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A novel class of programmable integrated photonic circuits has emerged over the past years, strongly driven by approaches to tackle unsolved computing problems in the optical domain. Photonic neuromorphic and quantum computing are examples of optical systems implemented in complex photonic circuits, which are reconfigured before and during operation. However, a key building block to enable efficient reconfigurable optical network architectures is still missing: a non-volatile optical phase shifter. Here we demonstrate such an element—compatible with silicon photonics—based on the monolithic integration of BaTiO3 thin films with silicon waveguides. By manipulating ferroelectric domains in BaTiO3 with electrical control signals, we achieve analogue and non-volatile optical phase tuning with no absorption changes. We demonstrate an eight-level long-term-stable photonic device with non-destructive optical readout and switching energy as low as 4.6 pJ. With our results, an analogue non-volatile photonic element is added to the integrated photonics toolbox, enabling a new generation of power-efficient programmable photonic circuits. ISSN:1749-4885 ISSN:1749-4893