Magnetic-Field-Compatible Superconducting Transmon Qubit
A. Kringhøj, T. W. Larsen, O. Erlandsson, W. Uilhoorn, J. G. Kroll, M. Hesselberg, R. P. G. McNeil, P. Krogstrup, L. Casparis, C. M. Marcus, K. D. Petersson
MMagnetic-Field-Compatible Superconducting Transmon Qubit
A. Kringhøj,
1, 2, ∗ T. W. Larsen,
1, 2, ∗ O. Erlandsson,
1, 2
W. Uilhoorn, J. G. Kroll, M. Hesselberg,
1, 2
R. P. G. McNeil,
1, 2
P. Krogstrup,
1, 4
L. Casparis,
1, 2
C. M. Marcus,
1, 2 and K. D. Petersson
1, 2 Center for Quantum Devices, Niels Bohr Institute,University of Copenhagen, 2100 Copenhagen, Denmark Microsoft Quantum Lab-Copenhagen, Niels Bohr Institute,University of Copenhagen, 2100 Copenhagen, Denmark QuTech and Kavli Institute of Nanoscience, Delft University of Technology, 2600 GA Delft, The Netherlands Microsoft Quantum Materials Lab-Copenhagen, 2800 Lyngby, Denmark
We present a hybrid semiconductor-based superconducting qubit device which remains coherentat magnetic fields up to 1 T. The qubit transition frequency exhibits periodic oscillations withmagnetic field, consistent with interference effects due to the magnetic flux threading the crosssection of the proximitized semiconductor nanowire junction. As induced superconductivity revives,additional coherent modes emerge at high magnetic fields, which we attribute to the interaction ofthe qubit and low-energy Andreev states.
I. INTRODUCTION
Superconductor-semiconductor-superconductor (S-Sm-S) nanowire Josephson junctions have been integratedinto various superconducting circuits, including gate volt-age tunable transmon qubits, known as gatemons [1, 2],tunable superconducting resonators [3], and Andreevqubits [4, 5]. These hybrid junction elements allow insitu voltage control of their Andreev spectra and current-phase relation [6–9], in turn influencing measurable qubitproperties such as anharmonicity [10] and charge disper-sion [11, 12]. Moreover, S-Sm nanowires in the presenceof strong magnetic fields may host Majorana zero modes -as evidenced by both dc tunneling and Coulomb blockadespectroscopy measurements [13, 14] - potentially formingthe basis of robust topological qubits [15].Recent work has demonstrated the coherent operationof gatemons with S-Sm-S nanowire junctions at moder-ate magnetic fields, ∼
100 mT [16, 17]. Spectroscopyof S-Sm-S nanowire fluxonium qubits [18] and graphene-based gatemons [19] at high magnetic fields ( ∼ /f flux noise to be further elucidated through studying ∗ These authors contributed equally.
B V cut V lplg V rplg Island1 µ m (a) (c)(b) µ m FIG. 1. Magnetic field-compatible device. (a) Micrograph ofthe transmon qubit island capacitively coupled to a λ/ V lplg and V rplg ) thattune the chemical potential in sections (green) of the proxim-itized InAs. A small region of the superconductor betweenthese two segments is removed to create a Josephson junc-tion, controlled by V cut . A magnetic field, B , is applied alongthe wire axis. the polarization of spin impurities [16, 25, 26].In this work, we present a high-magnetic-field-resilientnanowire-based transmon circuit. We demonstrate co-herent qubit operation for in-plane magnetic fields up to1 T. Further, we observe a field dependent periodic lobestructure in the qubit spectrum, attributable to interfer-ence effects as an integer number of flux quanta threadthe nanowire cross section. Finally, we observe a richspectrum of additional energy excitations as we transi-tion into the first and second lobes of the qubit spectrum.We associate these excitations with Andreev states, vis- a r X i v : . [ c ond - m a t . m e s - h a ll ] J a n ible due to their coupling to the qubit. II. MAGNETIC FIELD COMPATIBLEGATEMON DEVICE
Figure 1 shows the qubit device. A 20 nm-thickNbTiN-film on a high resistivity silicon substrate waspatterned by electron-beam-lithography and a chlorine-based dry-etch process to form the λ/ ∼
100 nm, with two out of six facetscovered by a 7 nm thick epitaxially matched aluminumfilm [29]. Prior to the initial NbTiN deposition, a localregion of 5 nm thick HfO was deposited using atomic-layer-deposition techniques to ensure no leakage betweenthe closely spaced gates through the silicon substrate [30].A second thicker HfO layer (15 nm) was deposited ontop of the bottom gates as a gate dielectric. To form theJosephson junction, a small segment of the aluminumshell was removed by wet etching ( ∼
100 nm) [2].To complete the gatemon qubit circuit, the nanowirewas connected to the T-shaped qubit island, with sim-ulated charging energy E C /h = 230 MHz [31], and tothe surrounding ground plane, see Fig. 1(b). A lightRF mill was used to remove the native oxide of InAsprior to depositing ∼
200 nm NbTiN sputtered contacts.The qubit island was capacitively coupled to the λ/ f r ∼ .
95 GHz for readoutand microwave control. Large plunger electrodes, V lplg and V rplg , allowed for tuning of the chemical potential ofthe two proximitized nanowire segments on each side ofthe Josephson junction [green segments of Fig. 1(c)]. Athird electrode, V cut , located under the junction tunedthe Josephson energy, E J , and in turn the qubit fre-quency, f q . On-chip LC -filters (not shown) on each gateelectrode suppressed microwave dissipation through thecapacitively coupled gates [32]. A second qubit with noplunger gates was coupled to the same resonator (notshown).We present data from the qubit device shown in Fig. 1,which maintained coherence up to magnetic fields of 1 T.For multiple similar devices we observed coherent oper-ation up to ∼
500 mT. The sample was placed inside aCuBe enclosure filled with microwave absorbing Eccosorbfoam to reduce stray microwave and infrared radiation.The enclosure was mounted inside a bottom-loading di-lution refrigerator equipped with a 6-1-1 T 3-axis vectormagnet and with a base temperature <
50 mK (see Ap-pendix B for further details, including a schematic of thesetup).
III. QUBIT MEASUREMENTS IN LARGEMAGNETIC FIELDS
We investigated the qubit behavior by performing two-tone spectroscopy as a function of magnetic field, B ,aligned along the nanowire axis. A varying drive toneat frequency f d was applied, followed by a readout tonefor each B . During these measurements, the cavity res-onance was first measured for each B in order to correctfor any changes in the readout frequency. Out-of-planemagnetic fields on the order of 10 µ T modified the res-onance frequency of the cavity, however we did not ob-serve any degradation in the resonator Q factor as thetotal magnetic field was varied. While changing B, inter-mittent corrections to the magnetic field alignment werealso applied to minimize the out-of-plane magnetic fieldcomponent (see Appendix A for details).Figure 2 shows the qubit spectrum as a function of B up to 1 T. The qubit spectrum exhibits a lobe structurewith three lobes separated by minima at B ∼ .
225 Tand B ∼ .
675 T and a reduced maximum qubit fre-quency in higher lobes. These minima may occur dueto a suppression of the induced superconducting gap,∆ ∗ , in the leads of the junction due to interference ef-fects [33]. Depending on gate voltage the charge densityin the semiconductor nanowire leads may be confined tothe surface, see Fig. 2 inset. As analysed by Winkler et al. [34], a segment of this cross-sectional geometryeffectively forms a superconducting ring interrupted bya semiconductor Josephson junction with the supercon-ducting gap modulated by the periodic flux-biased phasedifference [Fig. 2, inset]. For the case of half a flux quan-tum threading the nanowire at B = 0 .
225 T, the ap-plied flux Φ in units of flux quanta Φ is shown alongthe top horizontal axis of Fig. 2. From this period, weestimate the effective diameter of the interference loop tobe d eff = (cid:112) /πB (Φ = Φ /
2) = 76 nm. As the chargeaccumulation layer will have a finite thickness one ex-pects a slightly smaller effective diameter compared tothat of the nanowire ( ∼
100 nm) [35]. Simulations ofrealistic wire geometries [34] also predict a reduced max-imum superconducting gap in higher lobes due to inho-mogeneity in the effective diameter. This is consistentwith our measured data where the qubit frequency, f q ,is expected to scale with √ ∆ ∗ . Similar oscillations withmagnetic field have also been observed for nanowires intransport experiments [36] and were attributed to inter-ference effects in the junction itself, which may also playa significant role here. We note that the field dependenceis strongly influenced by the nanowire charge distributionand the oscillations observed here were for a particularrange of plunger-gate values [34, 37]. Periodic oscillationsin qubit frequency have also been observed for gatemonswith nanowire junctions where the Al shell fully enclosedthe leads, which were interpreted as the Little-Parks ef-fect [17].We next consider the qubit behavior in each of thethree lobes. In the zeroth lobe measured from B ∼ B (T)2.02.53.03.54.0 f d ( G H z ) /2 (cid:301) /2 2(cid:301) -11 V H ( a . u . ) B Al shelllow highProximitized InAs charge density Φ
FIG. 2. Two-tone spectroscopy as a function of magnetic field B at V cut = − . V lplg = V rplg = − . f d , was applied and immediately followed by a readout tone at the cavity resonance frequency, allowing readout ofthe demodulated transmission voltage, V H . The qubit drive power was adjusted between traces to account for varying lifetimeand detuning from the readout cavity, which may cause changes in the background signal and linewidths of transitions. Dataaround 0 .
58 T omitted due to too low applied signal power during two-tone spectroscopy. A line average is subtracted fromdata for each B . Inset: Sketch illustrating the cross section of a two-facet nanowire with the hypothesis that the electrondensity accumulates at the InAs surface, as illustrated by the color gradient (green/white). A superconducting ring is createdby the superconducting Al shell (blue) and the proximitized InAs (green). For an axial magnetic field, B , a flux, Φ, threadsthe nanowire cross section resulting in a periodic modulation of the qubit frequency. The top horizontal axis is constructed byinferring that a half-integer number of flux quanta, Φ (= h/ e ), thread the nanowire at B = 225 mT. ∼
150 mT, the qubit behaves indistinguishably from astandard gatemon device. Due to the high drive power,multi-photon transitions are observed, exciting higher en-ergy states of the qubit. Around 150 mT the system be-came unmeasurable due to the second qubit on the chipanti-crossing with the readout resonator, see Fig. 5. Fig-ures 3(a) and 3(b) show Rabi oscillations and lifetimedecay at B = 0 and B = 50 mT. At B = 0 we observelifetimes of ∼ . µ s similar to previous gatemon deviceswith a single junction gate, indicating that the additionalplunger gates and dielectric layers do not compromisequbit performance. The measurements show almost nodifference between B = 0 and B = 50 mT demonstratingexcellent resilience to parallel magnetic fields consistentwith other recent studies of gatemon qubits [16]. Further-more, as the field was not perfectly aligned, these data in-dicate that small out-of-plane magnetic fields ( ∼ µ T)do not degrade qubit quality. This suggests that ourqubit design mitigates the need for extensive magneticshielding, as typically required for superconducting qubitdevices.Moving to the first lobe between B ∼
250 mT and B ∼
650 mT, two main resonances appear (Fig. 2). Bothstates behave as weakly anharmonic oscillator modeswith a broad single-photon transition frequency and asharper two-photon transition separated by ∼
100 MHz.While the presence of two anharmonic states is consis-tent with a large Majorana coupling across the junctionmediated by two overlapping zero modes [20], it is un-likely that the splitting is due to Majorana physics as thetopological phase is typically expected to occur at higher t (ns)01 V H ( a . u . ) B =0 T B =50 mT 0 100 200 t (ns) B =1T0 5 10 15 (cid:856) ( (cid:541) s)01 V H ( a . u . ) B =0T T =5.5 (cid:541) s B =50mT T =5.0 (cid:541) s 0 0.5 1 1.5 (cid:856) ( (cid:541) s) B =1T T =0.57 (cid:541) s0 100 200 t (ns)01 V H ( a . u . ) B =0 T B =50 mT 0 100 200 t (ns) B =1T0 5 10 15 (cid:856) ( (cid:541) s)01 V H ( a . u . ) B =0T T =5.5 (cid:541) s B =50mT T =5.0 (cid:541) s 0 0.5 1 1.5 (cid:856) ( (cid:541) s) B =1T T =0.57 (cid:541) s (a) (c)(d)(b) FIG. 3. Time domain measurements as a function of B at V cut = − . V lplg = V rplg = − . B = 0 and B = 50 mT. Wemeasured the demodulated transmission, V H , as a function ofdrive duration, t , applied at the qubit frequency. Fits are ex-ponentially damped sinusoids. Data are normalized to the ex-tracted fit parameters. (b) T -lifetime measurement at B = 0and B = 50 mT. We measured V H as a function of delay time, τ , between the drive and readout tones. To excite the qubit,we applied a π -pulse calibrated from (a) at f q = 4 . f q = 4 . T . (c) [(d)] same as (a) [(b)] at B = 1 T with f q = 2 .
300 350 400 450 500 B (mT)2.633.43.8 f d ( G H z ) -2.0 -1.0 0 1.0 V H (a.u.)-1.84 -1.82 -1.8 -1.78-1.84 -1.82 -1.8 -1.782.533.544.5 f d ( G H z ) V cut (V) Vf cut (V) B = 350 mT B = 360 mT (a)(b) V = -1.8 V cut q FIG. 4. Junction states as a function magnetic field andgate. (a) Two-tone spectroscopy for varying f d and B re-veals oscillating behavior of junction states at gate voltage V cut = − . V lplg = V rplg = − . f q (arrow) decayingas B increases with multiple new transitions emerging and ex-hibiting multiple avoided crossings with the qubit transition.(b) Two-tone spectroscopy as a function of f d and V cut at B = 350 mT [left, black rectangle in (a)], and 360 mT [right,blue rectangle in (a)]. Again, a clear qubit transition is vis-ible, weakly dependent on V cut with two strongly dispersingtransitions coupling to the qubit. The gate-independent tran-sition at f d ∼ . magnetic fields for InAs-based wires. Rather, the split-ting might be connected to low-energy Andreev statesinteracting with the qubit mode, as indicated by sev-eral transitions dispersing strongly with magnetic fieldthroughout the first lobe. In this regime, it was not pos-sible to probe the qubit states using time domain mea-surements due to very low lifetimes.In the second lobe above B ∼
650 mT, a single qubitresonance revives and is clearly visible all the way upto B = 1 T. The two-photon 0 → B = 1 T with life-time T = 0 . µ s. We speculate that the decrease in T a B = 1 T is due to a reduction in ∆ ∗ compared to at B = 0, resulting in an increase in quasiparticle poisoningrates [38, 39]. IV. ANOMALOUS JUNCTION STATES
To investigate the anomalous qubit-resonance split-tings in the first lobe, we focus on a voltage regime wheresharp additional transitions and avoided crossings in thequbit transition are observed, as shown in Fig. 4(a).A clear, uninterrupted qubit transition frequency f q isslowly reduced from f q ∼ . . B is in-creased from 300 to 500 mT [arrow in Fig. 4(a)]. Ad-ditionally, around the qubit transition, several new res-onances appear for B >
350 mT, oscillating with mag-netic field. When these oscillating state transitions areon resonance with the qubit, we observe avoided cross-ings, indicating strong coupling to the qubit. We asso-ciate these resonances with low-energy Andreev boundstates that couple to the resonator via the qubit, inagreement with recent numerical simulations of similarnanowire structures [40]. We speculate that the coex-istence of the coupled and uncoupled spectra, as seenemerging at B ∼
350 mT and f q ∼ . >
10 s for each vertical trace).To further probe the spectrum, we swept V cut at fixed B , see Fig. 4(b). Here, the qubit transition is weaklydispersing around f q ∼ . f d ∼ f d ∼ . V cut is consistent with An-dreev states that are localized in the junction and there-fore expected to be strongly dependent on the electro-statics of the junction. V. CONCLUSIONS
We have presented a magnetic-field resilient gatemoncircuit with excellent relaxation times of 5 µ s at moderatemagnetic fields, ∼
50 mT. The qubit retains coherenceup to magnetic fields of 1 T with a lifetime T ∼ . µ s,demonstrating compatibility of our gatemon circuit de-sign with magnetic fields typically needed for Majoranazero modes. Future work could integrate additional gatesto allow greater control of the charge carrier distribu-tion along the nanowire or use a SQUID-like geome-try to allow control of the superconducting phase acrossthe Josephson junction. Combining the microwave spec-troscopy techniques with dc transport measurements [42]may also provide further insights into the underlying ori-gin of observed features. ACKNOWLEDGMENTS
We thank Arno Bargerbos, Bernard van Heck, AngelaKou, Leo Kouwenhoven, and Gijs de Lange for valuablediscussions. Research was supported by Microsoft, theDanish National Research Foundation, and the EuropeanResearch Council under grant HEMs-DAM No.716655.
Appendix A: Readout frequency corrections
When applying an in-plane magnetic field, B , thereadout resonator frequency, f r , was modulated due tochanges in the kinetic inductance of the NbTiN film. Wetherefore corrected the readout frequency before eachtwo-tone spectroscopy measurement by measuring thetransmission voltage, S , as a function of frequency witha vector network analyzer, see Fig. 5. Following eachmeasurement, we fitted S to a skewed Lorentzian todetermine the readout frequency. These measurementswere interleaved with the two-tone spectroscopy measure-ments shown in Fig. 2. We observe a slight degradationin f r until the avoided crossing with the second qubit at B ∼
150 mT is observed. The large jumps in f r around B ∼
200 mT are due to corrections to the out-of-planefield components carried out in between measurements,after observing a steady decrease in f r when sweepingdown from B = 1 T. No significant degradation in thepeak width is observed, highlighting the magnetic fieldcompatibility of the readout resonators. S magnitude (V) 2 6 8 120 0.2 0.4 0.6 0.8 1 B (T) 4.914.924.934.944.954.96 C a v i t y f r equen cy ( G H z ) FIG. 5. Transmission voltage, S , as a function of cavitydrive frequency and B showing the field modulation of theresonance frequency of the λ/ B = 0 . ∼ . B ∼
150 mTthe avoided crossing between the resonator and the secondqubit is observed.
Appendix B: Experimental setup
Figure 6 shows the experimental setup used for themeasurements presented in the paper. The readout res-onance frequency was determined by transmission mea-surements with a vector network analyzer (VNA). Two-tone spectroscopy and time domain measurements wereacquired with a heterodyne demodulation readout cir-cuit. With this circuit we measured the transmission ofa pulse modulated RF signal. We amplified the transmit-ted signal at 4 K and further at room temperature andthen mixed down with a reference signal before samplingand digital down conversion. The demodulation circuitand VNA were connected to an RF switch matrix to allowswitching between the two measurement configurations.Experiments were carried out in a dilution refrigeratorwith a 6-1-1 T vector magnet.
AWG I Microwave driveReadoutGate drive
L I CH1
VNA
CH2
DIGITIZERTRIG.
CH1CH2CH3 I D/A d B d B d B d B d B d B CLOCKREF. K Sample
300 K
PSPL55089 SRS 350 MHzPreamp SR445A10 Tektronix low passfilter PSPL591511 Marki MixerM8-0420 . K < m K
12 Tektronix Power divider PSPL533313 API DC BlockInmet 803914 Miteq AmplifierAFS2-00101200 15 Low Noise Factory4K Amp LNC4_8C16 QuinStar isolatorCWJ1019-K41417 CuBe box with Eccosorb19202119 Mini-Circuits low pass filter LFCN-80 20 Mini-Circuits low pass filter LFCN-1450 21 Mini-Circuits low pass filter LFCN-500 18 Mini-Circuits low pass filterBLP-1.9+ R
11 2
FIG. 6. Schematic of the experimental setup used for theexperiments presented. The readout resonator was driven ei-ther by the VNA or an AWG-modulated RF source (greenlines). The output signal (red lines) was amplified and readout either with the VNA or down converted by mixing with areference signal. All microwave equipment was synchronizedwith a 10 MHz clock reference. Three DC lines (blue) wereconnected to the three gates, V lplg , V rplg , and V cut , to tunethe nanowire chemical potential and junction, respectively. [1] G. de Lange, B. van Heck, A. Bruno, D. J. vanWoerkom, A. Geresdi, S. R. Plissard, E. P. A. M.Bakkers, A. R. Akhmerov, and L. DiCarlo, Realiza-tion of Microwave Quantum Circuits Using HybridSuperconducting-Semiconducting Nanowire JosephsonElements, Phys. Rev. Lett. , 127002 (2015).[2] T. W. Larsen, K. D. Petersson, F. Kuemmeth, T. S.Jespersen, P. Krogstrup, J. Nyg˚ard, and C. M. Marcus,Semiconductor-Nanowire-Based Superconducting Qubit,Phys. Rev. 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