Nontrivial evolution and geometric phase for an orbital angular momentum qutrit

Area of Science:

• Quantum Information Science
• Quantum Optics
• High-Dimensional Quantum Systems

Background:

• Photonic orbital angular momentum (OAM) is a key resource for high-dimensional quantum information processing.
• Geometric phase (GP) is essential for fault-tolerant quantum computation, but its measurement in OAM states is underdeveloped.
• Existing methods for GP measurement are limited in the OAM state space.

Purpose of the Study:

• To propose an experimental scheme for detecting GP shifts in OAM qutrit states.
• To explore a novel cyclic evolution path within the SU(3)/U(2) parameter space for OAM states.
• To demonstrate the potential of twisted photons in high-dimensional quantum computation.

Main Methods:

• Theoretical proposal for detecting GP shifts in OAM qutrit states.
• Utilizing a combination of X-gates, dove prisms, and double cylindrical lenses for cyclic evolution.
• Employing a designed Sagnac interferometer for analyzing the resultant geometric phase.

Main Results:

• A scheme to detect GP shifts resulting from cyclic evolution of OAM qutrit states is proposed.
• The proposed method involves a nontrivial cyclic evolution path within the SU(3)/U(2) parameter space.
• The Sagnac interferometer successfully analyzes the geometric phase acquired during the evolution.

Conclusions:

• The proposed scheme provides a method for measuring geometric phase in OAM qutrit states.
• This work has potential applications in high-dimensional quantum computation using twisted photons.
• The study contributes to understanding the geometric structure of optical systems utilizing OAM.