Asymmetric Structures in Systems of Non-equilibrium Bose-Einstein Condensates

In this thesis, we investigate the nature and applications of systems of interacting Bose-Einstein condensates. The focus of the work is on non-equilibrium condensates that exist within gain-dissipative systems, such as polaritonic or photonic condensates. We first elucidate the nature of an “asymmetric dyad”. In such a structure, two interacting condensates have unequal densities and a nontrivial phase difference, despite being pumped with equal intensity. Examining a generic gain-saturation model, we present a linear stability analysis which revealed that the nonlinearity of the system is responsible for the formation of such stable asymmetric states. The effect of the coupling strength in transitioning the system between its various possible states is then examined. This includes an analysis of non-stationary states, revealing the transition from periodic to chaotic oscillations. Following this, we introduce a more complex model that includes reservoir dynamics and present a series of bifurcation diagrams showing regions of parameter space in which asymmetric dyads form. We then show that asymmetric stationary states can be used to combine discrete and continuous degrees of freedom within a single system. This is achieved by interacting two asymmetric dyads with each other through weak couplings between their individual condensates. The density asymmetry within each asymmetric dyad provides a discrete degree of freedom for the system, while each condensate’s individual phase provides a continuous degree of freedom. The behaviour of systems of three and four equally coupled condensates are then investigated. The analysis revealed, in both cases, a family of exotic ground state configurations in which the condensates have unequal densities. We propose that such exotic structures can be considered a type of artificial molecule. We then study the nature of longer chains of interacting asymmetric dyads, showing that such dyads can be employed as the fundamental unit in an Ising chain. Numerical simulations reveal the effect of the weak, inter-dyad coupling strength on the condensate densities and the alignment of condensate phases. We then propose a model of a physical random number generator, constructed using chains of such dyads to represent a binary string in which the orientation of density asymmetry specifies each binary value. We show that the two possible directions of the final dyad orientation are equally likely and that slight modifications of the pumping strength at one condensate site can ensure that this remains the case even in the presence of small asymmetries in the physical sample. It was also found that by modifying the weak, external couplings, one can bias the likelihood of dis-aligned to aligned asymmetric dyads in a precise way. This enabled the construction of three example chains of dyads demonstrating both uniform and biased random number distributions. Finally, we present a separate piece of work examining the effectiveness of a gain-dissipative algorithm in finding the ground state of traditional and modified Möbius ladder graphs comprised of non-equilibrium condensates.

Name dc:type.qualificationname

Doctor of Philosophy (PhD)

Level dc:type.qualificationlevel

Doctoral

Grantor dc:publisher.institution

University of Cambridge

Year dc:date.issued

2022

Author dc:creator

• Johnston, Alexander

Advisor dc:contributor.advisor

• Berloff, Natalia

• Bose-Einstein condensates
• Polariton condensates
• Non-equilibrium systems

Licence

• https://www.rioxx.net/licenses/all-rights-reserved/

Language dc:language

eng

DOI dc:identifier.doi

https://doi.org/10.17863/CAM.89071

OAI identifier oai:identifier

oai:www.repository.cam.ac.uk:1810/341645