Trapped Ion Magnetic Resonance: Concepts and Designs

A novel spectroscopy of trapped ions is proposed which will bring single-ion detection sensitivity to the observation of magnetic resonance spectra and resolve the apparent incompatibility in existing techniques between high information content and high sensitivity. Methods for studying both electron spin resonance (ESR) and nuclear magnetic resonance (NMR) are designed. They assume established techniques for trapping ions in high magnetic field and observing electrically the trapping frequencies with high resolution (<1 Hz) and sensitivity (single -ion). A magnetic bottle field gradient couples the spin and spatial motions together and leads to the small spin -dependent force on the ion exploited by Dehmelt to observe directly the perturbation of the ground-state electron's axial frequency by its spin magnetic moment. A series of fundamental innovations is described to extend magnetic resonance to molecular ions ( cong 100 amu) and nuclear magnetic moments. It is demonstrated how time-domain trapping frequency observations before and after magnetic resonance can be used to make cooling of the particle to its ground state unnecessary. Adiabatic cycling of the magnetic bottle off between detection periods is shown to be practical and to allow high-resolution magnetic resonance to be encoded pointwise as the presence or absence of trapping frequency shifts. Methods of inducing spin -dependent work on the ion orbits with magnetic field gradients and Larmor frequency irradiation are proposed which greatly amplify the attainable shifts in trapping frequency. The first proposal presented builds on Dehmelt's experiment to reveal ESR spectra. A more powerful technique for ESR is then designed where axially synchronized spin transitions perform spin-dependent work in the presence of a magnetic bottle, which also converts axial amplitude changes into cyclotron frequency shifts. The most general approach presented is a continuous Stern-Gerlach effect in which a magnetic field gradient modulated at both the Larmor and cyclotron frequencies leads to cyclotron acceleration proportional to the transverse magnetic moment of a coherent state of the particle and radiation field. A preferred method of using this to observe NMR as an axial frequency shift is described. A new quantum mechanical description of ion cyclotron resonance is combined with spin degrees of freedom to provide a full description of the proposals.