Dynamical Fermionization and Bose-Fermi Oscillation in One-Dimensional Bose Gases
Open Access
- Author:
- Wilson, Joshua
- Graduate Program:
- Physics
- Degree:
- Doctor of Philosophy
- Document Type:
- Dissertation
- Date of Defense:
- February 21, 2020
- Committee Members:
- David S. Weiss, Dissertation Advisor/Co-Advisor
David S. Weiss, Committee Chair/Co-Chair
Marcos Rigol, Committee Member
Vincent Henry Crespi, Committee Member
Tae-Hee Lee, Outside Member
Nitin Samarth, Program Head/Chair - Keywords:
- Tonks Girardeau
Lieb-Liniger
Many-body Quantum Dynamics
Dynamical Fermionization - Abstract:
- The integrable Lieb-Liniger Hamiltonian, describing particles in one-dimension (1D) interacting via delta-function potentials, can be physically realized in the experimental medium of ultra-cold bosons trapped in a two-dimensional optical lattice. In the strongly coupled regime of this Hamiltonian, interacting bosons and non-interacting fermions (NIF) share the same many-body wavefunction up to an absolute value. This correspondence implies that observables which depend on the wavefunction squared will be the same for both systems, while other observables (like momentum distributions) will generally be quite different. Dynamical fermionization, occurs when the highly peaked momentum distribution of a harmonically confined 1D Bose gas has its confinement removed suddenly. As the gas expands in 1D, the interactions among particles decrease, and the asymptotic momentum distribution is the same as the initial, conserved, momentum distribution of a NIF gas in the same trap. I will discuss an experiment we performed in which we observed dynamical fermionization. Our results are in remarkable agreement with exact theory in the infinite coupling limit. Additionally, our experiment constitutes the first ever direct measurement of a distribution of rapidities, the set of conserved quantities which characterizes integrable quantum systems. In this dissertation I will also discuss Bose-Fermi oscillations of the momentum distribution. This is the response of a 1D Bose gas when its harmonic trapping is quenched to a new non-zero depth. The spatial distribution of the bosons begins to breath in spatial size, and the momentum distribution oscillates back and forth, from being like an equilibrium bosonic distribution to having the shape of an equilibrium NIF distribution. This momentum oscillation occurs twice for each breathing oscillation in space. Stark changes in coupling strength during the oscillation prevent strong-coupling theory from exactly matching the results in our experiment. There is, however, a marked agreement between the fermionic shape during the oscillation for both theory and experiment. This shape is seemingly robust against changes in the coupling strength. Our experiments on a Lieb-Liniger gas have led to observations of phenomena that had long been theoretically predicted, but never verified experimentally. We also have results that can provide a testing ground for current and future theoretical approaches to understanding the Lieb-Liniger Hamiltonian, and potentially other more complicated many-body quantum systems.