Using a density matrix approach, we study the simplest systems that display both gain and feedback: clusters of 2 to 5 atoms, one of which is pumped. The other atoms supply feedback through multiple scattering of light. We show that, if the atoms are in each other's near field, the system exhibits large gain narrowing and spectral mode redistribution. The observed phenomena are more pronounced if the feedback is enhanced. Our system is to our knowledge the simplest exactly solvable microscopic system which shows the approach to laser oscillation.
We present an extension of the T-matrix approach to scattering of light by a three-level system, using a description based on a Master equation. More particularly, we apply our formalism to calculate the T-matrix of a pumped three-level atom, providing an exact and analytical expression describing the influence of a pump on the light scattering properties of an atomic three-level system.
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PDO is in the process of transforming its well and urban planning by adopting digital technologies and Artificial Intelligence (AI) to improve organizational efficiency and maximize business value through faster quality decision. In 2020, PDO collaborated with a third-party contractor to provide a novel solution to an industry-wide problem: "how to effectively plan 100's of wells in a congested brownfield setting?". This paper describes an innovative AI-assisted well planning method that is a game-changer for well planning in mature fields, providing efficiency in urban and well trajectory planning. It was applied in one of PDO's most congested fields with a targeted infill of 43m well spacing. The novel well planning method automatically designs and optimizes well trajectories for 100-200 new wells while considering surface, subsurface and well design constraints. Existing manual workflows in the industry are extremely time consuming and sequential (multiple man-months of work) - particularly for fields with a congested subsurface (350+ existing wells in this case) and surface (limited options for new well pads). These conventional and sequential ways of working are therefore likely to leave value on the table because it is difficult to find 100+ feasible well trajectories, and optimize the development in an efficient manner. The implemented workflow has the potential to enable step change in improvements in time and value for brownfield well and urban planning for all future PDO developments. The innovative AI assisted workflow, an industry first for an infill development of this size, evaluates, generates and optimizes from thousands of drillable trajectories to an optimized set for the field development plan (based on ranked value drivers, in this case, competitive value, cost and UR). The workflow provides a range of drillable trajectories with multi-scenario targets and surface locations, allowing ranking, selection and optimization to be driven by selected metrics (well length, landing point and/or surface locations). The approach leads to a step change reduction in cycle time for well and urban planning in a complex brownfield with 100-200 infill targets, from many months to just a few weeks. It provides potential game-changing digital solutions to the industry, enabling improved performance, much shorter cycle times and robust, unbiased well plans. The real footprint and innovation from this AI-assisted workflow is the use of state-of-the-art AI to enhance team collaboration and integration, supporting much faster and higher quality field development decisions. This paper describes a novel solution to integrated well planning. This is a tangible example of real digital transformation of a complex, integrated and multi-disciplinary problem (geologists, well engineers, geomatics, concept engineers and reservoir engineers), and only one of very few applied use cases in the industry. This application also gives an example of "augmented intelligence", i.e. how AI can be used to truly support integrated project teams, while the teams remain fully in control of the ultimate decisions. The success of this approach leans on the integrated teamwork across multiple technical disciplines, not only involving PDO's resources, but also WhiteSpace Energy as a 3rd party service provider. The enhanced collaboration allowed all parties to highlight their constraints in an integrated way from the start, strengthening the technical discussion between disciplines and learning from each constraint impact and dependencies. (e.g. dog leg severity). In summary, the change in process flow moving from a sequential well planning and urban planning method to an iterative and fast AI solution – including all technical considerations from beginning represented for PDO an added value of over 6 months of direct cycle time HC acceleration.
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