Veer Chand Rakhecha

On measuring the Pancharatnam phase. II. SU(2) polarimetry

Abstract We put forth a polarimetric method for determining the Pancharatnam phase in a general non-cyclic SU (2) evolution.

On measuring the Pancharatnam phase. I. Interferometry

Abstract The Pancharatnam connection prescribes the phase acquired by a quantal system in any arbitrary evolution. The correct method of observing the Pancharatnam phase with an interferometer is delineated.

Neutron polarimetric separation of geometric and dynamical phases

Abstract We present a neutron polarimetric experiment clearly demarcating geometric and dynamical phases. Here a relative rotation between two identical π spin flippers produces a pure geometric phase and their relative translation yields a pure dynamical phase. The experiment agrees with theory to within about 1%.

Geometric phase in neutron interferometry

Abstract We revisit a recent proposal by Wagh to test the dependence of spinor phase on the orientation of the precession axis. We identify the spinor phase shift originating from the misalignment between π-flippers in the two branches of a neutron interferometer with a geometric phase. We also interpret quantum beats in polarised neutron interferometry observed by Rauchs group as a manifestation of a time-dependent geometric phase shift.

Nonadiabatic geometric spinor phase in rotating magnetic fields

Abstract We describe exact cyclic spinor evolutions in cyclic and noncyclic magnetic Hamiltonians, each resulting in a pure geometric phase. These evolutions are realisable in neutron interferometric and polarimetric experiments.

A polarised SUSANS facility to study magnetic systems

Using a right-angled magnetic air prism, we have achieved a separation of ∼10 arcsec between ∼2 arcsec wide up and down-spin peaks of 5.4 Å neutrons. The polarised neutron option has thus been introduced into the SUSANS instrument. Strongly spindependent SUSANS spectra have been observed over ±1.3 × 10−4 Å−1 range for several magnetic alloy samples. Spatial pair-distribution functions for the up and down-spins as well as the nuclear and magnetic scattering length density distributions in the micrometer domain, have been deduced from these spectra.

Magnon dispersion measurement in MnFe2O4

Abstract Using the polarised neutron diffraction technique, the acoustic magnon dispersion curve in MnFe 2 O 4 has been measured up to 30% of the zone boundary and discussed in terms of a polynomial expression for the magnon energy and the Heisenberg model.

Geometric phasea la Pancharatnam

In mid-1950s, Pancharatnam [1] encountered the geometric phase associated with the evolution along a geodesic triangle on the Poincaré sphere. We generalize his 3-vertex phase and employ it as the fundamental building block, to geometrically construct a general ray-space expression for geometric phase. In terms of a reference ray used to specify geometric phase, we delineate clear geometric meanings for gauge transformations and gauge freedom, which are generally regarded as mere mathematical abstractions.

Geometric phase as a simple closed-form integral

For a general evolution of a quantal system, the geometric phase measured with reference to a given initial state is derived as an integral of a function of the pure state density operator by invoking the Pancharatnam connection continuously.

Geometric Phase Associated with Spinor Rotations

It was thirty five years ago that Pancharatnam1 encountered an “unexpected geometrical result”, viz. the geometric phase, for polarization circuits of light on the Poincare’ sphere. Geometric phase was rediscovered recently2,3 in the context of excursions of a quantal system around closed circuits in parameter space. In this paper, we will confine our attention to the geometric phase acquired by a spinor4,5 in traversing a closed circuit on the spin sphere, with an emphasis on its observation in neutron interferometric experiments.