© 2026 Aqora Quantum S.A.S.

Terms Privacy Legal Notice

Journal of Optics A Pure and Applied Optics

Topological phase evolving from the orbital angular momentum of ‘coiled’ quantum vortices

Constantine N. Alexeyev, M. A. Yavorsky

Published Jul 13, 2006• 28 citations

Abstract

The propagation of a scalar field that satisfies the Schrodinger equation in a coiled helical potential well is studied. It is demonstrated that on propagation the scalar wave acquires an additional phase whose value is determined only by geometric parameters of the helix. It is established that this geometric phase is proportional to the orbital angular momentum of the particle and the solid angle subtended by the trajectory of the state on the orbital Poincare sphere. It is shown that this phase increment takes place for any state with well-defined orbital angular momentum and can be obtained through a simple rotational transformation of the Schrodinger equation into some effective rotating frame. A possible way of detection of such a phase in an interferometric experiment is also discussed. A connection is made with the propagation of optical vortices in coiled few-mode optical fibres.

DOI: 10.1088/1464-4258/8/9/008

Related papers

On the gauge-invariant orbital angular momentum of vector optical vortices in the paraxial approximation and beyond

E. V. Maliutina, E. A. Vashukevich, V. A. Leonov +2 more

In this paper we present a gauge-invariant formalism for describing the spin and orbital angular momenta of scalar and vector optical vortices. The correction term, arising from consistent incorporation of the transverse vector potential's nonlocality, restores gauge invariance and makes it possible to separate the total angular momentum into spin and orbital components. We propose a method for calculating the orbital and spin angular momenta of multimode vector vortex fields and show that the orbital angular momentum of such beams contains two qualitatively different components. The polarization-independent contribution to the orbital angular momentum is related to the topological charge that determines the order of the phase singularity, while the polarization-dependent one is proportional to the helical topological charge that determines the spatial inhomogeneity of the polarization. We also discuss the quantization procedure for fields with spatially inhomogeneous polarization in terms of modes with a helical topological charge, and examine the limits of applicability of the proposed formalism.

physics.opticsCross-listedarXiv:2610.40523•Oct 30, 2026

Nontrivial evolution and geometric phase for an orbital angular momentum qutrit

Fangqing Tang, Dongkai Zhang, Lixiang Chen

Photonic orbital angular momentum (OAM) offers a promising platform for high-dimensional quantum information processing. While geometric phase (GP) is the crucial tool in enabling intrinsically fault-tolerant quantum computation, the measurement of GP using linear optics remains relatively unexplored in the OAM state space. Here, we propose an experimental scheme to detect GP shifts resulting from the cyclic evolution of OAM qutrit states. Distinguished with the conventional evolution along cyclic path on the Poincaré sphere (PS), the nontrivial evolution in our theoretical scheme is along a cyclic path residing within the SU(3)/U(2) parameter space. By employing a combination of X-gates, dove prisms, and double cylindrical lenses, we achieve the cyclic evolution and analyse the resultant GP through our designed Sagnac interferometer. Our theoretical study may find potential in high-dimensional quantum computation using twisted photons and in exploring the geometric structure of such optical systems.

Optics Express•May 15, 2024•3 citations

Wigner representation and geometric transformations of optical orbital angular momentum spatial modes

Gabriel F. Calvo

An exact Wigner representation of optical spatial modes carrying orbital angular momentum is found in closed form by exploiting the underlying SU(2) Lie-group algebra of their associated Poincaré sphere. Orthogonality relations and observables of these states are obtained within the phase space picture. Development of geometric phases on mode transformations is also elucidated.

Optics Letters•May 15, 2005•64 citations

Geometric phase evolution

Nathan A. Hagen, Luis A. Garza-Soto

Geometric phase has historically been defined using closed cycles of polarization states, often derived using differential geometry on the Poincare sphere. Using the recently-developed wave model of geometric phase, we show that it is better to define geometric phase more generally, allowing every polarized wave to have a well-defined value at any point in its path. Using several example systems, we show how this approach provides more insight into the wave's behavior. Moreover, by tracking the continuous evolution of geometric phase as a wave propagates through an optical system, we encounter a natural explanation of why the conventional Poincare sphere solid angle method uses geodesic paths rather than physical paths of the polarization state.

arXiv:2407.19887•Jul 29, 2024•0 citations

Berry's phase and orbital angular momentum

Paolo Martelli, Annalaura Fasiello, Mario Martinelli

In 1984 Berry showed that a quantum system evolving in a cyclic and adiabatic way acquires in addition to the dynamic phase also a phase which of geometric nature, depending on the path on the parameter space [1]. This geometric phase, also named Berry's phase, can be generalized to non-adiabatic situations [2] and presents some classical analogues, as in the case of the motion of a Foucault pendulum [3].

Conference on Lasers and Electro-Optics Europe & European Quantum Electronics Conference (CLEO/Europe-EQEC)•Jun 1, 2017•2 citations

Twisted superfluids in moving frame

A. Yu. Okulov

Helical waveguide filled by superfluid is shown to transform rotations of the reference frame $\vec Ω_{\oplus}$ into linear displacements of the atomic ensemble and vise versa the linear displacements of the reference frame $\vec V$ initialize rotations $\vec Ω_{\oplus}$ of ensemble. In the mean-field Gross-Pitaevskii equation with a weakly modulated gravitation potential the exact solutions for macroscopic wavefunction $Ψ$ demonstrate the emergence of $redshift$ phase factor. For helical waveguides formed by phase-conjugated optical vortices with high angular momentum $L_z=\pm \ell \hbar \sim \pm \hbar \cdot 10^{3 ÷4}$ one may expect the significant improvement of the phase-sensitivity $δϕ$ by factor containing $2 \ell$ compared to the conventional nonsingular matter-wave interferometry.

arXiv:1912.07073•Dec 15, 2019•0 citations

The propagation of a scalar field that satisfies the Schrodinger equation in a coiled helical potential well is studied. It is demonstrated that on propagation the scalar wave acquires an additional phase whose value is determined only by geometric parameters of the helix. It is established that this geometric phase is proportional to the orbital angular momentum of the particle and the solid angle subtended by the trajectory of the state on the orbital Poincare sphere. It is shown that this phase increment takes place for any state with well-defined orbital angular momentum and can be obtained through a simple rotational transformation of the Schrodinger equation into some effective rotating frame. A possible way of detection of such a phase in an interferometric experiment is also discussed. A connection is made with the propagation of optical vortices in coiled few-mode optical fibres.

In this paper we present a gauge-invariant formalism for describing the spin and orbital angular momenta of scalar and vector optical vortices. The correction term, arising from consistent incorporation of the transverse vector potential's nonlocality, restores gauge invariance and makes it possible to separate the total angular momentum into spin and orbital components. We propose a method for calculating the orbital and spin angular momenta of multimode vector vortex fields and show that the orbital angular momentum of such beams contains two qualitatively different components. The polarization-independent contribution to the orbital angular momentum is related to the topological charge that determines the order of the phase singularity, while the polarization-dependent one is proportional to the helical topological charge that determines the spatial inhomogeneity of the polarization. We also discuss the quantization procedure for fields with spatially inhomogeneous polarization in terms of modes with a helical topological charge, and examine the limits of applicability of the proposed formalism.

Photonic orbital angular momentum (OAM) offers a promising platform for high-dimensional quantum information processing. While geometric phase (GP) is the crucial tool in enabling intrinsically fault-tolerant quantum computation, the measurement of GP using linear optics remains relatively unexplored in the OAM state space. Here, we propose an experimental scheme to detect GP shifts resulting from the cyclic evolution of OAM qutrit states. Distinguished with the conventional evolution along cyclic path on the Poincaré sphere (PS), the nontrivial evolution in our theoretical scheme is along a cyclic path residing within the SU(3)/U(2) parameter space. By employing a combination of X-gates, dove prisms, and double cylindrical lenses, we achieve the cyclic evolution and analyse the resultant GP through our designed Sagnac interferometer. Our theoretical study may find potential in high-dimensional quantum computation using twisted photons and in exploring the geometric structure of such optical systems.

Geometric phase has historically been defined using closed cycles of polarization states, often derived using differential geometry on the Poincare sphere. Using the recently-developed wave model of geometric phase, we show that it is better to define geometric phase more generally, allowing every polarized wave to have a well-defined value at any point in its path. Using several example systems, we show how this approach provides more insight into the wave's behavior. Moreover, by tracking the continuous evolution of geometric phase as a wave propagates through an optical system, we encounter a natural explanation of why the conventional Poincare sphere solid angle method uses geodesic paths rather than physical paths of the polarization state.

Helical waveguide filled by superfluid is shown to transform rotations of the reference frame

\vec Ω_{\oplus}

into linear displacements of the atomic ensemble and vise versa the linear displacements of the reference frame

\vec V

initialize rotations

\vec Ω_{\oplus}

of ensemble. In the mean-field Gross-Pitaevskii equation with a weakly modulated gravitation potential the exact solutions for macroscopic wavefunction

Ψ

demonstrate the emergence of

redshift

phase factor. For helical waveguides formed by phase-conjugated optical vortices with high angular momentum

L_z=\pm \ell \hbar \sim \pm \hbar \cdot 10^{3 ÷4}

one may expect the significant improvement of the phase-sensitivity

δϕ

by factor containing

2 \ell

compared to the conventional nonsingular matter-wave interferometry.