We apply an online optimization process based on machine learning to the production of Bose-Einstein condensates (BEC). BEC is typically created with an exponential evaporation ramp that is optimal for ergodic dynamics with two-body s-wave interactions and no other loss rates, but likely sub-optimal for real experiments. Through repeated machine-controlled scientific experimentation and observations our ‘learner’ discovers an optimal evaporation ramp for BEC production. In contrast to previous work, our learner uses a Gaussian process to develop a statistical model of the relationship between the parameters it controls and the quality of the BEC produced. We demonstrate that the Gaussian process machine learner is able to discover a ramp that produces high quality BECs in 10 times fewer iterations than a previously used online optimization technique. Furthermore, we show the internal model developed can be used to determine which parameters are essential in BEC creation and which are unimportant, providing insight into the optimization process of the system.

We investigate quantum synchronization theoretically in a system consisting of two cold ions in microtraps. The ions' motion is damped by a standing-wave laser while also being driven by a blue-detuned laser which results in self-oscillation. Working in a nonclassical regime, where these oscillations contain only a few phonons and have a sub-Poissonian number variance, we explore how synchronization occurs when the two ions are weakly coupled using a probability distribution for the relative phase. We show that strong correlations arise between the spin and vibrational degrees of freedom within each ion and find that when two ions synchronize their spin degrees of freedom in turn become correlated. This allows one to indirectly infer the presence of synchronization by measuring the ions' internal state.Introduction. Two macroscopic self-oscillators synchronize when their relative phase locks to a fixed value [1]. Important studies of synchronization effects were carried out using lasers [2], with arrays of Josephson junctions [3] and over the last few years much attention has been devoted to exploring synchronization in micromechanical oscillators [4]. Recently, theoretical work has begun to explore synchronization in the quantum regime [5][6][7][8][9][10][11][12][13][14]: the formation of a relative phase preference between two (or more) weakly coupled quantum oscillators operating in a regime far from the classical correspondence limit. Differences between classical and quantum predictions for the synchronization of van der Pol oscillators have been identified in the case where the oscillators are only weakly excited [5]. Nevertheless, many important questions about quantum synchronization remain open, such as how it should be quantified and how it can best be probed experimentally.Cold ions in microtraps provide a natural platform for exploring synchronization in the quantum regime [5]. The generation of self-oscillations in the motional state of ions, phonon lasing, has already been observed [15]. Furthermore, precise control of trapping potentials of the individual ions can now be achieved with microtraps [16] allowing the vibrational frequencies of individual ions and the coupling between different ions to be tuned. Here, we investigate synchronization in two trapped-ion phonon lasers which are pumped in a similar way to that demonstrated in recent experiments [15].We identify a parameter regime where phonon lasing of an individual ion occurs with just a few quanta leading to a nonclassical state of the phonons and investigate the emergence of synchronization in this regime when a weak interion coupling is introduced (weak as it is the slowest time scale in the system). Our model includes two of the electronic levels of the ions used in the pumping process (which we refer to as "spin"), allowing us to uncover strong correlations which arise between the electronic and vibrational degrees of freedom of the individual ions. We study the degree of synchronization as the strength and detuning of the pumping lase...