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Measurements of Quasiparticle Tunneling Dynamics in a Band-Gap-Engineered Transmon Qubit

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Measurements of Quasiparticle Tunneling Dynamics in a Band-Gap-Engineered Transmon Qubit week ending PRL 108, 230509 (2012) PHYSICAL REVIEW LETTERS 8 JUNE 2012 Measurements of Quasiparticle Tunneling Dynamics in a Band-Gap-Engineered Transmon Qubit L. Sun,1 L. DiCarlo,1,2 M. D. Reed,1 G. Catelani,1 Lev S. Bishop,1,3 D. I. Schuster,1,4 B. R. Johnson,1,5 Ge A. Yang,1,4 L. Frunzio,1 L. Glazman,1 M. H. Devoret,1 and R. J. Schoelkopf1 1Department of Physics and Applied Physics, Yale University, New Haven, Connecticut 06520, USA 2Kavli Institute of Nanoscience, Delft University of Technology, Delft, The Netherlands 3Joint Quantum Institute and Condensed Matter Theory Center, Department of Physics, University of Maryland, College Park, Maryland 20742, USA 4Department of Physics and James Franck Institute, University of Chicago, Chicago, Illinois 60637, USA 5Raytheon BBN Technologies, Cambridge, Massachusetts 02138, USA (Received 11 December 2011; published 8 June 2012) We have engineered the band gap profile of transmon qubits by combining oxygen-doped Al for tunnel junction electrodes and clean Al as quasiparticle traps to investigate energy relaxation due to quasiparticle tunneling. The relaxation time T1 of the qubits is shown to be insensitive to this band gap engineering. Operating at relatively low-EJ=EC makes the transmon transition frequency distinctly dependent on the charge parity, allowing us to detect the quasiparticles tunneling across the qubit junction. Quasiparticle kinetics have been studied by monitoring the frequency switching due to even-odd parity change in real time. It shows the switching time is faster than 10 s, indicating quasiparticle-induced relaxation has to be reduced to achieve T1 much longer than 100 s. DOI: 10.1103/PhysRevLett.108.230509 PACS numbers: 03.67.Lx, 42.50.Pq, 74.55.+v, 85.25.Àj Quantum information processing based on supercon- qubit relaxation and odd-even parity switching, with rates Àqp ¼j j2 ð Þ Àqp ¼j j2 ð Þ ducting qubits has made tremendous progress toward real- 1!0 M01 Sqp !01 and oe;i Moe;i Sqp i respec- izing a practical quantum computer in the last few years tively, where !01=2 is the qubit ground-to-excited tran- [1–3]. However, the coherence times of superconducting sition frequency, i=2 is the odd-to-even transition qubits still need to improve to reach the error correction frequency for state i ¼ 0, 1, and M01 and Moe;i are the threshold. For example, the single-qubit gate error rate is matrix elements describing the interaction between the limited by qubit decoherence [4–6]. Understanding deco- qubit and quasiparticles [12]. herence mechanisms, in particular those responsible for The dynamics of quasiparticle tunneling in single- qubit relaxation, is therefore crucial. Quasiparticles have Cooper-pair transistors (SCPTs) and Cooper-pair box received significant attention recently as one such possible qubits have been studied extensively, although the under- limiting factor [7–9]. At low temperatures, thermal- standing is still incomplete. The measured odd-even parity equilibrium quasiparticles should be irrelevant because switching time falls in a large range from the order of 1 s their density is exponentially suppressed. In practice, how- to the order of 1 ms [10,17–20], or possibly even longer in ever, nonequilibrium quasiparticles are present from un- some cases [21–23] that have no observable quasiparticle known sources [10,11]. The key question is then whether ‘‘poisoning.’’ One way to suppress quasiparticle tunneling these nonequilibrium quasiparticles are currently limiting is to engineer the band gap profile near the tunnel junction qubit relaxation and, if not, what limit they will ultimately [10,17–21]. This band gap engineering technique has been impose. The answer will be relevant to all superconducting shown to be effective in extending the parity switching qubits. time dramatically from 1 s to above 1 ms [20]. Quasiparticles in qubit electrodes do not themselves In this Letter, we employ band gap engineering for the cause significant qubit decoherence. Instead, it is the dis- first time in transmon qubits, in an attempt to make the sipative and incoherent tunneling of quasiparticles across a odd-even parity switching time in the measurable range Josephson junction that leads to decoherence [12]. The >100 s, which would then eliminate quasiparticles as a tunneling process is characterized by the quasiparticle source of decoherence. We measure the qubit relaxation ð Þ current spectral density Sqp ! . The low frequency com- time T1 as a function of temperature of transmon qubits, ponent in Sqpð!Þ can cause dephasing, but this dephasing which have significantly different band gaps. At low tem- channel can be eliminated by reducing the qubit’s sensi- peratures, the saturation of T1 of both transmons at ap- tivity to charge noise, as in flux [13,14], phase [15], and proximately the same level suggests a mechanism other transmon [16] qubits. The high frequency component will than thermal quasiparticles for qubit relaxation. To inves- cause energy relaxation in all types of superconducting tigate if nonequilibrium quasiparticles are limiting T1,we qubits. A transmon qubit has the energy level structure then study the quasiparticle kinetics in a band gap– shown in Fig. 1(a). Quasiparticle tunneling causes both engineered transmon operated in the low-EJ=EC regime, 0031-9007=12=108(23)=230509(5) 230509-1 Ó 2012 American Physical Society week ending PRL 108, 230509 (2012) PHYSICAL REVIEW LETTERS 8 JUNE 2012 where EJ and EC are the Josephson and the charging tunnel junction. The energy gaps of oxygen-doped layers energy, respectively. Qubit spectroscopy shows two qubit are determined by independent Tc measurements (not transition frequencies associated with the even- and odd- shown) of thin films evaporated under the same nominal charge states, demonstrating the presence and tunneling of conditions as for the tunnel junction. quasiparticles across the qubit junction. This indicates that, However, our band gap engineering does not appear to with our design, nonequilibrium quasiparticles have not affect T1 (see Table I in Supplemental Material [26] for a been removed by band gap engineering, contrary to the list of devices). A comparison of T1 as a function of results of experiments in SCPTs [10,18,20]. We study the temperature for two representative devices is shown in Àqp Àqp ground-state parity switching rate oe oe;0 in the time Fig. 2(a): one qubit is fabricated with clean Al only and qp domain finding 1=Àoe < 10 s. For typical device parame- the other with oxygen-doped Al without the third layer ters, the expected ratio of parity switching rate to quasiparticle trap. The decrease of T1 with temperatures qp qp quasiparticle-induced qubit relaxation rate, Àoe=À1!0 above 150 mK for the red curve and 250 mK for the blue 10–100 [12]. Therefore, while we cannot establish quasi- curve, respectively, indicates the effect of thermally gen- particle tunneling as the dominant source of energy relaxa- erated quasiparticles [6,12]. The higher corner temperature tion in our devices, our bound indicates that reducing the confirms that oxygen-doped Al indeed has a larger energy quasiparticle-induced decay rate will be necessary to gap. The saturation of T1 at low temperatures for both achieve T1 much longer than 100 s. clean and oxygen-doped Al devices at the same value Our transmon qubits are measured using a coplanar indicates that thermal quasiparticles are not limiting T1. waveguide cavity in a conventional circuit-quantum- Figure 2(b) shows the saturated T1 as a function of fre- electrodynamics architecture [24]. All devices are mea- quency for four qubits, each of which has its own flux bias sured in a cryogen-free dilution refrigerator with a line allowing individual tuning of the qubit frequency [2], 20 mK base temperature. Oxygen-doped Al, which has fabricated with both oxygen-doped Al and quasiparticle an energy gap Á 280 eV (Tc 1:9K) about 60% traps described earlier. The qubit lifetimes are limited to a 65 000 higher than clean Al (Á 180 eV, Tc 1:2K), is quality factor Q ; , similar to previously reported used as the electrodes of Josephson tunnel junctions de- T1 on qubits fabricated with clean Al only [27]. posited by standard double-angle evaporation [25]. The Nonequilibrium quasiparticles have been observed in oxygen dopants are introduced with a continuous O2 flow the band gap–engineered devices, as will be shown later, during the Al deposition. The same technique has also been so here we will only focus on the effect on T1 from those used in SCPTs to realize a large band gap [10,18]. To nonequilibrium quasiparticles. The lack of qualitative create quasiparticle traps, a third layer of clean Al is 5 5 deposited to cover the whole oxygen-doped Al layers to (a) (b) Qubit 1 100 nm Qubit 2 within from the junctions [Fig. 1(b)]. Figure 1(c) Qubit 3 shows the expected band gap profile near the junction. This Qubit 4 s) s) μ μ ( profile is expected to trap quasiparticles away from the ( 1 1 1 1 T T clean Al oxygen-doped Al oxygen-doped Al + quasiparticle traps 0.2 0.2 0.10 0.20 0.30 4 6 8 10 temperature (K) frequency (GHz) FIG. 2 (color online). (a) Measured qubit relaxation time T1 as a function of temperature for two transmon qubits: one qubit is fabricated with clean Al only with a transition frequency f01 ¼ 4:25 GHz and the other with oxygen-doped Al, but without the third layer of quasiparticle traps, with f01 ¼ 5:16 GHz. The device layout is identical to Fig. 1(a) in Ref. [1]. Dashed black and magenta lines are theory for relaxation due to thermal FIG.
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