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A key beforehand in this hybrid-CNT accessory is the accomplishing of a automated alteration at ambient conditions. The aforementioned marks the aftermost footfall of sample fabrication. After the complete RF and DC circuitries are fabricated, the dent is affirmed on a printed ambit lath and bankrupt with a anemic argon claret to aish oxides and artifact balance from the contacts. We abound CNTs on the fork-like structures of a abstracted chip, which acquiesce a resist- and ebeam radiation-free automated alteration of the CNTs to the source/drain electrodes on a colonnade anatomy (inset Fig. 1a). Forks are accumbent with the colonnade application an optical microscope of a micro-manipulator bureaucracy and acknowledged transfers are monitored through voltage biased (200 mV) attrition measurements. We can again actuate bandgap characteristics of transferred CNTs by barometer the conductance acknowledgment to an activated aboideau voltage. Furthermore, we can aish tubes with exceptionable characteristics, such as a brownish response, by applying a ample bent voltage, and after alteration and assay accession CNT on the aforementioned device. These capabilities accomplish our adjustment of alteration a deterministic one with accord accessory yield. Added capacity of the CNT advance and alteration adjustment can be begin in the Supplementary Agenda 2.

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(a) Architecture of an impedance-matching ambit based on two manual curve with hardly altered lengths l and d, both aing to λ/4. The band d terminates in an accessible end while the axial aqueduct of l connects to the antecedent (S) of the CNT device. A false-colour SEM angel is apparent in b with larboard (LG), average (MG) and appropriate (RG) basal gates. CNTs are transferred mechanically from angle structures to the affirmed accessory dent in the final artifact step, schematically apparent in the inset of a. The account displays about position of CNTs with bogus gates and aegis contacts. The cesspool (D) is affiliated to the arena alike of the Niobium film, not arresting here. (c) Agnate analogous ambit based on lumped elements. L and C are bent by the lengths l and d, while the phenomenological conductance GLoss captures the accident of the manual lines. GCNT is the accessory conductance of the CNT.

A manual band based impedance-matching circuit, termed tuner28, can be accomplished by two manual curve affiliated in parallel, with the accessory placed on one end, the added catastrophe in an accessible ambit (Fig. 1a). Though simple lumped LC circuits can additionally be employed, they appeal a diffuse accepted architecture action back acclimated at frequencies of gigahertz due to devious capacitances of about femtofarads. By utilizing manual lines, we are not alone able to abbreviate abject effects, such as devious capacitances, but are additionally able to atone for them, as they alone change the able breadth of the lines.

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The bake acknowledgment of the tuner is mainly bent by the lengths of the two curve l and d, which are alleged such that a specific accessory impedance, alleged the akin amount ZMatch, will be adapted to the appropriate impedance of the band Z0 at one specific resonance frequency. At this load, the assimilation accessory is minimized, implying best ability transfer. To get the reflectance Γ, we account the impedance Zin of the amalgam device, consisting of a alongside aggregate of the two manual lines28,29 as

γ=α iβ is the advancement affiliated with α and actuality the accident and appearance constants, respectively, the able dielectric constant, c the acceleration of light, f the frequency, Z0 the manual band impedance, and the circuitous admission 1/ZCNT=Y=GCNT iBCNT with GCNT conductance, and BCNT susceptance of the CNT device.

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The ambit is acute to changes in both the conductance and susceptance, as apparent in Fig. 2a, breadth we artifice a set of assimilation spectra for altered amount admittances Y, with lengths alleged for a resonance at 3 GHz and a akin amount of 4.8 μS, d no losses. Varying GCNT from 3 to 4 μS increases both the abyss and amplitude of the resonance, but not the resonance frequency. In contrast, a change in the susceptance B mainly accouterment the resonance, with a accessory change in its depth. To allegorize the furnishings that losses accept on this device, we can alter the ambit by an agnate lossless one while introducing a phenomenological conductance GLoss alongside to the CNT amount (Fig. 1c) and appropriately defining a absolute able amount Geff=GCNT GLoss apparent by the microwaves. In Fig. 2b, we artifice Γ at the resonance as a action of Geff. The reflected arresting is the aboriginal aing to the akin amount alms acute ability transfer. The closing is added important for barometer baby noise-power emitted from the device. Due to the added accident conductance GLoss, the CNT amount which matches the ambit is abate than GMatch and is accustomed by . In particular, if GLoss>GMatch abounding analogous is precluded and the assimilation accessory as a action of amount becomes monotonic (see inset of Fig. 2b).

(a) Assimilation spectra of a loss-less tuner with 4.8 μS akin amount at 3 GHz for altered loads. Alteration the absolute allotment of the amount changes the linewidth and abyss of the resonance, while alteration the abstract allotment mainly accouterment the resonance frequency. (b) The reflectance at the resonance abundance as a action of a absolute able amount (Geff=GCNT GLoss) shows a non-monotonic acknowledgment and the aboriginal reflected arresting at the akin load. Its appropriate changes to a monotonic acknowledgment for GLoss>GMatch as apparent in the inset (same as the abject box) for GLoss=6 μS.

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The presented CNT accessory has three recessed bounded basal gates with added antecedent and cesspool contacts animated by ∼150 nm (Fig. 1b). Basal gates are afar by ≈200 nm from anniversary added and from the antecedent cesspool contacts bearing a abeyant breadth of the CNT of ≈800 nm. The manual curve are blooming on a Nb blur and crop a resonance abundance ωr/2π=2.9 GHz. All abstracts are performed at the abject temperature of the cryostat ∼20 mK (Supplementary Agenda 3). The antecedent is affiliated to the axial aqueduct of the manual band (l branch) while the cesspool is affiliated to the arena plane. For the assuming of the devices, the CNT is acquainted into the bandgap to present an absolute attrition and appropriately an accessible end. By barometer the assimilation spectrum, it is accessible to abstract the accordant ambit (l, d, α and ). The extracted accident α=[0.0074,0.0082] m−1 for delving ability in the ambit [−110,−140] dBm corresponds to centralized affection factors of 10,000 to 9,000 for an agnate half-wave resonator, assuming that we are able to accomplish low-loss bake circuits in aggregate with CNT devices. Due to abject inductances from the bogus contacts, the analogous ambit has a lower able GMatch≈1.6 μS compared with GLoss≈3.2 μS and operates accordingly in the internal-loss-dominated regime. Abstracts of the analogous ambit acknowledgment can be begin in the Supplementary Agenda 4, as able-bodied as the altitude of an added sample breadth abounding analogous is approved (Supplementary Agenda 5).

Room temperature DC assuming during the accessory accumulation allows us to accomplish several CNT automated alteration trials on the aforementioned accessory and accept nanotubes based on their aboideau dependence. In accurate for semiconducting nanotubes, we can use the basal gates to locally about-face the Fermi akin aloft or beneath the valence and advice bands of the nanotube. The closing allows for creating gate-defined bonds potentials forth the nanotube and appropriately for affability the location, admeasurement and cardinal of breakthrough dots13. With no RF ability activated to the tuner and the average aboideau VMG=0 V, we aboriginal admeasurement the allegation adherence diagram of the CNT device. A aboideau ambit application larboard (VLG) and appropriate gates (VRG) at VSD=10 mV DC bent is apparent in the Fig. 3a. The accepted acknowledgment acutely displays the ambipolar behaviour of breakthrough dots about a semiconducting gap of ∼30 meV with larboard and appropriate gates affability the CNT into n–n, n–p, p–n and p–p bifold dots. Actuality we accept acclimated a aboideau batten arm of ≈0.2 meV mV−1 extracted from the Coulomb design measurements. In addition, we beam the exact allegation activity of electrons and holes at agnate aboideau voltages12. The aerial conductance in the n–n administration is possibly due to n-doping a the source/drain contacts. We additionally begin p-doping for abounding samples for the aforementioned Pd contacts and do not absolutely accept the attributes of the empiric acquaintance doping.

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(a) DC abstracts of the CNT accessory at VSD=10 mV and VMG=0 appearance a semiconducting gap and the accumulation of bipolar bifold dots about it back VLG and VRG are swept. We beam the accession of electrons and holes in anniversary administration starting from complete burning in the bandgap. n–n bifold dots appearance about ample conductance due to n-doping of the contacts. (b) Accompanying abstracts of current, reflected amplitude and appearance at the resonance abundance in the p–p double-dot arena at −10 mV bent adumbrated by a abject box in a. Co-tunneling curve are acutely arresting in all the plots. Inter-dot coupling curve not present in DC artifice are arresting in the amplitude and appearance acknowledgment due to abundance accouterment at aboideau voltages apparent by abject circles. The arrow credibility at afflicted gate-tunable curve best acceptable constant from allegation traps, which do not necessarily accord to the accepted but do change the susceptance. A delving ability of −110 dBm is applied.

We now accomplish accompanying abstracts of DC and RF reflectometry to access a aggregate acknowledgment of the bifold breakthrough dots. Γ is abstinent a the resonance abundance with a delving ability alleged to be so low that no out-of-equilibrium accuse are induced back applying bake arresting to the tuner. Figure 3b shows a qualitatively agnate bore allegation adherence diagram in current, amplitude and appearance responses taken at VSD=−10 mV bias. We acutely beam co-tunnelling lines3, continued edges of the honeycomb, in all plots suggesting acceptable acuteness to impedance changes alike in case of a ambit whose centralized losses boss the affection agency of the resonances. Actuality we agenda an important acumen of the tuner. For half-wave resonators, the RF arresting for co-tunnelling curve acerb depend on the backbone of the capacitive coupling to agnate lead-dot transitions and their ante with account to the resonance frequency30. DC-coupled tuner, in contrast, still responds through conductance changes that accommodate an alien coupling by shunting the microwaves via the cesspool acquaintance into the arena plane. This is added apparent in Fig. 3b breadth beyond accepted after-effects in beyond |ΔΓ| and Δφ (see Supplementary Fig. 3a,b). In addition, we additionally beam alloyed bifold dots at degeneracy, the aals of two honeycombs at the two abate edges, apparent by abject circles in Fig. 3b, in the appearance and amplitude plots. The arresting after-effects from the susceptance changes acquired by dipole coupling of the alloyed allegation states to the bake resonance. The responses at altered allegation degeneracies are altered due to the audible dot coupling energies tc, which are afflicted by all aboideau voltages in our sample.

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To allegorize the ascendancy over the bonds abeyant of the bifold breakthrough dots in this apple-pie CNT device, VMG is acclimated to tune the tunnelling barrier amid the two breakthrough dots. In the DC measurements, the backbone of the tunnelling coupling is arresting as the break amid the allegation amateur credibility with the beyond amount agnate to a stronger coupling or weaker barrier (Supplementary Fig. 5). For a quantitative analysis, the appearance acknowledgment of the tuner can be abstinent application a anemic delving ability (−130 dBm) a the admixture of two allegation states (m, n 1) and (m 1, n) as apparent in Fig. 4a. We accomplish in the zero-bias regime, acceptance the dots to break in calm and aphorism out any conductance changes which could affect the resonance response. Such a appearance about-face is apparent in Fig. 4c aing to (2,2) to (1,3) aperture transition. We infer the abundance accouterment Δf from the appearance variations which are about linearly activated a resonance (see Fig. 4e, absurdity <10% in our case). Following a semiclassical archetypal anecdotic the coupling of a qubit with abundance to a resonator with abundance ωr (Supplementary Agenda 7), the burning Δf of the resonator is accustomed by

(a) Activity levels of a bifold breakthrough dot with an inter-dot admixture activity of tc, basic a two-level arrangement with activity ωd. (b) The tuner resonance adventures a abrogating dispersive about-face Δf for ωr<2tc due to its coupling to the two-level system. (c) The appearance acknowledgment abstinent at the resonance abundance as a action of VLG and VMG yields a arresting inter-dot alteration due to admixture of the allegation states (2,2) and (1,3). (d) A cut adumbrated by the abject arrow in c with a fit to blueprint (2) to abstract the inter-dot coupling activity tc=20 GHz. (e) The tuner appearance acknowledgment at VMG=130 mV about the dot abasement (open circles) and bachelor dots (solid circles) apparent by credibility 2 and 1 in c, respectively. (f) Extracted tc and Γtot as a action of VMG. Absurdity confined represent uncertainties in the atomic aboveboard fitting. (g) The best appearance acknowledgment ΔΦ adumbrated in d is suppressed at beyond VMG due to accretion Γtot apparent by the blah area. (h) The reflected ability acknowledgment at VMG=260 mV displays near-resonant assimilation admitting negligible dispersion. Solid curve are the fits to blueprint (2). Syms accept the aforementioned acceptation as in e.

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where Γtot=γ/2 Γφ with γ and Γφ are the able alleviation and dephasing ante of the alloyed bifold dot, respectively, Δ=ωd–ωr and actuality the detuning, g0 the aught temperature coupling backbone with the resonator and the animosity of the double-dot alteration at cyberbanking temperature T. We use the blueprint to aboriginal abstract g0 in a administration breadth tc is ample (VMG is small) so that ωd2tc≫ωr, Γtot. This yields a assurance of the abundance about-face Δf proportional to , now absolute of Γtot. A fit with this blueprint to the abstracts at VMG=130 mV is apparent in Fig. 4d, acquiescent g0/2π=37 MHz. We acquisition the aforementioned g0 for VMG=110 mV acknowledging the acceptance that Γtot is about baby in this regime. Fixing this g0 for appearance responses at added VMG, we artifice the extracted tc and Γtot in Fig. 4f and beam a abridgement of tc on accretion VMG assimilation a abridgement in the adit coupling backbone amid the dots. The appearance acknowledgment starts to be suppressed for VMG >200 mV due to more fast double-dot relaxation, acquiescent Γtot>tc. The changed assurance of Γφ on tc has been apparent in agnate systems7,31 and could be due to the 1/f allegation babble environment32 of the nanotube. The assurance of the abundance about-face consistently charcoal negative, added blame that the resonator activity is consistently <2tc. Accretion VMG to >250 mV, we do not apprehension any burning because of the ample Γtot. However, the alloyed dots still appearance a acknowledgment agnate to Fig. 2a, now alone in the reflectance amplitude. For VMG=260 mV, the tuner acknowledgment for accompanying and bachelor dots regimes is presented in Fig. 4h. The fit to the resonance at the double-dot abasement (open circles) shows a abate abyss and α=0.0086, m−1 compared with the one in the bachelor administration (solid circles) with α=0.0082, m−1. This behaviour is a aftereffect of an added accident approach that is, assimilation from the two-level alloyed dots back 2tc becomes commensurable to ωr, which is additionally constant with the change in the resonance abyss due to the conductance access for our accessory ambit (Supplementary Figs 3a and 6b).

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