Entanglement in Ramsey interferometry, optical atomic clocks and trapped ions

Abstract

This thesis describes new results on the entanglement of atomic spins in Ramsey interferometry, optical atomic clocks and trapped ions. It is divided into three parts: First, we investigate improvements to conventional Ramsey interferometry with entanglement and adding only rotations of the collective spin to adjust the signal and measurement directions. The geometric degrees of freedom, connected to the rotations, are analytically optimized for a large class of generalized Ramsey protocols to allow efficient optimization of all parameters. Besides a unification of existing approaches, the main result is that there is only one new protocol, where a previously unused double inversion is applied. Studies of the local sensitivity show that this protocol reaches the fundamental quantum Fisher information limit and is yet robust against errors during preparation and measurement. In the second section we investigate the conditions under which optical atomic clocks exhibit increased long-term stability when applying weakly entangled, spin squeezed states. We discuss the common case of an atomic clock with a single ensemble, typical Brownian frequency noise and finite dead time. Theoretical modelling of the servo loop allows quantitative predictions of the optimal stability for given values of dead time and laser noise, in very good agreement with numerical simulations of the closed feedback loop. The main result is that, even with the current most stable lasers, the clock stability can only be improved for ensembles below a critical atom number of about one thousand in optical Sr lattice clocks. Even with a future improvement of the laser performance by one order of magnitude, the critical atom number still remains below 100,000. In contrast, clocks based on smaller, non-scalable ensembles, such as ion clocks, can already benefit from squeezed states with current clock lasers. Thus the last section considers the robust generation of entanglement in ion traps. An error budget including relevant experimental error sources is calculated for state-of-the-art quantum gates, driven by oscillating microwave gradients in surface traps. Amplitude modulation of the driving fields is shown to efficiently counteract the current limitations from motional mode instability. The predicted increase of the gate quality was demonstrated by the group of C. Ospelkaus at PTB Braunschweig, who measured gates with errors as low as ~ 10^(-3). In a similar approach, interactions between spin and motion can also be generated by combining oscillating rf-fields with a static magnetic field gradient. Penning traps designed for precision spectroscopy already feature large magnetic field gradients at the edge of a magnetic bottle configuration. We present parameters and conditions under which laser-free coupling of spin and quantized motion for (anti-)protons is possible at these points, in a step towards quantum logic spectroscopy for (anti-)protons.