Site-resolved magnon and triplon dynamics on a programmable quantum dot spin ladder
Pablo Cova Fariña, Daniel Jirovec, Xin Zhang, Elizaveta Morozova, Stefan D. Oosterhout, Stefano Reale, Tzu-Kan Hsiao, Giordano Scappucci, Menno Veldhorst, Lieven M. K. Vandersypen
Quasi-particle dynamics in interacting systems in the presence of disorder challenges the notion of internal thermalization, but proves difficult to investigate theoretically for large particle numbers. Engineered quantum systems may offer a viable alternative, as witnessed in experimental demonstrations in a variety of physical platforms, each with its own capabilities and limitations. Semiconductor gate-defined quantum dot arrays are of particular interest since they offer both a direct mapping of their Hamiltonian to Fermi-Hubbard and Heisenberg models and the in-situ tunability of (magnetic) interactions and onsite potentials. In this work, we use an array of germanium quantum dots to simulate the dynamics of both single-spin excitations (magnons) and two-spin excitations (triplons). We develop a methodology that combines digital spin qubit operations for state preparation and readout with analog evolution under the full system Hamiltonian. Using these techniques, we can reconstruct quantum walk plots for both magnons and triplons, and for various configurations of Heisenberg exchange couplings. We furthermore explore the effect of single-site disorder and its impact on the propagation of spin excitations. The obtained results can provide a basis for simulating disorder-based solid-state phenomena such as many-body localization.
Quasi-particle dynamics in interacting systems in the presence of disorder challenges the notion of internal thermalization, but proves difficult to investigate theoretically for large particle numbers. Engineered quantum systems may offer a viable alternative, as witnessed in experimental demonstrations in a variety of physical platforms, each with its own capabilities and limitations. Semiconductor gate-defined quantum dot arrays are of particular interest since they offer both a direct mapping of their Hamiltonian to Fermi-Hubbard and Heisenberg models and the in-situ tunability of (magnetic) interactions and onsite potentials. In this work, we use an array of germanium quantum dots to simulate the dynamics of both single-spin excitations (magnons) and two-spin excitations (triplons). We develop a methodology that combines digital spin qubit operations for state preparation and readout with analog evolution under the full system Hamiltonian. Using these techniques, we can reconstruct quantum walk plots for both magnons and triplons, and for various configurations of Heisenberg exchange couplings. We furthermore explore the effect of single-site disorder and its impact on the propagation of spin excitations. The obtained results can provide a basis for simulating disorder-based solid-state phenomena such as many-body localization.
Understanding collective phases of strongly correlated quantum magnets relies on theoretically tractable model systems with precise microscopic control. Antiferromagnetic spin ladders provide such a setting, hosting field-tunable gapped and gapless phases at half filling and unconventional pairing tendencies upon doping. Here, we realize a programmable Heisenberg spin ladder in a half-filled germanium quantum dot array featuring site-resolved, continuously tunable exchange interactions. Under a fixed magnetic field, we vary the rung and leg coupling to map the rung-singlet, canted antiferromagnetic, and fully polarized phases. Hamiltonian-learning protocols combining equilibrium and dynamical measurements quantitatively characterize the ladder, incorporating spin-orbit interactions to reproduce the observed crossover behavior. Measurements of higher-order spin correlators -- including four-point correlations inaccessible to conventional bulk probes -- reveal signatures of the underlying phase structure despite the finite size. Our results establish germanium quantum dot arrays as a controllable platform for quantum magnetism, opening routes to investigate unconventional superconductivity in doped ladders.
Quantum-mechanical correlations of interacting fermions result in the emergence of exotic phases.Magnetic phases naturally arise in the Mott-insulator regime of the Fermi-Hubbard model, where charges are localized and the spin degree of freedom remains.In this regime, the occurrence of phenomena such as resonating valence bonds, frustrated magnetism, and spin liquids is predicted.Quantum systems with engineered Hamiltonians can be used as simulators of such spin physics to provide insights beyond the capabilities of analytical methods and classical computers.To be useful, methods for the preparation of intricate many-body spin states and access to relevant observables are required.Here, we show the quantum simulation of magnetism in the Mott-insulator regime with a linear quantum-dot array.We characterize the energy spectrum for a Heisenberg spin chain, from which we can identify when the conditions for homogeneous exchange couplings are met.Next, we study the multispin coherence with global exchange oscillations in both the singlet and triplet subspace of the Heisenberg Hamiltonian.Last, we adiabatically prepare the low-energy global singlet of the homogeneous spin chain and probe it with two-spin singlettriplet measurements on each nearest-neighbor pair and the correlations therein.The methods and control presented here open new opportunities for the simulation of quantum magnetism benefiting from the flexibility in tuning and layout of gate-defined quantum-dot arrays.
Quantum simulation promises to advance materials discovery by accurately simulating complex states of matter, their microscopic excitations, and macroscopic response functions. The central challenge in resolving the underlying interacting dynamics is to combine high-fidelity evolution with the sophisticated control necessary to manipulate individual quasi-particles in quantum many-body states. Here, we report on high-precision simulation of both linear and non-linear response functions in a 2D XY spin-1/2 magnet using an analog-digital superconducting processor of up to 97 qubits. By interleaving digital gates with analog evolution precisely characterized via Hamiltonian learning, we selectively excite magnons at tunable energy densities. Measuring first the linear magnon response -- a central probe in neutron-scattering experiments -- we extract temperature-dependent spectra and lifetimes. Our results reveal stark variations in magnon decay rates across the Brillouin zone, with enhancement near van Hove singularities and suppression for edge-localized modes. Next, we perform a suite of nonlinear measurements, including the study of self-scattering mechanisms, as well as pump-probe spectroscopy to directly characterize the magnon interactions. While matrix-product state simulations capture the dynamics well in either small systems or at low temperatures, their predictions become inaccurate away from these limits. This work demonstrates precise simulation of the interacting dynamics in quantum magnets, and provides key insights into quasi-particles and their microscopic scattering mechanisms.
We are entering the era of the second quantum revolution, where we aim to harness the power of quantum mechanics to create new technologies. Quantum technologies have the potential to revolutionize the fields of simulation, computation, communication, sensing, metrology, and many others. Here we discuss analog quantum simulation, which has attracted a lot of attention in the last few years from several platforms. Although arrays of gate-defined quantum dots exhibit significant potential for analog simulation, example experiments have been few and far between. This thesis focuses on simulating the Fermi-Hubbard model using two dimensional (2d) arrays of quantum dots. The first experiment describes the creation and measurement of a 2x2 quantum dot array. Historically, most experiments with quantum dots have been performed with linear arrays due to the relative ease of fabrication. We introduce a bi-layer gate structure, facilitated by the lift-off of sputtered silicon nitride, to create the 2x2 dot array. This gate design enables us to achieve unprecedented tunability of the tunnel coupling between all nearest-neighbor pairs of dots in 2d arrays. We also demonstrate individual control over the chemical potential and the electron occupation of each dot along with accurate measurement of the on-site and inter-site interaction terms. The use of virtual gates significantly aids in the tuning of tunnel coupling and chemical potential. The demonstrated high degree of control of the system along with fast single-shot spin-readout achieved through Pauli spin blockade establish this dot array as a promising simulator of the Fermi-Hubbard model. The 2x2 dot array is used to simulate Nagaoka ferromagnetism in the next experiment. This form of itinerant ferromagnetism arises from the Fermi-Hubbard model, and was first shown analytically in the limit of infinite interaction strengths and infinite lattices by Nagaoka in 1966. Nagaoka ferromagnetism has been a topic of rigorous theoretical studies ever since, but its experimental signature has eluded us for more than five decades. In this experiment, we load the four dot plaquette with three electrons and demonstrate the emergence of spontaneous ferromagnetism by measuring the spin correlation of two out of the three electrons. Changing the topology of the array to an open chain is shown to destroy the ferromagnetic signature, consistent with the Lieb-Mattis theorem. We also show indications that this ferromagnetic ground state can be destroyed by applying a perpendicular magnetic field, unlike most other forms of ferromagnetism. However, this ground state shows striking robustness to the offset in the local potential of any dot. This is the first experimental verification of Nagaoka’s prediction as well as the first simulation of magnetism using quantumdot arrays. The final experiment takes a different approach to simulate the Fermi-Hubbardmodel with a large 2d array of quantum dots. The dot array is created using only three gates in a top-down approach. This allows for only global control over the electron filling and tunnel coupling of the dots, contrary to the previous experiments. The readout is performed with capacitance spectroscopy, which allows us to directly probe the density of states of the two-dimensional electron systems. We measure the disorder levels and optimize both substrates and gating strategies to induce periodic potential, sufficiently stronger than the disorder level, at the 2d electron gas. Although we demonstrate a novel platformfor the realization of artificial lattices of interacting particles, this effort is currently limited by the substrate inhomogeneity.
Motivated by the recent Ge hole spin qubit experiments, we construct and study a two-leg spin ladder from a quantum dot array with spin-orbit couplings (SOCs), aiming to uncover the many-body phase diagrams and provide concrete guidance for the Ge hole spin qubit experiments. The spin ladder is described by an unprecedented, complex spin Hamiltonian, which contains antiferromagnetic Heisenberg exchange, Dzyaloshinskii-Moriya (DM), and anisotropic exchange interactions. We analyze the spin ladder Hamiltonian in two complementary situations, the strong rung coupling limit and the weak rung coupling limit. In the strong rung coupling limit, we systematically construct effective spin-1/2 chain models, connecting the well-studied one-dimensional spin models and providing a recipe for Hamiltonian engineering. It is worth emphasizing that effective DM interactions can be completely turned off while the microscopic DM interactions are generically inevitable. Moreover, the staggered DM interactions, which are not possible in the microscopic spin model, can also be realized in the effective spin-1/2 model. In the weak rung coupling limit, we employ Abelian bosonization and Luther-Emery fermionization, uncovering a multitude of phases. Several commensurate-incommensurate transitions are driven by both the longitudinal magnetic field and the DM interactions in the legs (chains). Remarkably, the low-energy phase diagrams show strong dependence in the DM interaction, providing a concrete way to identify the strength of SOC in the experiments. Our work bridges quantum many-body theory and spin qubit device physics, establishing spin ladders made of spin-orbit-coupled quantum dots as a promising platform for engineering exotic spin models, constructing quantum many-body states, and enabling programmable quantum computations.
The understanding of matter does not only require a precise analysis of individual characteristics of the fundamental constituents, but also the study of their collective behavior.Solid state physics, and in particular research in strongly correlated electron systems, deals with such collective phenomena.The properties of the electrons, charge and spin quantum numbers, do not on their own explain the rich world of states of matter, however mutual interactions lead to various states or phases of matter.This work focuses on phases in quantum spin systems.On the basis of the Heisenberg model one (1D) and two dimensional (2D) spin lattices are investigated.In a first part the bilayer Heisenberg Model and the 2D Kondo necklace model are studied.Both models exhibit a quantum phase transition between an ordered and disordered phase.For small interlayer couplings the models have antiferromagnetic long-range order, which is destroyed by increasing the coupling.However, even in the disordered phase the models show global features in terms of collective excitations called magnons.Coming from the disordered phase the gapped magnons condense at a critical coupling and form the order of the ordered phase.Here, another interesting question arises, namely that of the coupling of a single doped hole to such critical fluctuations.A self-consistent Born approximation predicts that the doped hole couples to the magnons such that the quasiparticle residue vanishes at the quantum critical point.In this work the delicate question about the fate of the quasiparticle residue across the quantum phase transition is also tackled by means of large scale quantum Monte Carlo simulations.Furthermore the dynamics of a single hole doped in the magnetic background is investigated.