Transmission lines and resonators based on quantum Hall plasmonics: electromagnetic field, attenuation and coupling to qubits

Quantum Hall edge states have some characteristic features that can prove useful to measure and control solid state qubits. For example, their high voltage to current ratio and their dissipationless nature can be exploited to manufacture low-loss microwave transmission lines and resonators with a characteristic impedance of the order of the quantum of resistance $h/e^2\sim 25\mathrm{k\Omega}$. The high value of the impedance guarantees that the voltage per photon is high and for this reason high impedance resonators can be exploited to obtain larger values of coupling to systems with a small charge dipole, e.g. spin qubits. In this paper, we provide a microscopic analysis of the physics of quantum Hall effect devices capacitively coupled to external electrodes. The electrical current in these devices is carried by edge magnetoplasmonic excitations and by using a semiclassical model, valid for a wide range of quantum Hall materials, we discuss the spatial profile of the electromagnetic field in a variety of situations of interest. Also, we perform a numerical analysis to estimate the lifetime of these excitations and, from the numerics, we extrapolate a simple fitting formula which quantifies the $Q$ factor in quantum Hall resonators. We then explore the possibility of reaching the strong photon-qubit coupling regime, where the strength of the interaction is higher than the losses in the system. We compute the Coulomb coupling strength between the edge magnetoplasmons and singlet-triplet qubits, and we obtain values of the coupling parameter of the order $100\mathrm{MHz}$; comparing these values to the estimated attenuation in the resonator, we find that for realistic qubit designs the coupling can indeed be strong

Self impedance matched Hall-effect gyrators and circulators

We present a model study of an alternative implementation of a two-port Hall-effect microwave gyrator. Our set-up involves three electrodes, one of which acts as a common ground for the others. Based on the capacitive-coupling model of Viola and DiVincenzo, we analyze the performance of the device and we predict that ideal gyration can be achieved at specific frequencies. Interestingly, the impedance of the three-terminal gyrator can be made arbitrarily small for certain coupling strengths, so that no auxiliary impedance matching is required. Although the bandwidth of the device shrinks as the impedance decreases, it can be improved by reducing the magnetic field; it can be realistically increased up to $150 \mathrm{MHz}$ at $50\mathrm{\Omega}$ by working at filling factor $\nu=10$. We examine also the effects of the parasitic capacitive coupling between electrodes and we find that, although in general they strongly influence the response of device, their effect is negligible at low impedance. Finally, we analyze an interferometric implementation of a circulator, which incorporates the gyrator in a Mach-Zender-like construction. Perfect circulation in both directions can be achieved, depending on frequency and on the details of the interferometer

A model study of present-day Hall-effect circulators

Stimulated by the recent implementation of a three-port Hall-effect microwave circulator of Mahoney et al. (MEA), we present model studies of the performance of this device. Our calculations are based on the capacitive-coupling model of Viola and DiVincenzo (VD). Based on conductance data from a typical Hall-bar device obtained from a two-dimensional electron gas (2DEG) in a magnetic field, we numerically solve the coupled field-circuit equations to calculate the expected performance of the circulator, as determined by the $S$ parameters of the device when coupled to 50$\Omega$ ports, as a function of frequency and magnetic field. Above magnetic fields of 1.5T, for which a typical 2DEG enters the quantum Hall regime (corresponding to a Landau-level filling fraction $\nu$ of 20), the Hall angle $\theta_H=\tan^{-1}\sigma_{xy}/\sigma_{xx}$ always remains close to $90^\circ$, and the $S$ parameters are close to the analytic predictions of VD for $\theta_H=\pi/2$. As anticipated by VD, MEA find the device to have rather high (k$\Omega$) impedance, and thus to be extremely mismatched to $50\Omega$, requiring the use of impedance matching. We incorporate the lumped matching circuits of MEA in our modeling and confirm that they can produce excellent circulation, although confined to a very small bandwidth. We predict that this bandwidth is significantly improved by working at lower magnetic field when the Landau index is high, e.g. $\nu=20$, and the impedance mismatch is correspondingly less extreme. Our modeling also confirms the observation of MEA that parasitic port-to-port capacitance can produce very interesting countercirculation effects

Andrew Menard, Sight Unseen: How Frémont’s First Expedition Changed the American Landscape.

How did the idea of America as ‘the nation of futurity’ relate to the need of territorial expansion across the continent in the mid-19th century? How did the notion of Manifest Destiny (first formulated by the journalist John O’Sullivan) come to be firmly connected with the progress across space besides that across time? How did Americans solve the dilemma between the moral imperative (of Puritanical origin) to civilize the continent and the theoretical need (expressed by Thomas Jefferson, am..

José Barreiro, Tim Johnson, eds.America is Indian Country: Opinions and Perspectives from Indian Country Today.

Indian Country Today is—or, better, was—the former name of what is now Indian Country Today Media Network, an online website and weekly newsletter that provides Native people across North America with an easily accessible news source over a variety of topics affecting American Indian people in the U.S., from politics and business to sports and environment. Starting in 1981, Indian Country Today remained a print weekly magazine until 2013 when it went online-only, after having moved its headqu..

Transmission Lines and Meta-Materials based on Quantum Hall Plasmonics

The characteristic impedance of a microwave transmission line is typically constrained to a value $Z_0$ = 50 $\Omega$, in-part because of the low impedance of free space and the limited range of permittivity and permeability realizable with conventional materials. Here we suggest the possibility of constructing high-impedance transmission lines by exploiting the plasmonic response of edge states associated with the quantum Hall effect in gated devices. We analyze various implementations of quantum Hall transmission lines based on distributed networks and lumped-element circuits, including a detailed account of parasitic capacitance and Coulomb drag effects, which can modify device performance. We additionally conceive of a meta-material structure comprising arrays of quantum Hall droplets and analyze its unusual properties. The realization of such structures holds promise for efficiently wiring-up quantum circuits on chip, as well as engineering strong coupling between semiconductor qubits and microwave photons

Hole spin qubits in thin curved quantum wells

Hole spin qubits are frontrunner platforms for scalable quantum computers because of their large spin-orbit interaction which enables ultrafast all-electric qubit control at low power. The fastest spin qubits to date are defined in long quantum dots with two tight confinement directions, when the driving field is aligned to the smooth direction. However, in these systems the lifetime of the qubit is strongly limited by charge noise, a major issue in hole qubits. We propose here a different, scalable qubit design, compatible with planar CMOS technology, where the hole is confined in a curved germanium quantum well surrounded by silicon. This design takes full advantage of the strong spin-orbit interaction of holes, and at the same time suppresses charge noise in a wide range of configurations, enabling highly coherent, ultrafast qubit gates. While here we focus on a Si/Ge/Si curved quantum well, our design is also applicable to different semiconductors. Strikingly, these devices allow for ultrafast operations even in short quantum dots by a transversal electric field. This additional driving mechanism relaxes the demanding design constraints, and opens up a new way to reliably interface spin qubits in a single quantum dot to microwave photons. By considering state-of-the-art high-impedance resonators and realistic qubit designs, we estimate interaction strengths of a few hundreds of MHz, largely exceeding the decay rate of spins and photons. Reaching such a strong coupling regime in hole spin qubits will be a significant step towards high-fidelity entangling operations between distant qubits, as well as fast single-shot readout, and will pave the way towards the implementation of a large-scale semiconducting quantum processor

High-fidelity spin qubit shuttling via large spin-orbit interaction

Shuttling spins with high fidelity is a key requirement to scale up semiconducting quantum computers, enabling qubit entanglement over large distances and favoring the integration of control electronics on-chip. To decouple the spin from the unavoidable charge noise, state-of-the-art spin shuttlers try to minimize the inhomogeneity of the Zeeman field. However, this decoupling is challenging in otherwise promising quantum computing platforms such as hole spin qubits in silicon and germanium, characterized by a large spin-orbit interaction and electrically-tunable qubit frequency. In this work, we show that, surprisingly, the large inhomogeneity of the Zeeman field stabilizes the coherence of a moving spin state, thus enabling high-fidelity shuttling also in these systems. We relate this enhancement in fidelity to the deterministic dynamics of the spin which filters out the dominant low-frequency contributions of the charge noise. By simulating several different scenarios and noise sources, we show that this is a robust phenomenon generally occurring at large field inhomogeneity. By appropriately adjusting the motion of the quantum dot, we also design realistic protocols enabling faster and more coherent spin shuttling. Our findings are generally applicable to a wide range of setups and could pave the way toward large-scale quantum processors

Hole spin qubits in Si FinFETs with fully tunable spin-orbit coupling and sweet spots for charge noise

The strong spin-orbit coupling in hole spin qubits enables fast and electrically tunable gates, but at the same time enhances the susceptibility of the qubit to charge noise. Suppressing this noise is a significant challenge in semiconductor quantum computing. Here, we show theoretically that hole Si FinFETs are not only very compatible with modern CMOS technology, but they present operational sweet spots where the charge noise is completely removed. The presence of these sweet spots is a result of the interplay between the anisotropy of the material and the triangular shape of the FinFET cross-section, and it does not require an extreme fine-tuning of the electrostatics of the device. We present how the sweet spots appear in FinFETs grown along different crystallographic axes and we study in detail how the behaviour of these devices change when the cross-section area and aspect ratio are varied. We identify designs that maximize the qubit performance and could pave the way towards a scalable spin-based quantum computer

Anomalous zero-field splitting for hole spin qubits in Si and Ge quantum dots

An anomalous energy splitting of spin triplet states at zero magnetic field has recently been measured in germanium quantum dots. This zero-field splitting could crucially alter the coupling between tunnel-coupled quantum dots, the basic building blocks of state-of-the-art spin-based quantum processors, with profound implications for semiconducting quantum computers. We develop an analytical model linking the zero-field splitting to spin-orbit interactions that are cubic in momentum. Such interactions naturally emerge in hole nanostructures, where they can also be tuned by external electric fields, and we find them to be particularly large in silicon and germanium, resulting in a significant zero-field splitting in the $\mu$eV range. We confirm our analytical theory by numerical simulations of different quantum dots, also including other possible sources of zero-field splitting. Our findings are applicable to a broad range of current architectures encoding spin qubits and provide a deeper understanding of these materials, paving the way towards the next generation of semiconducting quantum processors