Microscopy of the interacting Harper-Hofstadter model in the few-body limit (1612.05631v1)

Abstract: The interplay of magnetic fields and interacting particles can lead to exotic phases of matter exhibiting topological order and high degrees of spatial entanglement. While these phases were discovered in a solid-state setting, recent techniques have enabled the realization of gauge fields in systems of ultracold neutral atoms, offering a new experimental paradigm for studying these novel states of matter. This complementary platform holds promise for exploring exotic physics in fractional quantum Hall systems due to the microscopic manipulation and precision possible in cold atom systems. However, these experiments thus far have mostly explored the regime of weak interactions. Here, we show how strong interactions can modify the propagation of particles in a $2\times N$, real-space ladder governed by the Harper-Hofstadter model. We observe inter-particle interactions affect the populating of chiral bands, giving rise to chiral dynamics whose multi-particle correlations indicate both bound and free-particle character. The novel form of interaction-induced chirality observed in these experiments demonstrates the essential ingredients for future investigations of highly entangled topological phases of many-body systems.

• The paper demonstrates that strong interactions in a Harper-Hofstadter ladder induce distinct chiral dynamics via modified band populations.
• The paper employs quantum gas microscopy and perturbative analysis to quantify the impact of inter-particle interactions on the eigenstate spectrum.
• The paper’s findings pave the way for exploring topologically ordered matter and chiral ground states in ultracold atomic systems.

Analysis of the Interacting Harper-Hofstadter Model in the Few-Body Limit

The paper "Microscopy of the interacting Harper-Hofstadter model in the few-body limit" examines the interaction-induced modifications in particle dynamics within a ladder system described by the Harper-Hofstadter model. This model, known for capturing the physics of particles on a lattice in the presence of a magnetic field, is explored in the context of highly controllable ultracold atomic systems, offering a promising platform for studying topologically non-trivial phases of matter.

Key Contributions and Findings

In this work, the authors employ a two-dimensional optical lattice to isolate a ladder-like geometry and observe the effects of strong inter-particle interactions on chiral band populations. The experimental apparatus allows precise control over the synthetic gauge fields, tunneling parameters, and interaction strengths, thus enabling a meticulous exploration of particle propagation in the ladder structure. Key observations and contributions include:

• Chiral Dynamics and Band Populations: The paper finds that strong interactions notably affect how particles populate chiral bands. The presence of chiral bands in the Harper-Hofstadter ladder model gives rise to dynamics where motion in one dimension (along the ladder) is coupled with a bias towards specific spatial regions (legs of the ladder), reminiscent of Lorentz force effects on charged particles in a magnetic field.
• Inter-Paticle Interactions and Energie Spectrum: The interactions modify the eigenspectrum such that states exhibit both scattering and bound character. This modification provides avenues through which chiral dynamics can be induced even in situations where such dynamics would be absent in non-interacting systems despite a synthetic gauge field's presence.
• Observation of Chiral Ground States: The authors employ quantum gas microscopy to measure spatially resolved correlations, which confirm the interactions' role in generating these chiral dynamics, paving the way towards observing chiral ground states.

Numerical and Analytical Insights

The paper conducts both experimental and theoretical analyses, employing exact diagonalization methods and perturbative expansions to understand the dynamics at play deeply. Notable is a short-time perturbative expansion that yields non-trivial chiral signals dependent on the interaction strength and synthetic flux.

• Numerical Spectrum Analysis: The authors elucidate the interactions' effect on particle dynamics by analyzing eigenstate decompositions, demonstrating how interactions preferentially populate states with certain chiral trajectories.
• Perturbation Theory for Chirality: The work provides insight into the emergence of chirality through perturbative approaches, explicating how interactions introduce population imbalances that lead to the observed chiral behavior.

Implications and Future Directions

The results demonstrate critical aspects of interactions in topologically non-trivial band structures, suggesting increased control over creating and manipulating chiral bands in many-body states. This control is crucial for exploring exotic fractional quantum Hall physics in cold-atom systems, which could lead to new insights into topologically ordered matter.

Future experiments could extend these findings to larger systems or different geometries, potentially unearthing new states of matter or enabling new forms of quantum simulations. The methodological advances in manipulating synthetic gauge fields and controlling inter-particle interactions open pathways for a vast array of experimental possibilities, aligning with endeavors in quantum information science and computational many-body physics.

This paper makes significant strides toward leveraging the microscopic control inherent in cold-atom systems to probe and understand complex many-body quantum phenomena fundamentally. The experimental and analytical frameworks developed here set the stage for future investigations into topologically-protected properties and highly entangled states of matter.