Demonstrating geometric phases with a smarphone

Modern smartphones are versatile data collection devices that have become increasingly valuable in experimental physics. Equipped with micro-electromechanical system (MEMS) inertial sensors, they can measure accelerations, rotations, magnetic fields, pressure, and even sound and light levels. In this paper, we leverage the gyroscope functionality of a smartphone to design two experiments that demonstrate geometric phases in classical mechanics. The first experiment simulates the geometric phase of the Foucault pendulum by placing a smartphone on a turntable inclined at an angle. By measuring the integral of the angular velocity along an axis perpendicular to the smartphone, we obtain the angle of parallel transport on a sphere at latitude ( heta), corresponding to the rotation of the pendulum's plane of oscillation.

The second experiment models the rotation of light polarization in an optical fiber using a smartphone. Instead of propagating light through a coiled fiber, we slide a smartphone along a flexible helical track, analogous to an optical fiber winding around a cylinder. The gyroscope records the angular velocity along the smartphone's axis, allowing us to compute the Berry phase angle through integration. While this method introduces small experimental errors due to manual sliding, the measured phase remains consistent with theoretical predictions.