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Long-range interactions play a key role in several phenomena of quantum physics and chemistry. To study these phenomena, analog quantum simulators provide an appealing alternative to classical numerical methods. Gate-defined quantum dots have been established as a platform for quantum simulation, but for those experiments the effect of long-range interactions between the electrons did not play a crucial role. Here we present a detailed experimental characterization of long-range electron-electron interactions in an array of gate-defined semiconductor quantum dots. We demonstrate significant interaction strength among electrons that are separated by up to four sites, and show that our theoretical prediction of the screening effects matches well the experimental results. Based on these findings, we investigate how long-range interactions in quantum dot arrays may be utilized for analog simulations of artificial quantum matter. We numerically show that about ten quantum dots are sufficient to observe binding for a one-dimensional H2-like molecule. These combined experimental and theoretical results pave the way for future quantum simulations with quantum dot arrays and benchmarks of numerical methods in quantum chemistry., QCD/Vandersypen Lab, QN/Vandersypen Lab

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 singlet-triplet 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., Electrical Engineering, Mathematics and Computer Science, QuTech, QCD/Vandersypen Lab, QN/Vandersypen Lab

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 singlet-triplet 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., Electrical Engineering, Mathematics and Computer Science, QCD/Vandersypen Lab, QN/Vandersypen Lab

Electrostatically-defined semiconductor quantum dot arrays offer a promising platform for quantum computation and quantum simulation. However, crosstalk of gate voltages to dot potentials and interdot tunnel couplings complicates the tuning of the device parameters. To date, crosstalk to the dot potentials is routinely and efficiently compensated using so-called virtual gates, which are specific linear combinations of physical gate voltages. However, due to exponential dependence of tunnel couplings on gate voltages, crosstalk to the tunnel barriers is currently compensated through a slow iterative process. In this work, we show that the crosstalk on tunnel barriers can be efficiently characterized and compensated for, using the fact that the same exponential dependence applies to all gates. We demonstrate efficient calibration of crosstalk in a quadruple quantum dot array and define a set of virtual barrier gates, with which we show orthogonal control of all interdot tunnel couplings. Our method marks a key step forward in the scalability of the tuning process of large-scale quantum dot arrays., QCD/Vandersypen Lab, QuTech, QN/Vandersypen Lab

Electrostatically-defined semiconductor quantum dot arrays offer a promising platform for quantum computation and quantum simulation. However, crosstalk of gate voltages to dot potentials and interdot tunnel couplings complicates the tuning of the device parameters. To date, crosstalk to the dot potentials is routinely and efficiently compensated using so-called virtual gates, which are specific linear combinations of physical gate voltages. However, due to exponential dependence of tunnel couplings on gate voltages, crosstalk to the tunnel barriers is currently compensated through a slow iterative process. In this work, we show that the crosstalk on tunnel barriers can be efficiently characterized and compensated for, using the fact that the same exponential dependence applies to all gates. We demonstrate efficient calibration of crosstalk in a quadruple quantum dot array and define a set of virtual barrier gates, with which we show orthogonal control of all interdot tunnel couplings. Our method marks a key step forward in the scalability of the tuning process of large-scale quantum dot arrays., QCD/Vandersypen Lab, QN/Vandersypen Lab

Engineered, highly controllable quantum systems are promising simulators of emergent physics beyond the simulation capabilities of classical computers1. An important problem in many-body physics is itinerant magnetism, which originates purely from long-range interactions of free electrons and whose existence in real systems has been debated for decades2,3. Here we use a quantum simulator consisting of a four-electron-site square plaquette of quantum dots4 to demonstrate Nagaoka ferromagnetism5. This form of itinerant magnetism has been rigorously studied theoretically6–9 but has remained unattainable in experiments. We load the plaquette with three electrons and demonstrate the predicted emergence of spontaneous ferromagnetic correlations through pairwise measurements of spin. We find that the ferromagnetic ground state is remarkably robust to engineered disorder in the on-site potentials and we can induce a transition to the low-spin state by changing the plaquette topology to an open chain. This demonstration of Nagaoka ferromagnetism highlights that quantum simulators can be used to study physical phenomena that have not yet been observed in any experimental system. The work also constitutes an important step towards large-scale quantum dot simulators of correlated electron systems., Green Open Access added to TU Delft Institutional Repository ‘You share, we take care!’ – Taverne project https://www.openaccess.nl/en/you-share-we-take-care Otherwise as indicated in the copyright section: the publisher is the copyright holder of this work and the author uses the Dutch legislation to make this work public., QCD/Vandersypen Lab, QN/Vandersypen Lab

Quantum Hall edge channels offer an efficient and controllable platform to study quantum transport in one dimension. Such channels are a prospective tool for the efficient transfer of quantum information at the nanoscale, and play a vital role in exposing intriguing physics. Electric current along the edge carries energy and heat leading to inelastic scattering, which may impede coherent transport. Several experiments attempting to probe the concomitant energy redistribution along the edge reported energy loss via unknown mechanisms of inelastic scattering. Here we employ quantum dots to inject and extract electrons at specific energies, to spectrally analyse inelastic scattering inside quantum Hall edge channels. We show that the missing energy puzzle could be untangled by incorporating non-local Auger-like processes, in which energy is redistributed between spatially separate parts of the sample. Our theoretical analysis, accounting for the experimental results, challenges common-wisdom analyses which ignore such non-local decay channels., QCD/Vandersypen Lab, QuTech

Quantum Hall edge channels offer an efficient and controllable platform to study quantum transport in one dimension. Such channels are a prospective tool for the efficient transfer of quantum information at the nanoscale, and play a vital role in exposing intriguing physics. Electric current along the edge carries energy and heat leading to inelastic scattering, which may impede coherent transport. Several experiments attempting to probe the concomitant energy redistribution along the edge reported energy loss via unknown mechanisms of inelastic scattering. Here we employ quantum dots to inject and extract electrons at specific energies, to spectrally analyse inelastic scattering inside quantum Hall edge channels. We show that the missing energy puzzle could be untangled by incorporating non-local Auger-like processes, in which energy is redistributed between spatially separate parts of the sample. Our theoretical analysis, accounting for the experimental results, challenges common-wisdom analyses which ignore such non-local decay channels., QCD/Vandersypen Lab

Electrostatic confinement in semiconductors provides a flexible platform for the emulation of interacting electrons in a two-dimensional lattice, including in the presence of gauge fields. This combination offers the potential to realize a wide host of quantum phases. Capacitance spectroscopy provides a technique that allows one to directly probe the density of states of such two-dimensional electron systems. Here, we present a measurement and fabrication scheme that builds on capacitance spectroscopy and allows for the independent control of density and periodic potential strength imposed on a two-dimensional electron gas. We characterize disorder levels and (in)homogeneity and develop and optimize different gating strategies at length scales where interactions are expected to be strong. A continuation of these ideas might see to fruition the emulation of interaction-driven Mott transitions or Hofstadter butterfly physics., Vandersypen Lab, QN/Quantum Transport, General, QN/Vandersypen Lab

Semiconductor quantum dot arrays defined electrostatically in a 2D electron gas provide a scalable platform for quantum information processing and quantum simulations. For the operation of quantum dot arrays, appropriate voltages need to be applied to the gate electrodes that define the quantum dot potential landscape. Tuning the gate voltages has proven to be a time-consuming task, because of initial electrostatic disorder and capacitive cross-talk effects. Here, we report on the automated tuning of the inter-dot tunnel coupling in gate-defined semiconductor double quantum dots. The automation of the tuning of the inter-dot tunnel coupling is the next step forward in scalable and efficient control of larger quantum dot arrays. This work greatly reduces the effort of tuning semiconductor quantum dots for quantum information processing and quantum simulation., QuTech, QCD/Vandersypen Lab, QN/Vandersypen Lab

Electrostatic confinement in semiconductors provides a flexible platform for the emulation of interacting electrons in a two-dimensional lattice, including in the presence of gauge fields. This combination offers the potential to realize a wide host of quantum phases. Capacitance spectroscopy provides a technique that allows one to directly probe the density of states of such two-dimensional electron systems. Here, we present a measurement and fabrication scheme that builds on capacitance spectroscopy and allows for the independent control of density and periodic potential strength imposed on a two-dimensional electron gas. We characterize disorder levels and (in)homogeneity and develop and optimize different gating strategies at length scales where interactions are expected to be strong. A continuation of these ideas might see to fruition the emulation of interaction-driven Mott transitions or Hofstadter butterfly physics., QCD/Vandersypen Lab, QN/Quantum Transport, ALG/General, QN/Vandersypen Lab

We study the Zeeman splitting in lateral quantum dots that are defined in GaAs-AlGaAs heterostructures by means of split gates. We demonstrate a nonlinear dependence of the splitting on magnetic field and its substantial variations from dot to dot and from heterostructure to heterostructure. These phenomena are important in the context of information processing since the tunability and dot-dependence of the Zeeman splitting allow for a selective manipulation of spins. We show that spin-orbit effects related to the GaAs band structure quantitatively explain the observed magnitude of the nonlinear dependence of the Zeeman splitting. Furthermore, spin-orbit effects result in a dependence of the Zeeman splitting on predominantly the out-of-plane quantum dot confinement energy. We also show that the variations of the confinement energy due to charge disorder in the heterostructure may explain the dependence of Zeeman splitting on the dot position. This position may be varied by changing the gate voltages, which leads to an electrically tunable Zeeman splitting., QCD/Vandersypen Lab, QN/Nazarov Group

Semiconductor quantum dot arrays defined electrostatically in a 2D electron gas provide a scalable platform for quantum information processing and quantum simulations. For the operation of quantum dot arrays, appropriate voltages need to be applied to the gate electrodes that define the quantum dot potential landscape. Tuning the gate voltages has proven to be a time-consuming task, because of initial electrostatic disorder and capacitive cross-talk effects. Here, we report on the automated tuning of the inter-dot tunnel coupling in gate-defined semiconductor double quantum dots. The automation of the tuning of the inter-dot tunnel coupling is the next step forward in scalable and efficient control of larger quantum dot arrays. This work greatly reduces the effort of tuning semiconductor quantum dots for quantum information processing and quantum simulation., QCD/Vandersypen Lab, QN/Vandersypen Lab

Interacting fermions on a lattice can develop strong quantum correlations, which are the cause of the classical intractability of many exotic phases of matter. Current efforts are directed towards the control of artificial quantum systems that can be made to emulate the underlying Fermi-Hubbard models. Electrostatically confined conduction-band electrons define interacting quantum coherent spin and charge degrees of freedom that allow all-electrical initialization of low-entropy states and readily adhere to the Fermi-Hubbard Hamiltonian. Until now, however, the substantial electrostatic disorder of the solid state has meant that only a few attempts at emulating Fermi-Hubbard physics on solid-state platforms have been made. Here we show that for gate-defined quantum dots this disorder can be suppressed in a controlled manner. Using a semi-automated and scalable set of experimental tools, we homogeneously and independently set up the electron filling and nearest-neighbour tunnel coupling in a semiconductor quantum dot array so as to simulate a Fermi-Hubbard system. With this set-up, we realize a detailed characterization of the collective Coulomb blockade transition, which is the finite-size analogue of the interaction-driven Mott metal-to-insulator transition. As automation and device fabrication of semiconductor quantum dots continue to improve, the ideas presented here will enable the investigation of the physics of ever more complex many-body states using quantum dots., Accepted Author Manuscript, QCD/Vandersypen Lab, QuTech, Electrical Engineering, Mathematics and Computer Science

Interacting fermions on a lattice can develop strong quantum correlations, which are the cause of the classical intractability of many exotic phases of matter. Current efforts are directed towards the control of artificial quantum systems that can be made to emulate the underlying Fermi-Hubbard models. Electrostatically confined conduction-band electrons define interacting quantum coherent spin and charge degrees of freedom that allow all-electrical initialization of low-entropy states and readily adhere to the Fermi-Hubbard Hamiltonian. Until now, however, the substantial electrostatic disorder of the solid state has meant that only a few attempts at emulating Fermi-Hubbard physics on solid-state platforms have been made. Here we show that for gate-defined quantum dots this disorder can be suppressed in a controlled manner. Using a semi-automated and scalable set of experimental tools, we homogeneously and independently set up the electron filling and nearest-neighbour tunnel coupling in a semiconductor quantum dot array so as to simulate a Fermi-Hubbard system. With this set-up, we realize a detailed characterization of the collective Coulomb blockade transition, which is the finite-size analogue of the interaction-driven Mott metal-to-insulator transition. As automation and device fabrication of semiconductor quantum dots continue to improve, the ideas presented here will enable the investigation of the physics of ever more complex many-body states using quantum dots., Accepted Author Manuscript, QCD/Vandersypen Lab, Electrical Engineering, Mathematics and Computer Science

We present time-resolved measurements of spin-flip photon-assisted tunneling and spin-flip relaxation in a doubly occupied double quantum dot. The photon-assisted excitation rate as a function of magnetic field indicates that spin-orbit coupling is the dominant mechanism behind the spin-flip under the present conditions. We are able to extract the resulting effective “spin-flip tunneling” energy, which is found to be three orders of magnitude smaller than the regular spin-conserving tunneling energy. We also measure the relaxation and dephasing times of a qubit formed out of two two-electron states with different spin and charge configurations., QN/Quantum Nanoscience, Applied Sciences

We report that the electron spin-relaxation time T1 in a GaAs quantum dot with a spin-1/2 ground state has a 180° periodicity in the orientation of the in-plane magnetic field. This periodicity has been predicted for circular dots as being due to the interplay of Rashba and Dresselhaus spin orbit contributions. Different from this prediction, we find that the extrema in the T1 do not occur when the magnetic field is along the [110] and [11¯0] crystallographic directions. This deviation is attributed to an elliptical dot confining potential. The T1 varies by more than 1 order of magnitude when rotating a 3 T field, reaching about 80 ms for the optimal angle. We infer from the data that in our device the signs of the Rashba and Dresselhaus constants are opposite., QN/Quantum Nanoscience, Applied Sciences

We present time-resolved measurements of spin-flip photon-assisted tunneling and spin-flip relaxation in a doubly occupied double quantum dot. The photon-assisted excitation rate as a function of magnetic field indicates that spin-orbit coupling is the dominant mechanism behind the spin-flip under the present conditions. We are able to extract the resulting effective “spin-flip tunneling” energy, which is found to be three orders of magnitude smaller than the regular spin-conserving tunneling energy. We also measure the relaxation and dephasing times of a qubit formed out of two two-electron states with different spin and charge configurations., QN/Quantum Nanoscience, Applied Sciences

We report that the electron spin-relaxation time T1 in a GaAs quantum dot with a spin-1/2 ground state has a 180° periodicity in the orientation of the in-plane magnetic field. This periodicity has been predicted for circular dots as being due to the interplay of Rashba and Dresselhaus spin orbit contributions. Different from this prediction, we find that the extrema in the T1 do not occur when the magnetic field is along the [110] and [11¯0] crystallographic directions. This deviation is attributed to an elliptical dot confining potential. The T1 varies by more than 1 order of magnitude when rotating a 3 T field, reaching about 80 ms for the optimal angle. We infer from the data that in our device the signs of the Rashba and Dresselhaus constants are opposite., QN/Quantum Nanoscience, Applied Sciences

We report both photon- and phonon-assisted tunneling transitions in a linear array of three quantum dots, which can only be understood by considering the full three-dimensionality of the charge stability diagram. Such tunneling transitions potentially contribute to leakage of qubits defined in this system. A detailed understanding of these transitions is important as they become more abundant and complex to analyze as quantum dot arrays are scaled up., QN/Quantum Nanoscience, Applied Sciences

We report both photon- and phonon-assisted tunneling transitions in a linear array of three quantum dots, which can only be understood by considering the full three-dimensionality of the charge stability diagram. Such tunneling transitions potentially contribute to leakage of qubits defined in this system. A detailed understanding of these transitions is important as they become more abundant and complex to analyze as quantum dot arrays are scaled up., QN/Quantum Nanoscience, Applied Sciences

We investigate the electric manipulation of a single-electron spin in a single gate-defined quantum dot. We observe that so-far neglected differences between the hyperfine- and spin-orbit-mediated electric dipole spin resonance conditions have important consequences at high magnetic fields. In experiments using adiabatic rapid passage to invert the electron spin, we observe an unusually wide and asymmetric response as a function of the magnetic field. Simulations support the interpretation of the line shape in terms of four different resonance conditions. These findings may lead to isotope-selective control of dynamic nuclear polarization in quantum dots., QN/Quantum Nanoscience, Applied Sciences

Spin accumulation is generated by injecting an unpolarized charge current into a channel of GaAs two-dimensional electron gas subject to an in-plane magnetic field, then measured in a nonlocal geometry. Unlike previous measurements that have used spin-polarized nanostructures, here the spin accumulation arises simply from the difference in bulk conductivities for spin-up and spin-down carriers. Comparison to a diffusive model that includes spin subband splitting in magnetic field suggests a significantly enhanced electron spin susceptibility in the two-dimensional electron gas., Kavli Institute of Nanoscience, Applied Sciences

Spin accumulation is generated by injecting an unpolarized charge current into a channel of GaAs two-dimensional electron gas subject to an in-plane magnetic field, then measured in a nonlocal geometry. Unlike previous measurements that have used spin-polarized nanostructures, here the spin accumulation arises simply from the difference in bulk conductivities for spin-up and spin-down carriers. Comparison to a diffusive model that includes spin subband splitting in magnetic field suggests a significantly enhanced electron spin susceptibility in the two-dimensional electron gas., Kavli Institute of Nanoscience, Applied Sciences

We show that an insulated electrostatic gate can be used to strongly suppress ubiquitous background charge noise in Schottky-gated GaAs=AlGaAs devices. Via a 2D self-consistent simulation of the conduction band profile we show that this observation can be explained by reduced leakage of electrons from the Schottky gates into the semiconductor through the Schottky barrier, consistent with the effect of ‘‘bias cooling.’’ Upon noise reduction, the noise power spectrum generally changes from Lorentzian to 1/f type. By comparing wafers with different Al content, we exclude that DX centers play a dominant role in the charge noise., Kavli Institute of Nanoscience Delft, Applied Sciences

We show that an insulated electrostatic gate can be used to strongly suppress ubiquitous background charge noise in Schottky-gated GaAs=AlGaAs devices. Via a 2D self-consistent simulation of the conduction band profile we show that this observation can be explained by reduced leakage of electrons from the Schottky gates into the semiconductor through the Schottky barrier, consistent with the effect of ‘‘bias cooling.’’ Upon noise reduction, the noise power spectrum generally changes from Lorentzian to 1/f type. By comparing wafers with different Al content, we exclude that DX centers play a dominant role in the charge noise., Kavli Institute of Nanoscience Delft, Applied Sciences

The authors employ a cryogenic high electron mobility transistor (HEMT) amplifier to increase the bandwidth of a charge detection setup with a quantum point contact (QPC) charge sensor. The HEMT is operating at 1?K and the circuit has a bandwidth of 1?MHz. The noise contribution of the HEMT at high frequencies is only a few times higher than that of the QPC shot noise. The authors use this setup to monitor single-electron tunneling to and from an adjacent quantum dot. The authors measure fluctuations in the dot occupation as short as 400?ns, 20 times faster than in previous work., Kavli Institute of Nanoscience, Applied Sciences

Applied Sciences

The authors employ a cryogenic high electron mobility transistor (HEMT) amplifier to increase the bandwidth of a charge detection setup with a quantum point contact (QPC) charge sensor. The HEMT is operating at 1?K and the circuit has a bandwidth of 1?MHz. The noise contribution of the HEMT at high frequencies is only a few times higher than that of the QPC shot noise. The authors use this setup to monitor single-electron tunneling to and from an adjacent quantum dot. The authors measure fluctuations in the dot occupation as short as 400?ns, 20 times faster than in previous work., Kavli Institute of Nanoscience, Applied Sciences

Applied Sciences

We propose and implement a nondestructive measurement that distinguishes between two-electron spin states in a quantum dot. In contrast to earlier experiments with quantum dots, the spins are left behind in the state corresponding to the measurement outcome. By measuring the spin states twice within a time shorter than the relaxation time T1, correlations between the outcomes of consecutive measurements are observed. They disappear as the wait time between measurements becomes comparable to T1. The correlation between the postmeasurement state and the measurement outcome is measured to be ~90% on average., Kavli Institute of Nanoscience, Applied Sciences

We propose and implement a nondestructive measurement that distinguishes between two-electron spin states in a quantum dot. In contrast to earlier experiments with quantum dots, the spins are left behind in the state corresponding to the measurement outcome. By measuring the spin states twice within a time shorter than the relaxation time T1, correlations between the outcomes of consecutive measurements are observed. They disappear as the wait time between measurements becomes comparable to T1. The correlation between the postmeasurement state and the measurement outcome is measured to be ~90% on average., Kavli Institute of Nanoscience, Applied Sciences