Spin Pumping and Measurement of Spin Currents in Optical Superlattices

Local Readout and Control of Current and Kinetic Energy Operators in Optical Lattices

Quantum gas microscopes have revolutionized quantum simulations with ultracold atoms, allowing one to measure local observables and snapshots of quantum states. However, measurements so far were mostly carried out in the occupation basis. Here, we demonstrate how all kinetic operators, such as kinetic energy or current operators, can be measured and manipulated with single-bond resolution. Beyond simple expectation values of these observables, the single-shot measurements allow one to access full counting statistics and complex correlation functions. Our work paves the way for the implementation of efficient quantum state tomography and hybrid quantum computing protocols for itinerant particles on a lattice. In addition, we demonstrate how site-resolved programmable potentials enable a spatially selective, parallel readout in different bases as well as the engineering of arbitrary initial states.

Quantization and its breakdown in a Hubbard-Thouless pump

Geometric properties of wave functions can explain the appearance of topological invariants in many condensed-matter and quantum systems1. For example, topological invariants describe the plateaux observed in the quantized Hall effect and the pumped charge in its dynamic analogue-the Thouless pump2-4. However, the presence of interparticle interactions can affect the topology of a material, invalidating the idealized formulation in terms of Bloch waves. Despite pioneering experiments in different platforms5-9, the study of topological matter under variations in interparticle interactions has proven challenging10. Here we experimentally realize a topological Thouless pump with fully tuneable Hubbard interactions in an optical lattice and observe regimes with robust pumping, as well as an interaction-induced breakdown. We confirm the pump's robustness against interactions that are smaller than the protecting gap for both repulsive and attractive interactions. Furthermore, we identify that bound pairs of fermions are responsible for quantized transport at strongly attractive interactions. However, for strong repulsive interactions, topological pumping breaks down, but we show how to reinstate it by modifying the pump trajectory. Our results will prove useful for further investigations of interacting topological matter10, including edge effects11 and interaction-induced topological phases12-15.

Quantum Variational Learning of the Entanglement Hamiltonian

Learning the structure of the entanglement Hamiltonian (EH) is central to characterizing quantum many-body states in analog quantum simulation. We describe a protocol where spatial deformations of the many-body Hamiltonian, physically realized on the quantum device, serve as an efficient variational ansatz for a local EH. Optimal variational parameters are determined in a feedback loop, involving quench dynamics with the deformed Hamiltonian as a quantum processing step, and classical optimization. We simulate the protocol for the ground state of Fermi-Hubbard models in quasi-1D geometries, finding excellent agreement of the EH with Bisognano-Wichmann predictions. Subsequent on-device spectroscopy enables a direct measurement of the entanglement spectrum, which we illustrate for a Fermi Hubbard model in a topological phase.

Measurement of Spin Chern Numbers in Quantum Simulated Topological Insulators

The topology of quantum systems has become a topic of great interest since the discovery of topological insulators. However, as a hallmark of the topological insulators, the spin Chern number has not yet been experimentally detected. The challenge to directly measure this topological invariant lies in the fact that this spin Chern number is defined based on artificially constructed wave functions. Here we experimentally mimic the celebrated Bernevig-Hughes-Zhang model with cold atoms, and then measure the spin Chern number with the linear response theory. We observe that, although the Chern number for each spin component is ill defined, the spin Chern number measured by their difference is still well defined when both energy and spin gaps are nonvanished.

Recovering Quantum Correlations in Optical Lattices from Interaction Quenches

Quantum simulations with ultracold atoms in optical lattices open up an exciting path toward understanding strongly interacting quantum systems. Atom gas microscopes are crucial for this as they offer single-site density resolution, unparalleled in other quantum many-body systems. However, currently a direct measurement of local coherent currents is out of reach. In this Letter, we show how to achieve that by measuring densities that are altered in response to quenches to noninteracting dynamics, e.g., after tilting the optical lattice. For this, we establish a data analysis method solving the closed set of equations relating tunneling currents and atom number dynamics, allowing us to reliably recover the full covariance matrix, including off-diagonal terms representing coherent currents. The signal processing builds upon semidefinite optimization, providing bona fide covariance matrices optimally matching the observed data. We demonstrate how the obtained information about noncommuting observables allows one to quantify entanglement at finite temperature, which opens up the possibility to study quantum correlations in quantum simulations going beyond classical capabilities.

Spatial-Translation-Induced Discrete Time Crystals

A discrete time crystal is a phase unique to nonequilibrium systems, where discrete time translation symmetry is spontaneously broken. Most conventional time crystals proposed so far rely on the spontaneous breaking of on-site symmetries and their corresponding on-site symmetry operations. In this Letter, we propose a new time crystal dubbed the "spatial-translation-induced discrete time crystal," which is realized by spatial translation and its symmetry breaking. Owing to the properties of spatial translation, in this new time crystal, various time crystal orders can only emerge by changing the filling but not changing the driving protocol. We demonstrate that the local transport of charges or spins shows a nontrivial oscillation, enabling detection and applications of time crystal orders, and also provide promising platforms including quantum circuits. Our proposal opens up a new avenue of realizing time crystal orders by spatial translation in various quantum simulators.

Ab initio studies of coherent spin transport in Fe-hBN/graphene van der Waals multilayers

This paper presents the results of ab initio studies of the electronic spin inversion and filtering in a ferromagnetic multilayer heterostructure. Spin-polarized electronic structure calculations are performed based on van der Waals density functional theory to give unique insights in to the generation, manipulation and transport of coherent spin conductance. By using an exact theory of the self-consistent ground state of the Fe-hBN/graphene multilayer as a model of the magnetic tunnel junction, hidden asymmetries are unraveled in the spin-resolved charge densities. It is shown that the injection of spin into the graphene/boron nitride tunnel layer from a ferromagnetic contact gives rise to coherent spin current. The projected Fermi surfaces of the up and down spin channels are analyzed to reveal Fermi arc topologies and spin anisotropies. It is also demonstrated that the coherent transport of pure spin-down current in the topological Weyl semimetal phase is robust. The implications of the results on out-of-plane transport of spin polarized conductance in van der Waals multilayer spintronic devices is discussed. The insights derived from this study are expected to open up prospects for further exploration of van der Waals magnetic multilayer heterostructures as a versatile platform for developing materials for Weyltronic applications.

Scheme to Measure the Topological Number of a Chern Insulator from Quench Dynamics

We show how the topological number of a static Hamiltonian can be measured from a dynamical quench process. We focus on a two-band Chern insulator in two dimension, for instance, the Haldane model, whose dynamical process can be described by a mapping from the [k_{x},k_{y},t] space to the Bloch sphere, characterized by the Hopf invariant. Such a mapping has been constructed experimentally by measurements in cold atom systems. We show that, taking any two constant vectors on the Bloch sphere, their inverse images of this mapping are two trajectories in the [k_{x},k_{y},t] space, and the linking number of these two trajectories exactly equals the Chern number of the static Hamiltonian. Applying this result to a recent experiment from the Hamburg group, we show that the linking number of the trajectories of the phase vortices determines the phase boundary of the static Hamiltonian.