and an unwrapping process is needed. An algorithm is presented which avoids most of the inconsistency of the phase field. It can be applied to the relief determination of virtually any object shape. In this paper, two applications are performed using the projection of a parallel line grating with a pitch equal to 4 mm. The accuracy is shown to be around 0…1 mm.     

Formulation and picture of quantum phase

Based on the concept of classical phase, we formulate a new explanation for the quantum phase from the quantum mechanical point of view. The quantum phase is the canonically conjugate variable of an angular momentum operator, which corresponds to the angular position φ in an actual physical space with a classical reference frame, but it takes a complex exponential form e ^iφ≡cosφ+i sinφ in the abstract Hilbert space of a quantum reference frame. This formulation is simply the famous Euler formula in a complex number field. In particular, when φ = π/2, the correlative quantum phase is a unitary pure imaginary number e ^iπ/2≡cos(π/2)+i sin(π/2) ≡ i. By using a photon state-vector function that is the general solution of photon Schr?dinger equation and can completely describe a photon’s behavior, we discuss the relationship between the angular momentum of a photon and the phase of the photon; we also analyze the intrinsic relationship between the macroscopic light wave phase and the microscopic photon phase.     

Decay of a scalar σ meson near the critical end point in the PNJL model

Properties of a scalar a meson are investigated in the two-flavor Nambu-Jona-Lasinio model with the Polyakov loop (PNJL). Model analysis of the phase diagram of strong interacting matter is performed. The temperature dependence of the σ → ππ decay width is studied at the zero chemical potential and near the critical end point. The calculated strong coupling constant g _σππ and the decay width are compared with available experimental data and other model results. Nonthermal enhancement of the total decay width is noted for the σ meson near the critical end point when the condition m _σ ≥ 2m _π is broken.     

Two photons into π<Superscript>0</Superscript>π<Superscript>0</Superscript>

We perform a theoretical study based on dispersion relations of the reaction γγ → π ⁰ π ⁰ emphasizing the low-energy region. We discuss how the ƒ ⁰(980) signal emerges in γγ → ππ within the dispersive approach and how this fixes to a large extent the phase of the isoscalar S-wave γγ → ππ amplitude above the threshold. This allows us to make sharper predictions for the cross-section at lower energies and our results could then be used to distinguish between different ππ isoscalar S-wave parameterizations with the advent of new precise data on ππ → π ⁰ π ⁰. We compare our dispersive approach with an updated calculation employing the unitary chiral perturbation theory (U _gC PT). We also pay special attention to the role played by the σ-resonance in γγ → ππ and calculate its coupling and width to γγ, for which we obtain Γ(σ → γγ) = (1.68 ± 0.15) keV.     

Pion-Nucleon Interaction and Two-Pion-Exchange Three-Nucleon Forces

We compare the πN scattering amplitudes that underlie 2π-exchange three-nucleon forces (TBFs) with the experimental πN amplitudes in the form of partial-wave phase shifts and subthreshold invariant amplitudes. The amplitudes of the Tucson-Melbourne and Brazil TBFs when taken on-pion-mass-shell predict scattering lengths at threshold and phase shifts (slightly) above threshold which are in good agreement with the experimental amplitudes, except for the S-waves. Partial wave amplitudes from separable potentials, recently employed in a 2π-TBF calculation, were continued below threshold, summed into invariant amplitudes, and compared with the experimental amplitudes in this kinematic region, which is most relevant to the kinematics of TBFs. The separable-potential invariant amplitudes, in contrast to those of TM and Brazil TBFs, do not compare well quantitatively with the experimental amplitudes in this region but have a similar qualitative behaviour. The very small TBF effect in the triton of the separable-potential amplitude appears to be due to the πNN vertex function rather than the πN amplitude itself. Received April 27, 1994; revised August 2, 1994; accepted for publication August 31, 1994     

The sign of interband interaction and stability of the superconducting ground state in the multiband model

Summary It is stressed that the stability of the superconducting ground state in the two-band model is guaranteed for both signs of the leading interband interactionW. Thereby the requirement for the energy minimum fixed the phase differences of two order parameters as |ϕ₁-ϕ₂|=0,2π, … ifW<0 and |ϕ₁-ϕ₂|=π 3π, … ifW>0, and this difference is reflected in the ground-state wave function.     

Population difference study of few-cycle laser pulse propagating in near-resonant two-level atom medium

We have theoretically studied the propagation of few-cycle laser pulse in near-resonant two-level atom medium by solving Maxwell-Bloch equations with a predictor-corrector finite-difference time-domain method. Hyperbolic secant pulses with area 2π, 4π and 6π are adopted as the initial inputs. For large pulse area, the carrier-wave Rabi flopping occurs in the faster split 2π pulse and causes spectra broadening which subsequently increases the induced population difference. Combined with the contribution of periodically varying carrier-envelop phase, the maximum of population difference gives rise to an interesting phenomenon.     

ππ scattering and the meson resonance spectrum

A ππ, ˉKK, and ρρ(ωω) fully coupled channel model is used to predict the lowest isospin S, P, D, F-wave phase shifts and inelasticities for elastic ππ scattering from threshold to 2.0 GeV. As input the S-matrix is required to exhibit poles corresponding to the meson resonance table of the Particle Data Group. As expected, the ππ inelasticity is very strongly related to the opening of the ˉK channel near 1 GeV, and the opening of ρρ(4π) and ωω(6π) channels in the 1.5 GeV region. The predictions of this model are compared to the various elastic ππ→ππ amplitudes, that were obtained from analyses of π⁻ p →π⁻π⁺n data. The role of the various resonances, in particular the glueball candidate f ₀(1500) and the f _J(1710) is investigated. Received: 19 November 1997