Master Presentation: Vlad-Haralambie Ispas

Master Presentation:
Vlad-Haralambie Ispas

Date:
Friday 17 July 2026

Time:
13:00-14:30

Location:
Feringa Building, 5616.0144

Title:
Gyroscopic Stabilization and Spin Contrast of a Cylindrical Nanorotor in Stern–Gerlach Interferometry

Abstract:
This thesis develops a semiclassical and quantum description of a spin-embedded cylindrical nanorotor in a one-loop Stern--Gerlach interferometer.

We first establish the required rotational framework, including the relation between space-fixed and body-fixed frames, the $zxz$ Euler parametrization, angular velocity, the inertia tensor, the rotational kinetic metric, canonical momenta and the Hamiltonian dynamics of an axially symmetric rigid body. The nanorotor is then coupled to an embedded spin-$1$ defect and to external magnetic fields. The defect position and spin frame are treated within the complete three-dimensional rigid-body geometry, allowing for an off-center spin and a possible misalignment between the defect and cylinder axes.

The internal spin dynamics is described by the complete $3\!\times\!3$ Hamiltonian containing the Zeeman interaction and the axial and transverse zero-field splittings. Its instantaneous eigenvalues define adiabatic spin-dependent potential-energy surfaces. An analytical $2\!\times\!2$ Hamiltonian is derived through a Feshbach reduction and compared with the complete model, while retaining transverse-field corrections commonly neglected in simplified treatments. From the same branch energies, we derive the translational forces and rotational torques, including diamagnetic confinement, gravity, finite-size corrections and spin--rotation coupling.

The reference one-dimensional model is recovered only as a controlled centered, aligned and small-transverse-field limit. Its small-angle expansion identifies the gyroscopic-stability condition and shows how an initial rotation around the symmetry axis suppresses spin-dependent libration and rotational mismatch. The magnetic-trap parameters and Stern--Gerlach protocol are subsequently calibrated numerically. Classical trajectories are propagated using fourth-order Runge--Kutta integration, while Monte Carlo sampling quantifies their sensitivity to preparation uncertainty, trap parameters and control errors.

Finally, the motional and rotational degrees of freedom are quantized around the conditional classical trajectories, allowing the final wavefunction overlap, spin contrast and finite-temperature rotational effects to be evaluated.