Neuartige kryogene Penning-Falle für den Nachweis von Spin-Übergängen eines Protons und Bestimmung seines g-Faktors

This thesis presents the design, development, commissioni ng and characterization of a novel Penning trap in the framework of the experiment for the direct determination of the g -factor of a single proton. This trap is distinguished by the fact that the field lines of an external homogeneous magnetic field are distorte d around the trap center by means of a ferromagnetic ring electrode. The inhomogeneo us part of the resulting magnetic field, the so-called magnetic bottle, can be quanti fied by the the coefficient B 2 = 297(10) mT / mm² of the second-order term in the series expansion describing the field. Such an exceptionally strong field inhomogeneity is a f undamental prerequisite for the detection of the proton spin orientation via the continu ous Stern-Gerlach effect. This effect is based upon the coupling of the spin degree of freedom of the trapped proton to one of its eigenfrequencies, which occurs in the presence of the inhomogeneous magnetic field. Thus, a transition between the spin states can be detec ted as a frequency jump. The measurable change in frequency is proportional to B₂ and to the in the case of the proton extremely small ratio between its magnetic moment and its ma ss. The technical challenges due to the needed high magnetic inhomogeneity require a well -founded understanding and control of the the properties of the Penning trap and experimental conditions. The Penning trap developed in the present work allowed the first non-destructive detection of spin quantum jumps of a single trapped proton, which r epresented a breakthrough in the experiment for the direct determination of the g -factor with the aimed relative uncertainty of 10⁻⁹ . By means of a statistical method the Larmor and the cyclotron fre- quency of the proton could be measured in the inhomogeneous m agnetic field of the trap, from which the g -factor could be determined with a relative uncertainty of 8 , 9 × 10⁻⁶ . The experimental techniques and setup presented here can be transferred to an equiva- lent experiment for the determination of the g -factor of the antiproton in order to achieve the same relative uncertainty, thus tanking the first step to wards a new stringent test of CPT symmetry in the the baryonic sector