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Improving Quantum Clocks via Semidefinite Programming

Mike Mullan, National Institute of Standards and Technology

(Session 10a : Saturday from 4:30pm-5:00pm)

Abstract. The accuracies of modern quantum logic clocks have surpassed those of standard atomic fountain clocks. These clocks also provide a greater degree of control, as before and after clock queries, we are able to apply arbitrary unitary operations and measurements. Here, we take advantage of this freedom and present a numerical technique designed to increase the accuracy of these clocks by optimizing over these choices of quantum operations. We use a greedy approach, minimizing the phase variance of a noisy classical oscillator with respect to a perfect frequency standard after a single interrogation step; we do not optimize over sequences of interrogations nor over the time of each step. In contrast to prior work, which derived asymptotically optimal strategies under the assumption that all classical oscillator states are equiprobable, we are able to consider the more realistic situation where we have some prior knowledge of the frequency of this oscillator, either from experimental considerations or previous measurements. Additionally, we are able to compare clocks with varying numbers of ions and those subject to multiple, coherent queries. Our technique is based on the semidefinite programming formulation of quantum query complexity, a method first developed in the context of deriving algorithmic lower bounds. The application of semidefinite programming to an inherently continuous problem like that considered here requires discretization; we derive bounds on the error introduced and show that it can be made suitably small. While we can only simulate small systems, many quantum logic clocks, like the highly accurate Al+ optical clock at NIST, use relatively few ions and are therefore natural candidates for the techniques developed here. This work is in collaboration with Manny Knill and Till Rosenband.