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Dynamics of two-component quantum gases

Periodic Reporting for period 1 - TwoCompQuaGas (Dynamics of two-component quantum gases)

Reporting period: 2017-10-01 to 2019-09-30

Quantum mechanics revolutionized the 20th century, leading to an understanding of equilibrium states of matter – from the familiar solids, liquids and gases, to exotic ones such as superconductivity. This knowledge lead to myriad technological developments that enable the modern world around us, such as the transistors that underpin computer processors and NMR machines that allow high-resolution scans of the body. While there still remain mysteries, the general organizing principles for equilibrium phases of matter are well understood.

In the 21st century, non-equilibrium quantum physics has emerged as the new forefront in research. At heart such research aims to answer: How are the properties of a given material modified when it is driven out of equilibrium? This might occur, for example, when a laser is shone on its surface, or heat is applied to one end. In such a scenario, is it possible to abandon some of the equilibrium organizing principles, and in doing so realize completely new phases of matter? If yes, can we realize new phases of matter with unusual or useful properties? These questions are central to much contemporary research, and this project.

In this project, we study both the equilibrium and non-equilibrium properties of quantum gases. Quantum gases are ubiquitous in nature, describing collections of particles that move and interacting with another. Experimentally they can be realized by cooling and bring together many atoms, forming a so-called cold atomic gas. Quantum gases also arise as the effective low-energy description of almost any quantum system. This includes, for example, the electrons in a material that move by hopping between different atoms – despite experiencing the crystal lattice, at low-energies they behave as if they are in quantum gas. So, by understanding the properties of quantum gases we can gain insight into many different physical problems.

The project focus is to understand properties of multi-component quantum gases, where each particle has internal degrees of freedom that describe, say, the spin state of the electron or the hyperfine level of a cold atom. While such gases are very common, they present significant theoretical challenges and understanding their properties requires the development of new pen-and-paper and computational methods. The main objective of the project is develop these new methods, apply them to obtain new insights, and extend them to treat ever more challenging problems.
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.
The results produced as part of the program can be exploited in future works and have significant potential to provide interesting insights. The algorithms produced to tackle non-equilibrium dynamics are model agnostic, so can be applied to multi-component quantum gases or problems with a different structure. They also can treat reasonable numbers of particles, in a computationally efficient manner, opening the door to direct simulation of cold atoms experiments.

The topic of non-thermal states in theories with confinement has generated considerable impact, motivating numerous works by other groups. The results of the program significantly contribute to understanding of a fundamental topic, thermalization, and helped the community to question long-held beliefs about thermalization and its absence in quantum systems. These insights, among others, may play an important role in the development of quantum information storage technologies.