Pancharatnam, Bargmann and Berry phases-a retrospective

While Pancharatnam discovered the geometric phase in 1956, his work was not widely recognized until its endorsement by Berry in 1987, after which it received wide appreciation. However, because Pancharatnam's paper is unusually difficult to follow, his work has often been misinterpreted as referring to an evolution of states of polarization, just as Berry's work focused on a cycle of states, even though this consideration does not appear in Pancharatnam's work. We walk the reader through Pancharatnam's original derivation and show how Pancharatnam's approach connects to recent work in geometric phase. It is our hope to make this widely cited classic paper more accessible and better understood.While Pancharatnam discovered the geometric phase in 1956, his work was not widely recognized until its endorsement by Berry in 1987, after which it received wide appreciation. However, because Pancharatnam's paper is unusually difficult to follow, his work has often been misinterpreted as referring to an evolution of states of polarization, just as Berry's work focused on a cycle of states, even though this consideration does not appear in Pancharatnam's work. We walk the reader through Pancharatnam's original derivation and show how Pancharatnam's approach connects to recent work in geometric phase. It is our hope to make this widely cited classic paper more accessible and better understood.

arXiv:2301.04359Journal of the Optical Society of America AMar 22, 202317 citations

Pancharatnam-Berry phase in neutrino mixing

T. M. Manosh, N. Shaji, R. B. Thayyullathil +1 more

The Pancharatnam - Berry phase (PBP) of purely geometric origin appears as a reparametrization invariant quantity of ray Space. In this article, we investigate the properties exhibited by PBP in neutrino mixing. We map the neutrino flavour modes to independent flavour vacuum states and compute PBP using Bargmann invariant. We derive the exact formula for PBP in two flavour approximation using the kinematic approach. Our result reproduces previous results of Blasone et al. under cyclic condition. Inspired by the work of Mukunda and Simon, we investigate the total and dynamical phases separately. This method leads us to identify the existence of nodal points in the mixing parameter space. At nodal points, PBP changes by a value $π$ , and it originates from the total phase. We report the direct relation between nodal points and MSW resonance, giving physical meaning to nodal points. Our analysis shows the ability of PBP to differentiate between different mass hierarchies and set numerical bounds to $Δm^2$ by changing total energy. We extend our studies to three flavour model and found that PBP is sensitive to the Dirac $CP$ phase ( $δ_{CP}$ ). Using our $N$ -qubit architecture of the $N$ -flavour neutrino model, one can immediately study the dynamical characteristics like mode entanglement between neutrino flavour modes.The Pancharatnam - Berry phase (PBP) of purely geometric origin appears as a reparametrization invariant quantity of ray Space. In this article, we investigate the properties exhibited by PBP in neutrino mixing. We map the neutrino flavour modes to independent flavour vacuum states and compute PBP using Bargmann invariant. We derive the exact formula for PBP in two flavour approximation using the kinematic approach. Our result reproduces previous results of Blasone et al. under cyclic condition. Inspired by the work of Mukunda and Simon, we investigate the total and dynamical phases separately. This method leads us to identify the existence of nodal points in the mixing parameter space. At nodal points, PBP changes by a value $π$, and it originates from the total phase. We report the direct relation between nodal points and MSW resonance, giving physical meaning to nodal points. Our analysis shows the ability of PBP to differentiate between different mass hierarchies and set numerical bounds to $Δm^2$ by changing total energy. We extend our studies to three flavour model and found that PBP is sensitive to the Dirac $CP$ phase ($δ_{CP}$). Using our $N$-qubit architecture of the $N$-flavour neutrino model, one can immediately study the dynamical characteristics like mode entanglement between neutrino flavour modes.

arXiv:2104.12632Apr 26, 20210 citations

π

, and it originates from the total phase. We report the direct relation between nodal points and MSW resonance, giving physical meaning to nodal points. Our analysis shows the ability of PBP to differentiate between different mass hierarchies and set numerical bounds to

Δm^2

by changing total energy. We extend our studies to three flavour model and found that PBP is sensitive to the Dirac

CP

phase (

δ_{CP}

). Using our

N

-qubit architecture of the

N

-flavour neutrino model, one can immediately study the dynamical characteristics like mode entanglement between neutrino flavour modes.