This project will study the interface between quantum mechanics and thermodynamics. This is a cutting edge research direction because the way quantum systems come into equilibrium, or "thermalize", remains a mystery. The picture is clearer for isolated classical systems. For example, in classical dynamics if a system of interacting particles explores all possible configurations, then it can thermalize. Such a system is also said to be "chaotic" and to lack "integrability", which means the particle trajectories cannot be predicted with a sequence of integrals. For integrable systems, future dynamics can be predicted. Interestingly, however, if the conditions for integrability are weakly broken, there are still scenarios for which stable dynamics can be predicted. This is a consequence of the celebrated Kolmogorov-Arnold-Moser (KAM) theorem, which shows that small perturbations are insufficient to render the system chaotic. This effect is largely responsible for the orbital stability for our own solar system. Since quantum physics describes dynamics too, it is natural to ask if there is an analogue to the KAM theorem for quantum systems. This project will explore this question by first creating a quantum integrable system using a gas of ultracold atoms confined in one-dimensional traps. Changes to the system's behavior will then be caused by adjusting magnetic long-range interactions between the atoms. The time it takes for the gas to thermalize after a momentum kick will provide a measure of the breakdown of integrability in the system. This work will have an impact on quantum information processing, and other technologies that rely on the predictability of quantum dynamics. Students working on this project will also benefit from research training that will prepare them for jobs in high tech industry or academic careers.
To achieve these goals, this team will confine atoms of dysprosium (Dy), the most magnetic element, in two-dimensional optical lattices. The energy gap to the first transverse motional excited state will be larger than the gas temperature and chemical potential, ensuring that the gas in each cigar-shaped tube is in the quasi-1D regime. For large-enough scattering lengths, the gas will approximately realize the Tonks-Girardeau limit of the integrable Lieb-Liniger model. A magnetic field will set the angle of the dipoles with respect to the tube axis. The magnitude of the magnetic dipole-dipole interaction can be tuned by this angle, allowing us to control the integrability-breaking perturbation strength. A Bragg diffraction pulse will split the gas in two. These parts of the gas will collide every 10 ms due to weak longitudinal harmonic confinement. This dipolar version of the quantum Newton's cradle experiment will allow this team to explore analogs of the classical KAM scenario in the quantum realm. Moreover, spin-orbit coupling (previously demonstrated by this group with Dy) will be introduced in attempts to induce p-wave superfluidity near Feshbach resonances in one-dimensional gases of fermionic Dy. In this way, one-dimensional atomic systems will be used to explore novel types of superfluids that arise when the spin of the atom depends on the direction the atom is moving. This is important because exotic superfluids such as these support unusual excitations that may be useful for quantum information processing.
