Manuel Vogel

Trapped Ion Oscillation Frequencies as Sensors for Spectroscopy

The oscillation frequencies of charged particles in a Penning trap can serve as sensors for spectroscopy when additional field components are introduced to the magnetic and electric fields used for confinement. The presence of so-called “magnetic bottles” and specific electric anharmonicities creates calculable energy-dependences of the oscillation frequencies in the radiofrequency domain which may be used to detect the absorption or emission of photons both in the microwave and optical frequency domains. The precise electronic measurement of these oscillation frequencies therefore represents an optical sensor for spectroscopy. We discuss possible applications for precision laser and microwave spectroscopy and their role in the determination of magnetic moments and excited state life-times. Also, the trap-assisted measurement of radiative nuclear de-excitations in the X-ray domain is discussed. This way, the different applications range over more than 12 orders of magnitude in the detectable photon energies, from below μeV in the microwave domain to beyond MeV in the X-ray domain.

Radio-Frequency Spectroscopy: Penning-Trap Mass Spectrometry

This chapter takes a short look at mass spectrometry in Penning traps, which to some extent is one specific application of radio-frequency spectroscopy of the particle oscillations in the trap. We have a brief look at precision mass spectrometry, and then discuss mass spectrometry as an analytical tool for a quantitative determination of the trap content.

Magnetic Bottles as Implemented in Penning Traps

This chapter takes a look at the effects and possible implementations of specific magnetic field geometries, mainly of so-called ‘magnetic bottles’ which are a key ingredient to the application of the continuous Stern-Gerlach effect in Penning traps.

Motion of a Single Particle in an Idealised Penning Trap

This chapter is concerned with the motion that is performed by a single confined test particle in a Penning trap. For now we disregard any realisation of a Penning trap and see it as the abstract combination of an ideally homogeneous static magnetic field (B_0) perfectly aligned with a quadrupolar electrostatic potential U that creates a harmonic well across a ‘characteristic trap size’ d. We are concerned only with the motion of a single test particle of mass m and electric charge q in such an arrangement. Later we will discuss the effects that arise when each of these idealisations are dropped.

Radio-Frequency Spectroscopy: Outreach

This chapter gives a short review of the spectroscopic techniques that are specific to Penning traps, since they make dedicated use of the confining fields and their controllable properties. In particular, we show how precise measurements of the oscillation frequencies of particles in the radio-frequency domain may be used to infer spectroscopic information in the optical and microwave domains.

A Bit of History and Context

This chapter gives a brief account of the history of the Penning trap, the central characters involved in its development, and presents the main fields of operation of such traps together with a discussion of the sense in which the word ‘confinement’ needs to be understood in this context. It also clarifies some of the most important terminology and introduces the main ingredients of a quantitative description of confinement properties.

Application of the Continuous Stern Gerlach Effect: Magnetic Moments

This chapter briefly reviews the measurements of magnetic moments that have been performed by application of the continuous Stern-Gerlach effect to a single particle confined in a Penning trap with a magnetic bottle.

Motional Cooling in Penning Traps

The possibility to cool the motions of confined particles is one key motivation for the use of Penning traps, particularly in precision spectroscopy in any frequency domain. Here, we discuss the notion of a particle temperature, its measurement in different experimental situations, and review the most important cooling techniques applied in Penning traps.

Particle Ensemble Density: Rotating Wall

The particle number density and shape of an ensemble of confined in a Penning trap can be controlled by the so-called ‘rotating wall technique’, which is a specific, non-resonant excitation of the ensemble’s rotation. Here, we briefly discuss the requirements, technical implementations, and the phenomenology of such a rotating wall, mainly when used for compression of the confined ensemble.

Hyperbolic and Cylindrical Penning Traps

The oldest Penning trap geometry in use is the hyperbolic shape, which provides good confinement properties by design, however was difficult to machine to high precisions at the time of its introduction, and offers limited access for particles and laser beams. Thus, cylindrical designs were brought forward, including more open structures. Here, we briefly review the hyperbolic and the most important forms of cylindrical Penning traps. Following that, we will have a look at variations on the concept and at the confinement properties.