The central goal of the research program was to develop new theoretical frameworks in which one can study dynamical properties of two-component quantum gases. These present two significant challenges: (1) quantum gases are continuum theories (there is no lattice) and so are difficult to deal with computationally; (2) even in exactly solvable cases, their solutions are much more complicated than single-component gases. Thus multi-component quantum gases require new approaches, both for pen-and-paper calculations and computational approaches.
To address the first challenge, computational approaches were developed for non-equilibrium quantum gases. To remove the second challenge, we first focused on developing such methods for single-component quantum gases. Two cases were considered, the Lieb-Liniger Bose gas and the perturbed Ising theory. Using exact solutions of these models, new algorithms were developed that enabled the study of both equilibrium and non-equilibrium dynamics of these gases.
In the perturbed Ising theory, the numerical approach was used to study equilibrium dynamical correlation functions and non-equilibrium dynamics. In equilibrium, results were compared to inelastic neutron scattering on CoNb2O6, whose low-energy effective description is precisely the perturbed Ising theory. In non-equilibrium, sudden changes of an applied magnetic field were studied, revealing a surprising absence of thermalization. This discovery has interesting potential applications for quantum information storage.
The Lieb-Liniger model presented a number of challenges as compared to the perturbed Ising theory. Two new computational approaches were developed to tackle non-equilibrium dynamics. These new methods can tackle reasonably numbers of particles, are model agnostic, and versatile. They open the door to simulating non-equilibrium dynamics measured in experiments.
Paralleling the development and application of new numerical algorithms, a number of analytical studies were undertaken of multi-component gases, both in- and out-of-equilibrium.
It was illustrated that an effective coupled two-component quantum gas describes the dynamical conductivity of cuprate superconductors. This was an unexpected application of quantum gas physics to a long-standing and enigmatic problem. Another effective quantum gas description was used to study topological phases of spin ladders. These are interesting as their boundaries support Majorana zero modes (MZMs), a potential platform for quantum computing. We revealed a surprise: Some non-topological phases of the spin ladder are, in fact, topological phases of the quantum gas. In the spin ladder, however, the boundary MZMs of these phases are forbidden to form by symmetry constraints. Knowing this, one can make these MZMs reappear by relaxing the constraints. We showed that this can be realized in realistic lattice systems.
The non-equilibrium physics of a multi-component quantum gas was also studied in the context of quantum chromodynamics (QCD). This explored a link between the physics of the perturbed Ising theory and QCD, allowing us to show that non-thermal states carry over to QCD. This strengthens the link between confinement and the absence of thermalization established earlier.
Results of the research program were disseminated via: (1) Published articles, (2) Formal talks, seminars and poster presentations, (3) Press releases, popular summaries and accessible articles, (4) Formal and informal interactions with MSc and PhD students, (5) Outreach & community engagement. There is significant potential for future exploitation of the results, which is enabled via:
(a) Results detailed in ten publications, and works to follow, in a manner which is clear and reproducible;
(b) Detailed descriptions of new algorithms, which can be immediately exploited by the community.
Results of the program will be immediately exploited by a graduate student at the University of Amsterdam, who works on topics closely related to the program.
