Atomic clocks with nuclear transitions: theoretical aspects

The proposed research project will provide theoretical support for the experimental investigations aiming to identify the low-energy 7.6 eV vacuum ultraviolet transition in the 229-Thorium nucleus and for the creation of a new frequency standard based on this transition. Experimental activity in this direction has already started in the Institute for Atomic and Subatomic Physics, Vienna, Austria, in the framework of the FWF START project "Nuclear Physics with a Laser: 229-Thorium", (Thorsten Schumm). Results of the theoretical investigations will also be relevant for other experimental efforts performed by international collaborators of Thorsten Schumm (E.R. Hudson , University of California, USA; E. Peik, PTB, Germany; M. Chapman, Georgia Institute of Technology, USA). The main goals of the proposed research are: 1. Develop a simulation method for fluorescence and/or transmission of UV radiation in a Thorium-doped UV crystal. Consider the possible methods for excitation and detection of the ultraviolet transition in 229-Thorium nucleus and select the optimal ones. 2. Compare the result of simulation with experimental results and fit unknown parameters. 3. Investigate theoretically the interaction of Thorium nuclei with coherent radiation (frequency combs and cw regime). Consider various schemes of high-resolution spectroscopy. Quantify and reduce systematic effects. 4. Compare possible methods of laser stabilization and identify/develop the optimal one applicable to the transition in the Thorium nucleus. Determine the parameters that will limit clock performance. The proposed research project is oriented mainly on the needs of the experimental group, and will be carried out in direct everyday contact between theorist and experimentalists. Experimentalists will deliver information about possible experimental details: what parameters of incoming "probe" radiation (power, pulse duration, repetition rate, spectral characteristics, etc.) can be obtained by available sources, what level of signal is detectable by available detectors, what are the basic properties of a sample (crystal doped by Thorium ions), and what geometry is possible in experiments. The simulation and optimization of the experimental strategy will be performed using this information. For the investigation of nuclei excitation processes we plan to use the theoretical instrumentary of density matrix formalism. This formalism allows us to take into account the real Zeeman structure of nuclear levels, incoming radiation polarization, and systematic effects Thorium nuclei experience in a crystal-lattice environment such as relaxations, shifts, and broadenings.