# Fileset [PRXQuantum.3.020343.pdf](https://mdr.nims.go.jp/filesets/791f34c9-d352-4b1e-927b-b25abf676187/download) ## Creator Lisa Maria Gächter, Rebekka Garreis, Jonas Daniel Gerber, Max Josef Ruckriegel, Chuyao Tong, Benedikt Kratochwil, Folkert Kornelis de Vries, Annika Kurzmann, [Kenji Watanabe](https://orcid.org/0000-0003-3701-8119), [Takashi Taniguchi](https://orcid.org/0000-0002-1467-3105), Thomas Ihn, Klaus Ensslin, Wister Wei Huang ## Rights [Creative Commons BY Attribution 4.0 International](https://creativecommons.org/licenses/by/4.0/) ## Other metadata [Single-Shot Spin Readout in Graphene Quantum Dots](https://mdr.nims.go.jp/datasets/2d55a2b9-8b0f-4d5e-8bb2-9a1098a96e93) ## Fulltext Single-Shot Spin Readout in Graphene Quantum DotsPRX QUANTUM 3, 020343 (2022)Single-Shot Spin Readout in Graphene Quantum DotsLisa Maria Gächter ,1,*,‡ Rebekka Garreis ,1,†,‡ Jonas Daniel Gerber ,1 Max Josef Ruckriegel ,1Chuyao Tong ,1 Benedikt Kratochwil ,1 Folkert Kornelis de Vries ,1 Annika Kurzmann ,1Kenji Watanabe ,2 Takashi Taniguchi ,2 Thomas Ihn ,1 Klaus Ensslin ,1 and Wister Wei Huang 11Solid State Physics Laboratory, ETH Zurich, Zurich CH-8093, Switzerland2National Institute for Material Science, 1-1 Namiki, Tsukuba 305-0044, Japan (Received 21 December 2021; revised 11 March 2022; accepted 15 April 2022; published 26 May 2022)Electrostatically defined quantum dots in bilayer graphene offer a promising platform for spin qubitswith presumably long coherence times due to low spin-orbit coupling and low nuclear spin density. Wedemonstrate two different experimental approaches to measure the decay times of excited states. The first isbased on direct current measurements through the quantum device. Pulse sequences are applied to controlthe occupation of ground and excited states. We observe a lower bound for the excited state decay on theorder of a hundred microseconds. The second approach employs a capacitively coupled charge sensor tostudy the time dynamics of the excited state using the Elzerman technique. We perform single-shot readoutof our two-level system with a signal-to-noise ratio of about 7 and find relaxation times up to 50 ms forthe spin-excited state, with a strong magnetic field dependence, promising even higher values for smallermagnetic fields. This is an important step for developing a quantum-information processor in graphene.DOI: 10.1103/PRXQuantum.3.020343I. INTRODUCTIONSpin qubits in semiconductors [1,2] have the advantagethat the operation and fabrication of gate electrodes aresimilar to classical transistors. High-quality qubits havebeen demonstrated on traditional bulk MOSFETs [3–5]as well as on III-V [6–8], silicon- [9–12] and germa-nium- [13] based heterostructures. Furthermore, semi-industrial structures compatible with industrial Si tech-nologies, such as fully depleted silicon-on-insulator(FD SOI) transistors [14] and fin field-effect transistors(FinFETs) [15], have been investigated.Graphene offers several advantages as a host materialfor spin qubits, namely naturally low nuclear spin con-centrations and weak spin-orbit interactions, similar toSi. In addition, the two-dimensional nature of grapheneallows for much smaller and possibly more strongly cou-pled quantum devices [16]. Furthermore, bilayer graphenequantum dots (QDs) offer the flexibility of bipolar oper-ation [17]. Compared to the mature Si-based technol-ogy, the development of quantum devices in graphene is*lisag@phys.ethz.ch†garreisr@phys.ethz.ch‡These authors contributed equally to this paper.Published by the American Physical Society under the terms ofthe Creative Commons Attribution 4.0 International license. Fur-ther distribution of this work must maintain attribution to theauthor(s) and the published article’s title, journal citation, andDOI.in its infancy. Recent advances in the controllability ofindividual states in single QDs [17–20] and double QDs[21,22], as well as the implementation of charge detec-tion [23], enable the realization of spin qubits based onelectrostatically defined QDs in bilayer graphene. Majormilestones such as qubit manipulation and detection haveyet to be achieved to unlock the qubit potential ofgraphene.Single-shot readout is an essential first step towardsbuilding a universal quantum computer and implement-ing quantum algorithms and quantum error detection. Inorder to reach the single-shot readout limit, it is criticalfor the excited-state relaxation time to be longer than themeasurement time to resolve a single charge tunnelingevent. We first investigate the relaxation time by mea-suring the current flowing through a QD [24,25], whichallows us to extract a lower bound only, similar to previ-ous experiments [26]. In order to study the time dynamicsof the excited state beyond the microsecond regime, weadd a charge detector to the device design and performtime-resolved measurements of the tunneling events in theQD. This allows us to perform single-shot readout of thetwo-level system using the Elzerman technique [27]. Wemeasure spin-relaxation times up to 50 ms at B⊥ = 1.7 T.We find a strong dependence of T1 on the external mag-netic field, promising even higher values for smaller spinsplitting. The spin-relaxation time presented in this paperis a few orders of magnitude longer than typical spin-qubitoperation times [28,29] and competes very well with othergroup-IV elements, like silicon [30,31].2691-3399/22/3(2)/020343(7) 020343-1 Published by the American Physical Societyhttps://orcid.org/0000-0002-6501-7570https://orcid.org/0000-0002-1233-998Xhttps://orcid.org/0000-0002-4164-8765https://orcid.org/0000-0002-4776-699Xhttps://orcid.org/0000-0003-4947-6002https://orcid.org/0000-0001-8491-3023https://orcid.org/0000-0001-6732-6513https://orcid.org/0000-0001-5947-0400https://orcid.org/0000-0003-3701-8119https://orcid.org/0000-0002-1467-3105https://orcid.org/0000-0002-5587-6953https://orcid.org/0000-0001-7007-6949https://orcid.org/0000-0001-9996-6371https://crossmark.crossref.org/dialog/?doi=10.1103/PRXQuantum.3.020343&domain=pdf&date_stamp=2022-05-26http://dx.doi.org/10.1103/PRXQuantum.3.020343https://creativecommons.org/licenses/by/4.0/LISA MARIA GÄCHTER et al. PRX QUANTUM 3, 020343 (2022)II. PULSED-GATE SPECTROSCOPYA false-color atomic force micrograph of the device isshown in Fig. 1(a). It consists of a h-BN encapsulatedbilayer graphene flake on top of a global graphite backgate with gold electrodes patterned on top. The gate layersare separated by 30-nm atomic-layer-deposited aluminiumoxide [17]. We form an n-type channel connecting sourceand drain by operating the back gate at VBG = 5 V andthe split gates at VSG = −3.13 V. Three finger gates areused to control the potential locally along the channel[see Fig. 1(a)]. The outer two finger gates TL and TRact as tunable tunnel barriers separating the QD from theleft and right reservoirs. With increasingly negative volt-age applied to the middle finger gate (the plunger gate),we locally lower the Fermi energy set by the back gate,subsequently loading holes into the QD forming belowthe gate. The sample is mounted in a dilution refrigera-tor with a base temperature of 9 mK on a printed circuitboard equipped with low-pass-filtered dc lines and 50-�impedance matched ac lines to perform pulsed-gate exper-iments. The plunger gate is connected to a bias tee allowingfor dc and ac control [e.g., applying a pulse as sketched inFig. 1(b)] while all other gates and the Ohmic contacts areconnected to dc lines only.We first define our two-level system. Due to spin andvalley degrees of freedom in bilayer graphene, the single-particle orbital states are fourfold degenerate, with twospins (↑, ↓) and two valleys (K and K ′) [18,32]. A per-pendicular magnetic field, B⊥, lifts the degeneracy dueto the spin (s) and valley (v) Zeeman effect followingE(B⊥) = ±(1/2)gs,vμBB⊥, with the spin g factor gs, thevalley g factor gv , and the Bohr magneton μB. Typicalvalues around gv = 30 [17] ensure that at electron tem-peratures below 100 mK, the two lowest energy levels arevalley polarized already at perpendicular magnetic fieldsB⊥ > 50 mT. As we operate our device at much higherfields, above B⊥ = 1.75 T, we can consider our QD asan effective two-level spin system with the ground state(GS) |K ′ ↑〉 and the excited state (ES) |K ′ ↓〉 energeticallysplit by �E = �SO + gsμBB with the zero-field spin-orbitsplitting �SO with typical values on the order of 60 μeV[20–22,33,34].To experimentally access the single-particle spectrumwe perform finite-bias spectroscopy measurements aroundthe N = 0 to N = 1 hole transition at B⊥ = 1.75 T[Fig. 1(c)]. The two lowest K ′-polarized energy states|K ′ ↑〉 and |K ′ ↓〉, from now on denoted as |↓〉 and |↑〉for ease of notation, are well observable while the K statesare split off and would only become visible for a larger biaswindow.To confirm the nature of the ES we apply an additionalin-plane magnetic field B‖, which couples only to the spindegree of freedom. Keeping the perpendicular magneticfield B⊥ = 1.75 T and the plunger gate voltage VPG fixed500VA (mV)−7.16−7.14VPG (V)I (pA)−1 0 1VSD (mV)024B|| (T)−505dI/dV (nA/V)−1 0 1VSD (mV)−7.16−7.14VPG (V)−505dI/dV (nA/V)Read UnloadRRUVacVRVUtUtR 2VAt(a) (c)VTL VTRSGSG200 nmQDVPGVac(d)(f)(b)N = 0N = 1R(e)RUEFFIG. 1. (a) False-color micrograph of the device. The plungergate (green) is controlled with dc voltage (VPG) and ac pulses(Vac) combined by a bias tee. The black squares with crossesinside symbolize Ohmic contacts. (b) The ac pulse sequence con-sists of a read phase with pulse level VR = −VA and durationtR and an unload phase with pulse level VU = VA and durationtU. (c) Coulomb diamond of the first hole transition taken atB⊥ = 1.75 T. For large source-drain voltage VSD the excited-state resonance can be observed. (d) In-plane magnetic fielddependence at fixed plunger gate voltage, corresponding to greenhorizontal dashed line in (c). The splitting of the GS and the ESat high magnetic field is consistent with a spin g factor of 2. (e)Schematic of transport through |↑〉R and |↓〉R during read phaseand through |↑〉U during unload phase. For ease of understandingan electronlike level scheme is used, while hole states are probedin the experiment. (f) Coulomb resonance as a function of pulseamplitude at pulse frequency f = 1.25 MHz. VA = 0 V corre-sponds to a line cut along the orange vertical dashed line in (c) atVSD = 40 μeV. For finite pulse amplitudes VA, the transition |↑〉splits into two branches, |↑〉R and |↑〉U, due to the two-level puls-ing. For pulse amplitudes eαattαPGVA > EZ , see orange arrow,transport through the ES is allowed by the pulse during the readphase and shows up as |↓〉R in between the GS peaks.[horizontal dashed line in Fig. 1(c)] we perform finite-biasspectroscopy measurements, varying the in-plane mag-netic field B‖ [Fig. 1(d)]. The splitting �E as a functionof magnetic field corresponds to a g factor of 2 and azero-field spin-orbit splitting �SO ≈ 60 μeV, consistentwith a spin ES.We then perform transient current spectroscopy mea-surements at a source-drain voltage VSD = 40 μV kBT020343-2SINGLE-SHOT SPIN READOUT IN GRAPHENE... PRX QUANTUM 3, 020343 (2022)to study the relaxation of the ES to the GS. We apply an acpulse additional to the dc voltage on the plunger gate, effec-tively shifting the QD states with respect to the Fermi levelof the reservoirs in time. We start with two-level pulseseach consisting of a read and an unload phase as shownin Fig. 1(b) with corresponding voltages VR and VU andpulse widths tR and tU. During tU, both |↑〉 and |↓〉 arepulsed above the Fermi level EF of the leads and the QDis emptied. During tR, if |↑〉 is aligned with EF we observea steady current. If |↓〉 is aligned with EF during tR while|↑〉 lies below, holes can only tunnel through the QD ESuntil one of them relaxes with a spin flip or until directtunneling from the leads into the GS occurs. This effec-tively blocks transport until the QD gets emptied again inthe subsequent unload phase. Figure 1(f) shows the currentthrough the QD as a function of pulse amplitude VA andVPG for tU = tR = 400 ns. We observe the splitting of theCoulomb resonance into two peaks, corresponding to tran-sient current through the GS of the read level, |↑〉R, and theunload level, |↑〉U. At 2VA = 100 mV, the peaks are sepa-rated by �VPG = 21 mV. This splitting is consistent withthe 13-dB attenuation installed along the high-frequencyline of our setup. The slope of the GS splitting, togetherwith the plunger gate lever arm, give us the conversionfactor from pulse amplitude to energy scale αattαPG, whereαatt = 0.21 and αPG = 0.05. For pulse amplitudes largerthan the Zeeman splitting [indicated in Fig. 1(f)] the cur-rent peak corresponding to a transient current through theES of the read level, |↓〉R, becomes visible as well. Weobserve the |↓〉R peak, because a sufficiently high perpen-dicular magnetic field B⊥ is applied. This not only liftsspin and valley degeneracies but also reduces the tunnelingrates between the QD and the reservoirs. At low perpen-dicular magnetic field |↓〉R is not visible, as the reductionof tunneling rates solely by voltages applied to the tunnelbarrier gates TL and TR is not sufficient in this device (seeRef. [23]).The longer the QD stays in the read phase, the morelikely the hole relaxes into the GS |↑〉. Therefore, studyingthe dependence of the amplitude of |↓〉R on the pulse widthtR allows us to extract information about the relaxationtime. However, two-level pulsed-gate spectroscopy onlyallows one to extract a lower bound for T1, as this mea-surement scheme cannot distinguish between relaxationand direct tunneling into the GS during the read phase.Already Ref. [35] suffered from this limitation, stating alower bound of T1 = 500 ns. To improve on this limita-tion, we extend the pulsing sequence to four-level pulseswith added load and wait phases in which both |↑〉 and|↓〉 are pulsed below the bias window [26,36]. The voltageand time for the load phase is chosen such that the timeintegral over voltages in one pulse sequence is zero, inorder to avoid charging up the bias tee. The correspondingfour-level pulse scheme is depicted in Fig. 2(a) with pulsewidths tL = tR = tU = 1 μs, and tW = 400 ns and voltagesVPG (V)I (fA)0 5 10 15tL + tW (µs)I (fA)0 5 10 15tL + tW (µs)0.250.500.751.00n(t)/n(t0)VacttL tW tR tU(a)(b)(c)(d)50 µs20 µs10 µs100 µsRRead UnloadLoad and waitULR WRVUVRVWVLFIG. 2. (a) Four-level pulse scheme for relaxation-time mea-surements. The hole enters a random state during the load phase.If the hole is loaded into the GS it will stay there and no transportcurrent can flow. If the carrier is loaded into the ES and does notrelax during tL + tW, the charge carrier can tunnel out, resultingin a transport current in the read phase. The QD is then emptied inthe unload phase and the cycle is repeated. (b) Current as a func-tion of plunger gate voltage while applying the four-level pulse.We observe various peaks corresponding to GS and ES levels ofdifferent pulse phases being aligned with the bias window. Thismeasurement is taken in a second cooldown at a B⊥ = 1.9 T,leading to a slight shift of VPG. (c) Current corresponding to EStransport during the read phase [shaded in green in (b)] as a func-tion of loading and waiting time. We vary the waiting time whilethe loading time remains constant at tL = 1 μs. The decay resultsfrom a combination of lower cycling rate and ES relaxation time.As described in the main text the decay is dominated by sig-nal decay. (d) Normalized average number of charge carriers perpulse cycle. Dashed color lines represent the decays with the cor-responding relaxation time. Our result indicates that relaxationdoes not play a significant role during the measurement window.VL = −9 mV, VW = 0 V, VR = 1.5 mV, and VU = 7.5 mVfor the respective pulse periods. During the load and thewait phases both |↑〉 and |↓〉 levels are below the bias win-dow, allowing a hole to tunnel into either one of the twostates. During tR, the ES |↓〉 is aligned with the Fermi levelof the leads while the GS |↑〉 is still below, allowing forspin-selective tunneling.Applying the four-level pulsing scheme while sweep-ing the dc plunger gate voltage VPG results in a currenttrace as shown in Fig. 2(b). Assigning the observed cur-rent peaks to GS and ES levels being aligned with the biaswindow during various pulse phases, we identify the peak|↓〉R (shaded in green), originating from holes tunnelingthrough the ES from source to drain during the read phase.If it relaxes to |↑〉 before the readout, it does not contributeto this current as it cannot tunnel out of the QD, making the020343-3LISA MARIA GÄCHTER et al. PRX QUANTUM 3, 020343 (2022)amplitude of the current peak a measure of the relaxation.Therefore, we investigate the amplitude of the currentpeak, |↓〉R, as a function of the waiting time tL + tW asshown in Fig. 2(c). Increasing the waiting time inevitablydecreases the ratio between the time spent in the read phaseand the total pulse cycle time ttotal causing signal decay inaddition to relaxation. We find that the current can be fittedto [36] I = 〈n〉e−(tL+tW)/T1/ttotal + Ibg in the limit T1 → ∞,and therefore effectively to I = 〈n〉/ttotal + Ibg with highconfidence. In these expressions, 〈n〉 is the average numberof charge carriers per pulse cycle, ttotal is the total durationof the four-level pulse, and Ibg is the background currentlevel. This implies that, within our measurement time win-dow the decay of the measured current through |↓〉R isdominated by the signal strength reducing as the pulsecycle time ttotal becomes longer for increasing tW. Multiply-ing (I − Ibg) with the total time tL + tW the GS and the ESlevels are pulsed below EF , we find the normalized proba-bility 〈n(t)〉/〈n(t0)〉 = e−(tL+tW)/T1 of the hole still being inthe ES after the load and wait phase as a function of load-ing and waiting time, tL + tW, shown in Fig. 2(d). Basedon this we conservatively estimate a lower bound for therelaxation time T1 ≥ 100 μs. The data is acquired over8 h over which the background current fluctuation can belarger than 0.1 fA and leads to an uncertainty in the off-set current. Careful determination of Ibg is crucial as itaffects the slope in Fig. 2(d). Further extending the waitingtime inevitably leads to vanishingly small current beyondthe detection limit of transport measurements. To over-come the signal strength limit, a more advanced readoutmechanism is required.III. SINGLE-SHOT SPIN DETECTIONRecent progress in fabrication techniques enabled therealization of a fully electrostatically defined device withan integrated charge detector as described in Ref. [23]. Thedevice shown in Fig. 3(a) consists of two channels sep-arated by a depletion region underneath a 150-nm-widemiddle gate. Similar to the sample presented above wedefine a QD between two tunnel barriers (TL and TR) anduse a plunger gate (PG) to tune the QD to single-electronoccupation in channel 2. The charge detector is based ona second QD formed below a single finger gate (FG) inthe current biased channel 1. A charge carrier tunnelingon or off the QD in channel 2 changes the electrostaticpotential in its surroundings, therefore also in the nearbysensing QD in channel 1. This potential change shifts theCoulomb resonances in the sensing QD and leads to a step-like change in the voltage across channel 1 [see middlepanel of Fig. 3(d)], if the sensing QD is tuned to the steepslope of a conductance resonance. This sample is measuredin a dilution refrigerator with an electron temperature of45 mK, and the ac and dc signals are combined via tworesistors as a voltage divider.(a)(c) (d)VacttL tR tU(b) UnloadLoadVUVRVLReadVTLVPGVFGVTR200 nmReadVacDetectorQDCh1Ch20 20 40t (ms)–6.347–6.345VPG(V)0 1PinVdetector (arb. units)0 20 40 60t (ms)FIG. 3. (a) False-color micrograph of a single QD device witha nearby charge detector. The QD is formed beneath the plungergate (green) in channel 2. TL and TR serve as tunnel barriers(yellow) to the leads. Another QD is formed under one finger gate(purple) in channel 1 and used as a charge detector. The blacksquares with crosses inside symbolize Ohmic contacts. (b) Three-level pulse scheme applied to the plunger gate. (c) Probability ofthe QD being occupied as a function of time and plunger gate dcvoltage VPG extracted from 500 single-shot traces. (d) Exemplarytraces for different read levels. Top: ideal read-level configurationallowing for single-shot ES-selective readout. Middle: GS levelis aligned with EF corresponding to multiple tunneling events.Bottom: both the ES and GS level are pushed above EF duringthe read phase, which results in a single tunneling-out event.At a perpendicular magnetic field of 2.1 T, we find aspin ES split from the GS of the one-electron quantumdot by about 315 μeV [see Fig. S1(a) within the Supple-mental Material [37]]. Extracting the energetic splitting ofthe ES |↓〉 from the GS |↑〉 for different magnetic fieldsyields a spin g factor of 2 and a spin-orbit coupling of�SO ≈ 70 μeV as presented in Fig. S1(b) within the Sup-plemental Material [37], which is consistent with previousresults [20–22].For the single-shot charge-detection experiment, we fol-low the scheme introduced by Elzerman in Ref. [27].Figure 3(b) shows the voltage pulses applied to the plungergate PG. Again, in the load phase either |↑〉 or |↓〉 can beloaded as both energy levels reside below the Fermi energyEF of the leads. During the loading time tL the chargecarrier is trapped on the QD and Coulomb blockade pre-vents an additional electron from entering. After tL thepulse amplitude is changed to VR such that the energylevel of the ES is pushed above EF while the GS level020343-4SINGLE-SHOT SPIN READOUT IN GRAPHENE... PRX QUANTUM 3, 020343 (2022)remains below. Therefore, the charge carrier can only tun-nel off the QD if it was loaded onto the ES in the previousphase. Once the charge carrier has left the QD from theES, the Coulomb blockade is lifted and another chargecarrier can tunnel into the GS. The combination of thesetwo processes, tunneling out from the ES, followed bytunneling into the GS, leads to a characteristic “blip” inthe detector voltage, indicative of ES loading during theload phase. Note that here we pulse the ES above EFof the leads, in contrast to the transport measurementsbefore, where we aligned the ES level with the leads dur-ing the read phase. After tR we enter the unload phase,where the pulse amplitude is changed to VU, and bothenergy levels are pushed above EF emptying the QD. Asa response to the three-level pulse we expect a change ofvoltage across the sensing QD consisting of two contri-butions. First, due to capacitive coupling between PG andthe sensing QD the voltage will change proportionally tothe applied pulse amplitude. Second, the voltage across thesensing QD traces the charge occupation of the QD, step-ping up or down as soon as a charge carrier tunnels off oron the QD. Whenever we load the GS during load phase,the voltage trace should stay flat during tR. Therefore, mea-suring whether the voltage trace shows a blip or not duringthe readout phase forms the basis of our single-shot readoutmechanism.To find the appropriate alignment of the read level forES-dependent tunneling we sweep VPG while keeping thethree-level pulse amplitude constant. We choose pulseswith tL = 10 ms, tR = 30 ms, and tU = 20 ms, long enoughto allow the charge carrier to tunnel in and out of the QD.The pulse voltages VL and VU ensure that both energy lev-els are pushed below (above) EF of the leads during theload (unload) phase. Starting with VPG being too low, boththe |↑〉 and the |↓〉 level lie above EF , such that the chargecarrier can always tunnel off the QD regardless of beingin the ES or the GS. The characteristic voltage trace inthis regime only shows a step up corresponding to theunloading event, and then remains at this higher level asshown in Fig. 3(d) bottom panel. Increasing VPG we enterthe regime of random telegraph signals corresponding tothe |↑〉 level being aligned with EF of the leads such thata charge carrier can tunnel on and off the QD multipletimes within the read phase as observed in Fig. 3(d) middlepanel. Increasing VPG further we find the correct read levelwhere we can distinguish between the |↑〉 and the |↓〉 stateof the QD being occupied. A single blip at the beginningof the read phase corresponds to the ES tunneling off theQD and subsequent tunneling into the GS from one of theleads. A flat trace during tR indicates that the charge car-rier was loaded into the GS during the load phase, and isthus trapped on the QD. Alternatively, the ES could havebeen loaded relaxing into the GS, before tunneling out. Inthis region the condition μES > EF > μGS is fulfilled andwe can perform a single-shot projective measurement ofthe state of the charge carrier. Exemplary traces for thetwo cases are shown in Fig. 3(d) top panel, with the bluetrace corresponding to the GS and the orange one with thecharacteristic blip corresponding to the ES.Averaging the read-phase voltage across the sensing QD〈Vdetector〉 over 500 single-shot traces at different plungergate voltages VPG we estimate the probability of the QDbeing occupied as a function of time shown in Fig. 3(c).The correct readout configuration shows a lower prob-ability in the beginning of the read phase, as observedin the upper part of Fig. 3(c) from VPG = −6.3465 V toVPG = −6.3436 V.Analyzing a data set consisting of 7500 single-shot measurements we extract the histogram of thepeak values of the detector voltage Vdetector shown inFig 4(a). We identify two well-separated peaks indicat-ing that VDetector has two favorable values correspond-ing to the first electron being or not being in the QD.The two voltage levels are separated with a SNR =|μ1 − μ2| /√σ 21 + σ 22 = 6.95 as obtained from fitting twoskewed Gaussians A exp[−(x − μ)2/2σ 2][1 − erf(γ (x −μ)/√2σ)]. This SNR corresponds to an electrical readoutfidelity well above 99%. However, the tunneling-out andrelaxation rate of the ES are of the same order of magni-tude, reducing the fidelity of the spin-to-charge conversion.Tunneling-out events from the ES can only be observedif the ES does not decay into the GS after tunneling induring the load phase or before tunneling out during theread phase. Thus, varying the length of the load phasegives information about the spin-relaxation time T1, sincethe number of observed blips exponentially decays with alonger load phase. As shown in Fig. 4(b), the total numberof blips increases for short load times tL before decreasingexponentially with the characteristic spin-relaxation timescale T1. For short tL, the number of observed blips is lim-ited by the overall tunneling rate into either |↑〉 or |↓〉. Toextract T1, the function C(exp(−tL/T1) − exp(−�intL)) isfitted to the data with fitting parameters C and T1. Theparameter �in = 350 ± 12 Hz is the total tunneling rateinto the QD during the load phase. We find T1 = 8.37 ±0.34 ms at B⊥ = 2.1 T for the data in Fig. 4(b). As pre-sented in Fig. 4(c), the relaxation time tends to increasewith decreasing magnetic field. Data points for the samefield configuration are individual measurements where T1scatters randomly for different tunnel barrier voltages [seeFig. S1(c) within the Supplemental Material [37] ]. Whilewe could not observe a temperature-dependent change ofT1 for 45 mK < T < 120 mK, we find a strong dependenceon magnetic field and measure a maximum T1 = 50 ms atB⊥ = 1.7 T. Compared to GaAs [25,36], the measured T1is large as expected from the lower nuclear spin densityand the weaker spin-orbit interactions in graphene [38].For other group-IV elements, such as silicon, T1 timesbetween 1 ms and up to 9 s have been reported [30,31].020343-5LISA MARIA GÄCHTER et al. PRX QUANTUM 3, 020343 (2022)(a) (b) (c)0 10 20 30 40tL (ms)0500100015002000Nblip~ 1 − exp((−Γ in + 1/T1)tL)~ exp(−tL/T1)1.5 2.0 2.5 3.0B⟂ (T)1021031/T 1 (Hz)−2 0 2Vdetector (μV)0200400600CountsDataFitFIG. 4. (a) Histogram of maximum detector voltage values during the read phase. The histogram is fitted with two skewed Gaussianswith γGS = −1.7, μGS = −1.4 μV, σGS = −0.27 μV and γES = 2.76, μES = 2.3 μV, σES = −0.6 μV. (b) Number of blips observedduring read phase as a function of loading time. The relaxation time is extracted from the exponential decay. (c) Magnetic fielddependence of the relaxation rate 1/T1. Data points for one magnetic field correspond to statistically independent measurements.For bilayer graphene T1 lies within the same order of mag-nitude and shows a similar dependence on magnetic field,promising even higher values for smaller Zeeman splittingat lower magnetic field. A sufficient reduction of the tun-neling rates for further T1 measurements at lower magneticfields cannot be achieved with the current device. Typi-cal mechanisms that determine T1 are spin-orbit-inducedphonon scattering and hyperfine interaction. The limitingmechanism in bilayer graphene remains to be investi-gated. Nevertheless, we expect similar relaxation times forelectrons and holes in bilayer graphene.IV. CONCLUSIONIn conclusion, we first characterized the lifetime ofexcited states in a graphene QD through direct trans-port measurements. The measurement is limited by signalstrength rather than the relaxation time, comparable to pre-vious measurements performed in bilayer graphene QDs.In a second step we presented a QD device integrated witha capacitively coupled charge sensor capable of resolv-ing a single charge tunneling event in the time domain.The sensitivity of the charge detector enables excited-statereadout in the single-shot limit—an essential step towardsa fully controllable quantum processor in graphene. Wemeasured spin-relaxation times up to 50 ms at B⊥ = 1.7 T,where T1 strongly depends on the magnetic field applied,promising even longer times for lower fields. The extractedvalues of T1 are comparable to the spin-relaxation times inmost semiconductor spin qubits, showing that spin qubitsin bilayer graphene QDs are promising.ACKNOWLEDGMENTSWe are grateful for the technical support from PeterMärki, Thomas Bähler, and the staff of the ETH FIRSTcleanroom facility. 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INTRODUCTION II.. PULSED-GATE SPECTROSCOPY III.. SINGLE-SHOT SPIN DETECTION IV.. CONCLUSION . ACKNOWLEDGMENTS . 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