Nonlinear eigenmodes of a non-equilibrium harmonic oscillator

Abstract

We investigate theoretically the quantum oscillator-like states recently observed experimentally in polariton condensates (Nat. Phys. 8, 190 (2012)). We consider a complex Gross-Pitaevskii type model which includes the effects of self-interactions, and creation and decay of exciton-polaritons. We develop a perturbation theory for approximate solutions to this non-equilibrium condensate model and compare the results with numerically calculated solutions for both repulsive and attractive polariton-polariton interactions. While the nonlinearity has a weak effect on the mode selection their density profiles are modified at moderate gain strengths and becomes more dominant when a very large gain of polaritons implies an extended cloud with high condensate densities. Finally, we identify the relation of the observed patterns to the input pump configuration, and suggest this may serve as a generalized NOR gate in the tradition of optical computing.

Bright solitons in non-equilibrium coherent quantum matter

“…large occupation numbers of the condensed phase. Both phenomenological mean field models are connected by Taylor expanding the pumping term stated in [48] to the first order as outlined in [16]. Now, starting from (2.2) we approximate/simplify the complex terms of the condensate wave equation (3.1) by the reservoir and decay of particles as in [16,41],…”

“…In the last two decades, the phase transition of many-body systems to a BE condensed state has become feasible within a great variety of different physical systems such as solid-state light-matter systems, various species of atoms and molecules and for gases of photons or classical waves [3][4][5][6]. Among the most intriguing properties of all these condensed coherent matter states are regimes of frictionless flow (superfluidity) [7] below a critical velocity [8,9] or the response to motion via elementary excitations such as quantized vortex rings, quantum vortices and lattices thereof, dark and bright solitons [9][10][11][12][13][14][15][16] depending on the nature of the entities constituting them, such as variable inter-particle interactions due to Feshbach resonances when applying certain external fields in atomic and polariton condensates [17,18] or local particle sources and sinks in non-equilibrium condensates of exciton-polaritons [4,19] or atoms [20]. In turn the out of equilibrium aspect of open quantum systems as well as the nature of interactions between the coherent particles is key for the possible pattern formations in those condensates and thus the properties of its excitations [2,4,14].…”

“…Effective mechanisms to generate excitations in general BEC within the Gross-Pitaevskii (GP) mean-field parameter regime [2,4] are important tools for investigations on their properties both experimentally and theoretically [31] and carry the possibility for applications, e.g. in optical computing [16,32]. Vortices with quantized circulation in superfluids are a key example of a topologically stable excitation in a two-dimensional BEC system guided by a nonlinear Schrödinger-type equation.…”

Fractional quantum mechanics in polariton condensates with velocity-dependent mass

“…To introduce the concept of generalized kinetic energy we turn to the solid state system of polariton Bose-Einstein (BE) condensates -macroscopically occupied single mode states that highlight properties of fundamental quantum mechanics ranging from quantum harmonic oscillators [8,9] to interference [10,11] while providing control over key system parameters [12][13][14][15]. We show that the type of kinetic energy in Schrödinger like models is of fundamental importance for the modes and particularly for non-equilibrium polariton condensate behavior at different locations of the dispersion.…”