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arXiv:2410.10501 · Physical Review A

Topological chiral edge states in a synthetic dimension of atomic trap states

David G. Reid, Christopher Oliver, Patrick Regan, Aaron Smith, Thomas Easton, Grazia Salerno, Giovanni Barontini, Nathan Goldman, Hannah M. Price

Published Mar 3, 2025• 3 citations
arXivHTMLPDF

Abstract

A key hallmark of quantum Hall physics is the existence of topological chiral states at the system boundary. Signatures of these edge states have been experimentally observed in cold atoms by using different approaches, including notably that of “synthetic dimensions” in which internal states are coupled together and reinterpreted as sites along an artificial spatial dimension. However, previous atomic synthetic dimension implementations have been limited to relatively small system sizes with inflexible boundaries. In this paper, we propose instead how to use a synthetic dimension of atomic trap states to observe chiral edge states in a large quantum Hall system with a tunable edge. We present numerical simulations for relevant experimental parameters, showing how this scheme may be used to probe the properties and robustness of the edge states to defects. Our work opens the way for future experiments in topological physics with synthetic dimensions, while also providing new ways to manipulate and control highly excited trap states.

DOI
10.1103/physreva.111.033301

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A key hallmark of quantum Hall physics is the existence of topological chiral states at the system boundary. Signatures of these edge states have been experimentally observed in cold atoms by using different approaches, including notably that of “synthetic dimensions” in which internal states are coupled together and reinterpreted as sites along an artificial spatial dimension. However, previous atomic synthetic dimension implementations have been limited to relatively small system sizes with inflexible boundaries. In this paper, we propose instead how to use a synthetic dimension of atomic trap states to observe chiral edge states in a large quantum Hall system with a tunable edge. We present numerical simulations for relevant experimental parameters, showing how this scheme may be used to probe the properties and robustness of the edge states to defects. Our work opens the way for future experiments in topological physics with synthetic dimensions, while also providing new ways to manipulate and control highly excited trap states.
Quantum Hall physics is at the heart of research on both matter and artificial systems, such as cold atomic gases, with nontrivial topological order. We report on the observation of a chiral edge current by transferring atomic wave packets simultaneously to opposite edges of a synthetic Hall system realized in the two-dimensional state space formed by one spatial and one synthetic dimension encoded in the J=6J=6J=6 electronic spin of erbium atoms. To characterize the system, the Hall drift of the employed atomic Bose-Einstein condensate in the lowest Landau-like level is determined. The topological properties are verified by determining the local Chern marker, and upon performing low-lying excitations both cyclotron and skipping orbits are observed in the bulk and edges, respectively. Future prospects include studies of novel topological phases in cold-atom systems.
Chiral edge states are a hallmark of quantum Hall physics. In electronic systems, they appear as a macroscopic consequence of the cyclotron orbits induced by a magnetic field, which are naturally truncated at the physical boundary of the sample. Here we report on the experimental realization of chiral edge states in a ribbon geometry with an ultracold gas of neutral fermions subjected to an artificial gauge field. By imaging individual sites along a synthetic dimension, encoded in the nuclear spin of the atoms, we detect the existence of the edge states and observe the edge-cyclotron orbits induced during quench dynamics. The realization of fermionic chiral edge states opens the door for edge state interferometry and the study of non-Abelian anyons in atomic systems.
Since the experimental realization of synthetic gauge fields for neutral atoms, the simulation of topologically nontrivial phases of matter with ultracold atoms has become a major focus of cold-atom experiments. However, several obvious differences exist between cold-atom and solid-state systems, for instance the small size of the atomic cloud and the smooth confining potential. In this article we show that sharp boundaries are not required to realize quantum Hall or quantum spin Hall physics in optical lattices and, on the contrary, that edge states in a smooth confinement exhibit additional interesting properties, such as spatially resolved splitting and merging of bulk bands and the emergence of robust auxiliary states in bulk gaps to preserve the topological quantum numbers. In addition, we numerically validate that these states are robust against disorder. Finally, we analyze possible detection methods, with a focus on Bragg spectroscopy, to demonstrate that the edge states can be detected and that Bragg spectroscopy can reveal how topological edge states are connected to the different bulk bands.
Recent experimental advances in the field of cold atoms led to the development of novel techniques for producing synthetic dimensions and synthetic magnetic fields, thus greatly expanding the utility of cold atomic systems for exploring exotic states of matter. In this paper we investigate the possibility of using experimentally tunable interactions in such systems to mimic the physics of Majorana chains, currently a subject of intense research. Crucially to our proposal, the interactions, which are local in space, appear non-local in the synthetic dimension. We use this fact to induce coupling between counter-propagating edge modes in the quantum Hall regime. For the case of attractive interactions in a system composed of two tunneling-coupled chains, we find a gapless quasi-topological phase with a doubly-degenerate ground state. While the total number of particles in the system is kept fixed, this phase is characterized by strong fluctuations of the pair number in each chain. Each ground state is characterized by the parity of the total particle number in each chain, similar to Majorana wires. However, in our system this degeneracy persists for periodic boundary conditions. For open boundary conditions there is a small splitting of this degeneracy due to the single-particle hopping at the edges. We show how subjecting the system to additional synthetic flux or asymmetric potentials on the two chains can be used to control this nonlocal qubit. We propose experimental probes for testing the nonlocal nature of such a qubit and measuring its state.
I will report on very recent experiments performed at LENS with ultracold 173Yb Fermi gases in artificial gauge fields. We have engineered Raman transitions between different 173Yb nuclear spin states to synthesize an effective lattice dynamics in a finite-sized “extra dimension”, which is encoded in the internal degree of freedom of the atoms [1]. By using this innovative approach, we have realized synthetic magnetic fields for effectively-charged fermions in ladder geometries with a variable number of legs. Direct imaging of the individual legs allowed us to demonstrate the emergence of chiral edge currents and to observe edge-cyclotron orbits propagating along the edges of the system [2], thus providing a direct evidence of a fundamental feature of quantum Hall physics in condensed-matter systems. A. Celi et al., Synthetic gauge fields in synthetic dimensions, Phys. Rev. Lett. 112, 043001 (2014). M. Mancini et al., Observation of chiral edge states with neutral fermions in a synthetic Hall ribbon, preprint arXiv:1502.02495 (2015). ∗Speaker †Corresponding author: fallani@lens.unifi.it sciencesconf.org:bec2015:67564
We propose to simulate and detect quantum anomalous Hall phase with ultracold atoms in a one-dimensional optical lattice, with the other synthetic dimension being realized by modulating spin-orbit coupling. We show that the system manifests a topologically nontrivial phase with two chiral edge states which can be readily detected in this synthetic two-dimensional system. Moreover, it is interesting that at the phase transition point there is a flat energy band and this system can also be in a topologically nontrivial phase with two Fermi zero modes existing at the boundaries by considering the synthetic dimension as a modulated parameter. We also show how to measure these topological phases experimentally in ultracold atoms. Another model with a random Rashba and Dresselhaus spin-orbit coupling strength is also found to exhibit topological nontrivial phase, and the impact of the disorder to the system is revealed.