arXiv subjects

Benoit Bertrand

Publications and source records attributed to Benoit Bertrand.

At least 37 records · Page 2Linked to original sources

arXiv2021

Large dispersive interaction between a CMOS double quantum dot and microwave photons

We report fast charge state readout of a double quantum dot in a CMOS split-gate silicon nanowire transistor via the large dispersive interaction with microwave photons in a lumped-element resonator formed by hybrid integration with a superconducting inductor. We achieve a coupling rate $g_0/(2π) = 204 \pm 2$ MHz by exploiting the large interdot gate lever arm of an asymmetric split-gate device, $α=0.72$, and by inductively coupling to the resonator to increase its impedance, $Z_\text{r}=560~Ω$. In the dispersive regime, the large coupling strength at the double quantum dot hybridisation point produces a frequency shift comparable to the resonator linewidth, the optimal setting for maximum state visibility. We exploit this regime to demonstrate rapid dispersive readout of the charge degree of freedom, with a SNR of 3.3 in 50 ns. In the resonant regime, the fast charge decoherence rate precludes reaching the strong coupling regime, but we show a clear route to spin-photon circuit quantum electrodynamics using hybrid CMOS systems.

cond-mat.mes-hall↗

arXiv2021

Dispersively probed microwave spectroscopy of a silicon hole double quantum dot

Owing to ever increasing gate fidelities and to a potential transferability to industrial CMOS technology, silicon spin qubits have become a compelling option in the strive for quantum computation. In a scalable architecture, each spin qubit will have to be finely tuned and its operating conditions accurately determined. In this prospect, spectroscopic tools compatible with a scalable device layout are of primary importance. Here we report a two-tone spectroscopy technique providing access to the spin-dependent energy-level spectrum of a hole double quantum dot defined in a split-gate silicon device. A first GHz-frequency tone drives electric-dipole spin resonance enabled by the valence-band spin-orbit coupling. A second lower-frequency tone (approximately 500 MHz) allows for dispersive readout via rf-gate reflectometry. We compare the measured dispersive response to the linear response calculated in an extended Jaynes-Cummings model and we obtain characteristic parameters such as g-factors and tunnel/spin-orbit couplings for both even and odd occupation.

cond-mat.mes-hall↗

arXiv2020

Single-electron operation of a silicon-CMOS 2x2 quantum dot array with integrated charge sensing

The advanced nanoscale integration available in silicon complementary metal-oxide-semiconductor (CMOS) technology provides a key motivation for its use in spin-based quantum computing applications. Initial demonstrations of quantum dot formation and spin blockade in CMOS foundry-compatible devices are encouraging, but results are yet to match the control of individual electrons demonstrated in university-fabricated multi-gate designs. We show here that the charge state of quantum dots formed in a CMOS nanowire device can be sensed by using floating gates to electrostatically couple it to a remote single electron transistor (SET) formed in an adjacent nanowire. By biasing the nanowire and gates of the remote SET with respect to the nanowire hosting the quantum dots, we controllably form ancillary quantum dots under the floating gates, thus enabling the demonstration of independent control over charge transitions in a quadruple (2x2) quantum dot array. This device overcomes the limitations associated with measurements based on tunnelling transport through the dots and permits the sensing of all charge transitions, down to the last electron in each dot. We use effective mass theory to investigate the necessary optimization of the device parameters in order to achieve the tunnel rates required for spin-based quantum computation.

cond-mat.mes-hall↗

arXiv2020

Single-electron control in a foundry-fabricated two-dimensional qubit array

Silicon spin qubits have achieved high-fidelity one- and two-qubit gates, above error correction thresholds, promising an industrial route to fault-tolerant quantum computation. A significant next step for the development of scalable multi-qubit processors is the operation of foundry-fabricated, extendable two-dimensional (2D) arrays. In gallium arsenide, 2D quantum-dot arrays recently allowed coherent spin operations and quantum simulations. In silicon, 2D arrays have been limited to transport measurements in the many-electron regime. Here, we operate a foundry-fabricated silicon 2x2 array in the few-electron regime, achieving single-electron occupation in each of the four gate-defined quantum dots, as well as reconfigurable single, double, and triple dots with tunable tunnel couplings. Pulsed-gate and gate-reflectometry techniques permit single-electron manipulation and single-shot charge readout, while the two-dimensionality allows the spatial exchange of electron pairs. The compact form factor of such arrays, whose foundry fabrication can be extended to larger 2xN arrays, along with the recent demonstration of coherent spin control and readout, paves the way for dense qubit arrays for quantum computation and simulation.

cond-mat.mes-hall↗

arXiv2020

Charge detection in an array of CMOS quantum dots

The recent development of arrays of quantum dots in semiconductor nanostructures highlights the progress of quantum devices toward large scale. However, how to realize such arrays on a scalable platform such as silicon is still an open question. One of the main challenge resides in the detection of charges within the array. It is a prerequisite functionality to initialize a desired charge state and readout spins through spin-to-charge conversion mechanisms. In this paper, we use two methods based on either a single-lead charge detector, or a reprogrammable single electron transistor. Thanks to these methods, we study the charge dynamics and sensitivity by performing single shot detection of the charge. Finally, we can probe the charge stability at any node of a linear array and assess the Coulomb disorder in the structure. We find an electrochemical potential fluctuation induced by charge noise comparable to that reported in other silicon quantum dots.

cond-mat.mes-hall↗

arXiv2019

All-Electrical Control of an Electron Spin/Valley Quantum Bit in SOI CMOS Technology

We fabricated Quantum Dot (QD) devices using a standard SOI CMOS process flow, and demonstrated that the spin of confined electrons could be controlled via a local electrical-field excitation, owing to inter-valley spin-orbit coupling. We discuss that modulating the confinement geometry via an additional electrode may enable switching a quantum bit (qubit) between an electrically-addressable valley configuration and a protected spin configuration. This proposed scheme bears relevance to improve the trade-off between fast operations and slow decoherence for quantum computing on a Si qubit platform. Finally, we evoke the impact of process-induced variability on the operating bias range.

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arXiv2019

A Spin Quintet in a Silicon Double Quantum Dot: Spin Blockade and Relaxation

Spins in gate-defined silicon quantum dots are promising candidates for implementing large-scale quantum computing. To read the spin state of these qubits, the mechanism that has provided the highest fidelity is spin-to-charge conversion via singlet-triplet spin blockade, which can be detected in-situ using gate-based dispersive sensing. In systems with a complex energy spectrum, like silicon quantum dots, accurately identifying when singlet-triplet blockade occurs is hence of major importance for scalable qubit readout. In this work, we present a description of spin blockade physics in a tunnel-coupled silicon double quantum dot defined in the corners of a split-gate transistor. Using gate-based magnetospectroscopy, we report successive steps of spin blockade and spin blockade lifting involving spin states with total spin angular momentum up to $S=3$. More particularly, we report the formation of a hybridized spin quintet state and show triplet-quintet and quintet-septet spin blockade. This enables studies of the quintet relaxation dynamics from which we find $T_1 \sim 4 ~μs$. Finally, we develop a quantum capacitance model that can be applied generally to reconstruct the energy spectrum of a double quantum dot including the spin-dependent tunnel couplings and the energy splitting between different spin manifolds. Our results open for the possibility of using Si CMOS quantum dots as a tuneable platform for studying high-spin systems.

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arXiv2018

Gate-Based High Fidelity Spin Read-out in a CMOS Device

The engineering of electron spin qubits in a compact unit cell embedding all quantum functionalities is mandatory for large scale integration. In particular, the development of a high-fidelity and scalable spin readout method remains an open challenge. Here we demonstrate high-fidelity and robust spin readout based on gate reflectometry in a CMOS device comprising one qubit dot and one ancillary dot coupled to an electron reservoir to perform readout. This scalable method allows us to read out a spin with a fidelity above 99% for 1 ms integration time. To achieve such fidelity, we exploit a latched spin blockade mechanism that requires electron exchange between the ancillary dot and the reservoir. We show that the demonstrated high read-out fidelity is fully preserved up to 0.5 K. This results holds particular relevance for the future co-integration of spin qubits and classical control electronics.

cond-mat.mes-hall↗

arXiv2017

A linear triple quantum dot system in isolated configuration

The scaling up of electron spin qubit based nanocircuits has remained challenging up to date and involves the development of efficient charge control strategies. Here we report on the experimental realization of a linear triple quantum dot in a regime isolated from the reservoir. We show how this regime can be reached with a fixed number of electrons. Charge stability diagrams of the one, two and three electron configurations where only electron exchange between the dots is allowed are observed. They are modelled with established theory based on a capacitive model of the dot systems. The advantages of the isolated regime with respect to experimental realizations of quantum simulators and qubits are discussed. We envision that the results presented here will make more manipulation schemes for existing qubit implementations possible and will ultimately allow to increase the number of tunnel coupled quantum dots which can be simultaneously controlled.

cond-mat.mes-hall↗

arXiv2016

Injection of a single electron from static to moving quantum dots

We study the injection mechanism of a single electron from a static quantum dot into a moving quantum dot created in a long depleted channel with surface acoustic waves (SAWs). We demonstrate that such a process is characterized by an activation law with a threshold that depends on the SAW amplitude and the dot-channel potential gradient. By increasing sufficiently the SAW modulation amplitude, we can reach a regime where the transfer is unitary and potentially adiabatic. This study points at the relevant regime to use moving dots in quantum information protocols.

cond-mat.mes-hall↗

arXiv2014

Quantum manipulation of two-electron spin states in metastable double quantum dots

We studied experimentally the dynamics of the exchange interaction between two antiparallel electron spins in a so-called metastable double quantum dot where coupling to the electron reservoirs can be ignored. We demonstrate that the level of control of such a double dot is higher than in conventional double dots. In particular, it allows to couple coherently two electron spins in an efficient manner following a scheme initially proposed by Loss and DiVincenzo. The present study demonstrates that metastable quantum dots are a possible route to increase the number of coherently coupled quantum dots.

cond-mat.mes-hall↗

arXiv2013

Genus 0 characteristic numbers of the tropical projective plane

Finding the so-called characteristic numbers of the complex projective plane ${\mathbb C}P^2$ is a classical problem of enumerative geometry posed by Zeuthen more than a century ago. For a given $d$ and $g$ one has to find the number of degree $d$ genus $g$ curves that pass through a certain generic configuration of points and at the same time are tangent to a certain generic configuration of lines. The total number of points and lines in these two configurations is $3d-1+g$ so that the answer is a finite integer number. In this paper we translate this classical problem to the corresponding enumerative problem of tropical geometry in the case when $g=0$. Namely, we show that the tropical problem is well-posed and establish a special case of the correspondence theorem that ensures that the corresponding tropical and classical numbers coincide. Then we use the floor diagram calculus to reduce the problem to pure combinatorics. As a consequence, we express genus 0 characteristic numbers of $\CC P^2$ in terms of open Hurwitz numbers.

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arXiv2010

Tropical Open Hurwitz numbers

We give a tropical interpretation of Hurwitz numbers extending the one discovered in \cite{CJM}. In addition we treat a generalization of Hurwitz numbers for surfaces with boundary which we call open Hurwitz numbers.

math.AG↗

arXiv2009

On the number of connected components of the parabolic curve

We construct a polynomial of degree d in two variables whose Hessian curve has (d-2)^2 connected components using Viro patchworking. In particular, this implies the existence of a smooth real algebraic surface of degree d in RP^3 whose parabolic curve is smooth and has d(d-2)^2 connected components.

math.AG↗

arXiv2007

Euler Characteristic of real nondegenerate tropical complete intersections

We define nondegenerate tropical complete intersections imitating the corresponding definition in complex algebraic geometry. As in the complex situation, all nonzero intersection multiplicity numbers between tropical hypersurfaces defining a nondegenerate tropical complete intersection are equal to 1. The intersection multiplicity numbers we use are sums of mixed volumes of polytopes which are dual to cells of the tropical hypersurfaces. We show that the Euler characteristic of a real nondegenerate tropical complete intersection depends only on the Newton polytopes of the tropical polynomials which define the intersection. Basically, it is equal to the usual signature of a complex complete intersection with same Newton polytopes, when this signature is defined. The proof reduces to the toric hypersurface case, and uses the notion of $E$-polynomials of complex varieties.

math.AG↗

arXiv2007

Euler characteristic of primitive T-hypersurfaces and maximal surfaces

Viro method plays an important role in the study of topology of real algebraic hypersurfaces. The T-primitive hypersurfaces we study here appear as the result of Viro's combinatorial patchworking when one starts with a primitive triangulation. We show that the Euler characteristic of the real part of such a hypersurface of even dimension is equal to the signature of its complex part. We use this result to prove the existence of maximal surfaces in some three-dimensional toric varieties, namely those corresponding Nakajima polytopes. In fact, these results belong to the field of tropical geometry and we explain how they can be understood tropically.

math.AG↗

arXiv2007

Real Zeuthen numbers for two lines

Given three natural numbers $k,l,d$ such that $k+l=d(d+3)/2$, the Zeuthen number $N_{d}(l)$ is the number of nonsingular complex algebraic curves of degree $d$ passing through $k$ points and tangent to $l$ lines in $\PP^2$. It does not depend on the generic configuration $C$ of points and lines chosen. If the points and lines are real, the corresponding number $N_{d}^\RR(l,C)$ of real curves usually depends on the configuration chosen. We use Mikhalkin's tropical correspondence theorem to prove that for two lines the real Zeuthen problem is maximal: there exists a configuration $C$ such that $N_{d}^\RR(2,C)=N_{d}(2)$. The correspondence theorem reduces the computation to counting certain lattice paths with multiplicities.

math.AG↗

arXiv2007

A Non-Algebraic Patchwork

Itenberg and Shustin's pseudoholomorphic curve patchworking is in principle more flexible than Viro's original algebraic one. It was natural to wonder if the former method allows one to construct non-algebraic objects. In this paper we construct the first examples of patchworked real pseudoholomorphic curves in $Σ_n$ whose position with respect to the pencil of lines cannot be realised by any homologous real algebraic curve.

math.AG↗