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arXiv:2006.15846 · Physical Review Letters

Probing the Hall Voltage in Synthetic Quantum Systems

Maximilian Buser, Sebastian Greschner, Ulrich Schollwöck, Thierry Giamarchi

Published Jan 19, 2021• 19 citations
arXivHTMLPDF

Abstract

In the context of experimental advances in the realization of artificial magnetic fields in quantum gases, we discuss feasible schemes to extend measurements of the Hall polarization to a study of the Hall voltage, allowing for direct comparison with solid state systems. Specifically, for the paradigmatic example of interacting flux ladders, we report on characteristic zero crossings and a remarkable robustness of the Hall voltage with respect to interaction strengths, particle fillings, and ladder geometries, which is unobservable in the Hall polarization. Moreover, we investigate the site-resolved Hall response in spatially inhomogeneous quantum phases.

DOI
10.1103/physrevlett.126.030501

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In the context of experimental advances in the realization of artificial magnetic fields in quantum gases, we discuss feasible schemes to extend measurements of the Hall polarization to a study of the Hall voltage, allowing for direct comparison with solid state systems. Specifically, for the paradigmatic example of interacting flux ladders, we report on characteristic zero crossings and a remarkable robustness of the Hall voltage with respect to interaction strengths, particle fillings, and ladder geometries, which is unobservable in the Hall polarization. Moreover, we investigate the site-resolved Hall response in spatially inhomogeneous quantum phases.
Quantum simulators are attracting great interest because they promise insight into the behavior of quantum many-body systems that are prohibitive for classical simulations. The generic output of quantum simulators are snapshots, obtained by means of projective measurements. These provide new information, such as full distribution functions, that goes beyond the more commonly evaluated expectation values of observables while adding shot-noise uncertainty to the latter. Hence, a central goal of theoretical efforts must be to predict these exact same quantities that can be measured in experiments. Here, we report on a snapshot-based study of particle currents in quantum lattice models with a conserved number of particles. It is shown how the full probability distribution of locally resolved particle currents can be obtained from suitable snapshot data. Moreover, we investigate the Hall response of interacting bosonic flux ladders, exploiting snapshots drawn from matrix-product states. Flux ladders are minimal lattice models, which enable microscopic studies of the Hall response in correlated quantum phases, and they are successfully realized in current quantum-gas experiments. Using a specific pattern of unitary two-site transformations, it is shown that the Hall polarization and the Hall voltage can be faithfully computed from a realistic number of snapshots obtained in experimentally feasible quench and finite-bias simulations.
We characterize the Hall response of non-interacting fermionic MMM-leg ladders in the presence of an artificial magnetic flux, that can be realized in one-dimensional optical lattices supplemented with a synthetic dimension. We focus on the Hall imbalance, which can be directly measured in experiments with ultracold fermionic atoms. At relatively large synthetic flux we find a dependence of the density that contrasts with previously reported density-independent behavior. In particular, the Hall imbalance can be significantly enhanced in the limit of small density of particles (or holes), or it can vanish and change sign at specific fluxes, which we obtain analytically in the large inter-leg coupling regime. This behavior is explained in terms of Lifshitz transitions of the band structure, where the number of Fermi points changes as a function of the flux and density. Finally, we explore the connection between these transitions and the so-called Meissner-vortex transition for fermionic ladders by computing the site-resolved leg and rung currents and discussing the similarities and differences with the bosonic counterpart.
We explore the behavior of the Hall response of a Bose-Hubbard triangular ladder in a magnetic field as a function of the repulsive on-site atomic interactions. We consider a wide range of interaction strengths, from the weakly interacting limit to the hard-core regime. This is realized by computing the Hall polarization following the quench of a weak linear potential, which induces the flow of a current through the system, using time-dependent matrix product state numerical simulations. We complement our understanding in the regime of small magnetic fields by analytical calculations of the equilibrium value of the Hall polarization for noninteracting bosonic atoms and under a mean-field assumption. The Bose-Hubbard triangular flux ladder exhibits a rich phase diagram, containing Meissner, vortex, and biased-chiral, superfluid phases. We show that the Hall response can be employed to fingerprint the various chiral states, the frustration effects occurring in the limit of strong interactions, and the phase boundaries of the equilibrium phase diagram.
We theoretically study the Hall effect on interacting M-leg ladder systems, comparing different measures and properties of the zero temperature Hall response in the limit of weak magnetic fields. Focusing on SU(M) symmetric interacting bosons and fermions, as relevant for, e.g., typical synthetic dimensional quantum gas experiments, we identify an extensive regime in which the Hall imbalance Δ_{H} is universal and corresponds to a classical Hall resistivity R_{H}=-1/n for a large class of quantum phases. Away from this high symmetry point we observe interaction driven phenomena such as sign reversal and divergence of the Hall response.
The Hall effect, which originates from the motion of charged particles in magnetic fields, has deep consequences for the description of materials, extending far beyond condensed matter. Understanding such an effect in interacting systems represents a fundamental challenge, even for small magnetic fields. In this work, we used an atomic quantum simulator in which we tracked the motion of ultracold fermions in two-leg ribbons threaded by artificial magnetic fields. Through controllable quench dynamics, we measured the Hall response for a range of synthetic tunneling and atomic interaction strengths. We unveil a universal interaction-independent behavior above an interaction threshold, in agreement with theoretical analyses. The ability to reach hard-to-compute regimes demonstrates the power of quantum simulation to describe strongly correlated topological states of matter.
We explore the behavior of interacting bosonic atoms in an optical lattice subject to a large artificial magnetic field. We extend earlier investigations of this system where the number of magnetic flux quanta per unit cell $\ensuremath{\alpha}$ is close to a simple rational number [R. N. Palmer and D. Jaksch, Phys. Rev. Lett. 96, 180407 (2006)]. Interesting topological states such as the Laughlin and Read-Rezayi states can occur even if the atoms experience a weak trapping potential in one direction. An explicit numerical calculation near $\ensuremath{\alpha}=1/2$ shows that the system exhibits a striped vortex lattice phase of one species, which is analogous to the behavior of a two-species system for small $\ensuremath{\alpha}$. We also investigate methods to probe the encountered states. These include spatial correlation functions and the measurement of noise correlations in time-of-flight expanded atomic clouds. Characteristic differences arise which allow for an identification of the respective quantum Hall states. We furthermore discuss that a counterintuitive flow of the Hall current occurs for certain values of $\ensuremath{\alpha}$.