Tulip

TULIP

TULIP (acronym for QUANTUM DESCRIPTION OF SINGLE AND INTERACTING POLARITONS) is my Stanisław Ulam fellowship research project (funded by the Polish National Agency for Academic Exchange (NAWA), project number PPN/ULM/2020/1/00235) at the University of Warsaw, on the period 1 March (2021)—27 February (2023). Magdalena Stobińska is the scientist in charge of the fellowship and for the duration of the fellowship I'm a visiting researcher at her group.

Goals

TULIP pursues three objectives. The first of them is to obtain a mathematical description of a single particle in the framework of quantum mechanics. The macroscopical description of a quantum state of polaritons, by dint of the Gross-Pitaevskii equation (GPE), breaks in the limit of few particles. In such a regime, the description is done through a Master equation (which, rather than the fields, describes their excitations). However, the fundamental hypothesis of the project it that spatial description of single quantum particles should be possible. Especially, in the light of recent experiments showing the propagation of single polaritons. The second objective is the coherent manipulation of the quantum state of the polaritons. It will guarantee that the quantum information encoded in the quantum state of the polaritons (e.g., in their polarisation degree of freedom), can be processed without being corrupted. Analysing the coherent manipulation will be done by modelling polaritons as an interacting mode of the electromagnetic field or through the Jaynes-Cummings model. Lastly, TULIP will draw from the previous two objectives: it will make use of the description of the propagation of the single polariton and the schemes to coherently manipulate its quantum state. Having this knowledge, all the ingredients will be available to design a CNOT gate based on polaritons, thus paving the way to the era of quantum polaritonics.