Emergent Quantization in Interacting Thouless Pumps
Open Access
- Author:
- Jurgensen, Marius
- Graduate Program:
- Physics
- Degree:
- Doctor of Philosophy
- Document Type:
- Dissertation
- Date of Defense:
- February 12, 2024
- Committee Members:
- Mikael Rechtsman, Chair & Dissertation Advisor
Chaoxing Liu, Major Field Member
Xingjie Ni, Outside Unit & Field Member
Jorge Sofo, Major Field Member
Mauricio Terrones, Program Head/Chair - Keywords:
- Topology
Thouless Pump
Quantization
Interactions
Nonlinearity
Solitons
Fractional
Integer - Abstract:
- Topology has revolutionized our understanding of physics: physical observables are fully defined – up to natural constants – by topological invariants and thus independent of the exact details of the device. As a general wave phenomena, topological protection has found its way into many fields of physics, including photonics, that could profit tremendously from topologically protected transport of photons given that photons are the main information carriers in today’s communication infrastructure and projected to be an integral part of next-generation on-chip computation and quantum information devices. While non-interacting/linear topological photonics has been well understood, less is known in the presence of inter-particle interactions. In optics and at high optical power, interactions between photons are mediated by an underlying medium and described in the mean-field limit via Kerr nonlinearities, with spectacular consequences, amongst others: generation of entangled photon pairs, frequency combs, and solitons, the latter being self-forming, localized nonlinear eigenstates. This dissertation pioneers the field of topologically quantized transport in interacting/nonlinear Thouless pumps – 1+1 dimensional reduced versions of the integer quantum Hall effect, where one wavevector dimension is replaced with a periodic modulation as a synthetic dimension. We show theoretically and experimentally that nonlinearity can act to quantize transport via soliton formation in Thouless pumps and the emergence of a rich plateaux structure with integer as well as fractionally quantized transport, despite a non-uniform band projection required for linear Thouless pumps. Quantization occurs as the soliton solutions at the beginning and end of each cycle are identical – apart from translation invariance. By expanding the discrete nonlinear Schrödinger equation into Wannier states, we show analytically that the center of mass of a low-power soliton, and therefore its trajectory, tracks the position of Wannier states, that are dictated by the Chern number. Using evanescently coupled waveguides, we observe integer quantized soliton transport by one unit cell, with a nonlinear phase transition to a trapped soliton at higher power due to spontaneous symmetry breaking nonlinear bifurcations. In a separate experiment and at intermediate power, we observe fractionally quantized soliton Thouless pumping with a fraction of -1/2 after one period and integer quantization of -1 after two periods, as the soliton follows the trajectory of maximally-localized multi-band Wannier states. Furthermore, we theoretically describe fractional Thouless pumping in fermionic few-particle systems with integer filling and strong repulsive interactions, when every second multi-band Wannier is occupied. Using exact diagonalization and density matrix renormalization group calculations we confirm that small systems have a degenerate ground state manifold separated from higher bands and support average pumping of 1/2 particles per period at intermediate adiabaticity. Finally, we present experimental advances in the fabrication of deep-etched two-dimensional photonic crystals in doped crystalline YAG and demonstrate the ability to fabricate large arrays with sub-micrometer lattice constants and deterministically varying etching depth.