Advancements in nanoscale engineering of oxide interfaces and heterostructures have led to discoveries of emergent phenomena and new artificial materials. Combining the strengths of reactive molecular-beam epitaxy and pulsed-laser deposition, we show here, with examples of Sr 1+x Ti 1-x O 3+δ , Ruddlesden-Popper phase La n+1 Ni n O 3n+1 (n = 4), and LaAl 1+y O 3(1+0.5y) /SrTiO 3 interfaces, that atomic layer-by-layer laser molecular-beam epitaxy significantly advances the state of the art in constructing oxide materials with atomic layer precision and control over stoichiometry. With atomic layer-by-layer laser molecular-beam epitaxy we have produced conducting LaAlO 3 /SrTiO 3 interfaces at high oxygen pressures that show no evidence of oxygen vacancies, a capability not accessible by existing techniques. The carrier density of the interfacial two-dimensional electron gas thus obtained agrees quantitatively with the electronic reconstruction mechanism.npj Quantum Materials (2017) 2:10 ; doi:10.1038/s41535-017-0015-x INTRODUCTION Technological advances in atomic-layer control during oxide film growth have enabled the discoveries of new phenomena and new functional materials, such as the two-dimensional (2D) electron gas at the LaAlO 3 /SrTiO 3 interface, 1, 2 and asymmetric three-component ferroelectric superlattices. 3,4 Reactive molecular-beam epitaxy (MBE) and pulsed-laser deposition (PLD) are the two most successful growth techniques for epitaxial heterostructures of complex oxides. PLD possesses experimental simplicity, low cost, and versatility in the materials to be deposited. 5 Reactive MBE employing alternately-shuttered elemental sources (atomic layerby-layer MBE, or ALL-MBE) can control the cation stoichiometry precisely, thus producing oxide thin films of exceptional quality. [6][7][8] There are, however, limitations in both techniques. Reactive MBE can use only source elements whose vapor pressure is sufficiently high, excluding a large fraction of 4d and 5d metals. In addition, ozone is needed to create a highly oxidizing environment while maintaining low-pressure MBE conditions, which increases the system complexity. On the other hand, conventional PLD using a compound target often results in cation off-stoichiometry in the films. 9, 10 In this paper we present an approach that combines the strengths of reactive MBE and PLD: atomic layer-by-layer laser MBE (ALL-Laser MBE) using separate oxide targets. Ablating alternately the targets of constituent oxides, for example SrO and TiO 2 , a SrTiO 3 film can be grown one atomic layer at a time. Stoichiometry for both the cations and oxygen in the oxide films can be controlled. Although the idea of depositing atomic layers by PLD has been explored since the early days of laser MBE, 11,12 we show that levels of stoichiometry control and crystalline perfection rivaling those of