Abstract
Superconducting circuits have attracted growing interest in recent years as a promising candidate for faulttolerant quantum information processing. Extensive efforts have always been taken to completely shield these circuits from external magnetic fields to protect the integrity of the superconductivity. Here we show vortices can improve the performance of superconducting qubits by reducing the lifetimes of detrimental singleelectronlike excitations known as quasiparticles. Using a contactless injection technique with unprecedented dynamic range, we quantitatively distinguish between recombination and trapping mechanisms in controlling the dynamics of residual quasiparticle, and show quantized changes in quasiparticle trapping rate because of individual vortices. These results highlight the prominent role of quasiparticle trapping in future development of superconducting qubits, and provide a powerful characterization tool along the way.
Introduction
Superconducting quantum circuits have made rapid progress^{1} in realizing increasingly sophisticated quantum states^{2,3} and operations^{4,5} with high fidelity. Excitations of the superconductor, or quasiparticles (QPs), can limit their performance by causing relaxation and decoherence, with the rate approximately proportional to the QP density^{6}. Operating at 20 mK or lower temperature, superconducting aluminium in thermal equilibrium should have no more than one QP for the volume of the Earth. However, a substantial background of QPs has been observed in various devices from single electron^{7} or Cooperpair transistors^{8}, kinetic inductance detectors^{9,10} to superconducting qubits^{11,12,13}. A detailed understanding of the generation mechanism and dominant relaxation processes will eventually be necessary to suppress this small background of QPs and continue the improvement of these devices.
QP dynamics has been traditionally characterized by the ‘lifetime’ of excess QPs relaxing towards a steady state, τ_{ss}. A variety of techniques have been used to measure τ_{ss} in aluminium, including lowfrequency subgap electrical^{14,15} or thermal transport^{16,17}, resonance frequency shifts^{18,19} and more recently, qubit energy decay^{20,21}. Electron–phononmediated pair recombination has been established as the canonical mechanism of QP decay^{22}. SingleQP loss mechanisms in the presence of QP ‘traps’, such as normal metal contacts^{7,16,17,23,24}, engineered gap inhomogeneity^{8,25,26}, Andreev bound states^{27} or magnetic field penetration^{28,29}, have also been studied.
Ascertaining the relative importance of QPs to the decoherence of any superconducting qubit, versus other mechanisms such as dielectric loss or radiation, remains challenging. Ideally, one would like to probe and vary QP dynamics in a highly coherent qubit, without requiring additional circuit elements or constraints that compromise its performance. Here we introduce such a technique, capable of measuring the QP dynamics of a qubit in operation and quantifying the processes of recombination, trapping, diffusion and background generation of QPs. With this technique, we directly measure the trapping of QPs by a single vortex, a basic property of superconductors. We demonstrate that QP trapping by vortices can suppress the background QP density, resulting in surprising net improvement of qubit coherence in spite of the wellknown vortex flow dissipation^{30}.
In the following, we present timedomain measurements of QP relaxation in threedimensional (3D) transmon qubits^{31} over 2–3 orders of magnitude in density. We find that the QP dynamics can be dominated by either recombination or trapping effects depending on the device geometry and the resultant presence or absence of vortices. We demonstrate strong insitu control of QP dynamics by magnetic field, and measure an intrinsic singlevortex trapping ‘power’ of (6.7±0.5) × 10^{−2} cm^{2} s^{−1} (that is, τ_{ss}=1 s induced by a single vortex over an area of 6.7 × 10^{−2} cm^{2}). Improvements of relaxation time (T_{1}) and coherence time (T_{2E}) by more than a factor of 2 are observed in one geometric design of devices when the devices are cooled in a small magnetic field (10–200 mG). We measure a stray QP generation rate of about 1 × 10^{−4} s^{−1}, suggesting the long coherence time of the widely adapted design of 3D transmons^{12,31,32,33} may already be greatly assisted by unintentional vortices. Improved coherence by fieldcooling, also being reported in superconducting planar resonators^{34} and fluxonium qubits^{35} during the preparation of our manuscript, can be definitively correlated with QP trapping rates of vortices as probed by our measurements of QP dynamics.
Results
Injection and measurement of QPs
In our experiment, we inject QPs into two types of transmon qubits in a 3D cQED (circuit quantum electrodynamics) architecture^{31} using only the existing microwave ports. Each transmon qubit comprises a single Al/AlO_{x}/Al Josephson junction shunted by a large Al coplanar capacitor (electrodes) on a cplane sapphire substrate. Type A devices are very similar to those in ref. 31 with a pair of large 500 × 250 μm^{2} electrodes (Fig. 1b). The electrodes of type B devices are composed of a narrow (6–30 μm wide) coplanar gap capacitor and a pair of 80 × 80 μm^{2} ‘pads’ (see Fig. 1c and Supplementary Fig. 1), but provide total capacitance and qubit Hamiltonian parameters very similar to type A devices. Chips containing one or two qubits are mounted in 3D aluminium or copper rectangular waveguide cavities (Fig. 1a) and all measurements are done in an Oxford cryogenfree dilution refrigerator at base temperature of 15–20 mK, with magnetic field shielding, infrared shielding and filtering described in ref. 32. To inject QPs, similar to ref. 35 we apply a highpower microwave pulse at the bare cavity resonance frequency from the input port. The injection pulse creates about 10^{5} circulating photons in the cavity, resulting in an oscillating voltage across the Josephson junction that exceeds the superconducting gap, and produces ~10^{5} QPs per μs. The duration of the injection pulse is long enough (200–500 μs) so that the injected QPs can fully diffuse within the device, whereas the production and loss of QPs reach a dynamic balance. (See Supplementary Notes 1 and 2 for analysis of QP injection and diffusion.)
We use the recovery of the energy relaxation time (T_{1}) of the qubit as a direct and calibrated probe of the decay of QP density. Standard microwave pulse sequences are applied to determine the qubit T_{1} following a variable delay t after the QP injection (Fig. 1f and Supplementary Note 3), from which we extract the qubit relaxation rate Γ=1/T_{1} as a function of t as shown in Fig. 2. Despite possible heating due to the injection pulse, we find the effective temperature of the qubit and QP bath does not exceed 70 mK for the entire range of our measurement (Supplementary Note 4), therefore thermal generation of QPs and spontaneous g›→e› transition of the qubit can be neglected. We use x_{qp} to represent the QP density near the Josephson junction normalized by the Cooperpair density (n_{cp}≈4 × 10^{6} μm^{−3} for aluminium). It is related to the measured qubit decay rate by Γ(t)=Cx_{qp}(t)+Γ_{ex}, where Γ_{ex} is a constant qubit decay rate because of nonQP dissipation mechanisms, and is a calculated^{6} and confirmed^{31} constant involving only the superconducting gap Δ(≈180 μeV) and the angular frequency of the transmon ω_{q}(≈2π·6 GHz). As Γ_{ex} is strictly bounded by the qubit relaxation rate without QP injection, Γ_{ex}≤Γ_{0}=Γ(t→∞), for a significant range of the data, QP density can be approximated by x_{qp}(t)≈Γ(t)/C.
Distinguishing between QP recombination and trapping
The dynamics of the QP density x_{qp} near the junction in the presence of recombination and trapping can be modelled by the following equation (see Supplementary Note 5 for details):
The quadratic term describes the canonical QP recombination in pairs with a recombination constant r. The linear term describes trapping effects that localize or remove single QPs from tunnelling across the Josephson junction and inducing qubit relaxation. The effective trapping rate s depends not only on the property and density of the trapping sites, but also their geometric distribution and associated diffusion timescale. The constant term g describes QP generation rate by pairbreaking stray radiation or other unidentified sources^{36}. If trapping is dominant (s>>rx_{qp} for most of the measured range of x_{qp}), then decay of x_{qp} follows an exponential function. This is a surprisingly good approximation for the Γ(t) we measured in Device A1 (of type A; red fit in Fig. 2a). On the other hand, if recombination dominates, the decay of x_{qp} follows a hyperbolic cotangent function, with initially a steep 1/t decay crossing over to an exponential tail. We measure Γ(t) in Device B1 (of type B) strikingly close to this limit (green fit in Fig. 2b).
To analyse both recombination and trapping more quantitatively, we solve equation (1) analytically, yielding a four parameter fit for Γ(t) (black curves in Fig. 2):
where x_{i} is the initial injected QP density, Γ_{0}=Cx_{0}+Γ_{ex} is the qubit relaxation rate without QP injection, consisting of contributions from both background QP density x_{0} and other mechanisms. r′ is a dimensionless fit parameter (0<r′<1). Note that as t→∞, equation (2) approaches an exponential decay with time constant τ_{ss}. The recombination constant r and the trapping rate s can be determined from these fit parameters (Supplementary Note 5). For B1, a fit to equation (2) gives an exponential tail with τ_{ss}=18±2 ms, a recombination constant r=1/(170±20 ns) and a weak trapping rate . For A1, we find s≈1/τ_{ss}=1/(1.5±0.1 ms) and r=1/(105±30 ns), with the trapping term dominating most of the measurement range (x_{qp}<10^{−4}).
The qualitative difference between the functional forms of QP decay in the two devices can be better illustrated by plotting the excess QP density because of QP injection, δx_{qp}=x_{qp}(t)−x_{0}, as a function of time (Fig. 2 insets). For A1, the instantaneous QP decay rate indicated by the slope of δx_{qp}(t) remains equal to its steadystate value (1/τ_{ss}) even when the QP density is orders of magnitude higher than its background density (that is, when δx_{qp}(t)>>Γ_{0}/C≥x_{0}). For B1, the slope increases significantly when δx_{qp}(t)>x_{0}.
Controlling QP dynamics by cooling in magnetic field
Why do the two devices with identical material properties and similar qubit properties differ so much in QP relaxation dynamics? We attribute this to the trapping effect from vortices (regions with diminished superconducting gap) in the large electrodes in Device A1 despite the low level of residual field (B~1–2mG) achieved in our experiment by magnetic shielding. On the other hand, Device B1 is likely free of vortices because of the much narrower geometry of the electrodes. To test this hypothesis, we repeat Γ(t) measurements in B1 after cooling the device through the critical temperature (T_{c}) in a perpendicular magnetic field of variable magnitude B in either polarity. Indeed, as B increases, we observe significant acceleration of QP decay with increasingly pronounced singleexponential characteristics, indicating enhanced QP trapping (Fig. 3a). In comparison, changing the applied magnetic field at 20 mK does not produce measurable changes in QP dynamics.
By fitting Γ(t) to equation (2) at each cooling field, we find that: (i) the recombination constant r remains unchanged within fitting uncertainty, (ii) the trapping rate s increases in discrete and nearequal steps for small magnetic fields (B≲40 mG; Fig. 3c), (iii) over a broader field range, s increases approximately linearly with B and saturates at ≳1 ms^{−1} at high field (B≳100 mG; Fig. 3b).
Our observed critical field threshold, B_{k}, where the trapping rate s starts to increase, corresponds to the expected entry of the first vortex in one of the 80 × 80 μm^{2} pads. B_{k} can be estimated based on a thermodynamic analysis of a vortex in a thin superconducting disk^{37} together with consideration of vortex creationannihilation kinetics^{38}, giving B_{k}~8 mG, close to our observed values of 11 mG for B1 in an Al cavity, 14 and 10 mG for other two devices of type B, B2 and B3, in Cu cavities. In comparison, B_{k} for Device A1 is estimated to be about 0.5 mG, lower than the estimated residual field (and its possible inhomogeneity) of our setup and therefore cannot be observed experimentally.
QP trapping by individual vortices
The discrete trapping rates at small magnetic field are strongly suggestive of a fixed QP ‘trapping power’ for each individual vortex. We define trapping power, P, by modelling a vortex as a point object at a 2D spatial coordinate R_{0} with a deltafunction local trapping rate Pδ(R−R_{0}). P could be more microscopically modelled as the product of QP trapping rate in the vortex core and an effective trapping area^{28,34} (Supplementary Note 6). However, the ‘trapping power’ representation offers the advantage of a general formulation without invoking any microscopic models. In the limit that diffusion is much faster than trapping, the total microscopic trapping power of N vortices, NP, manifests itself macroscopically as the product of the measured trapping rate and the total area, A, of the device, that is, sA=NP. For a small number of vortices, we observe quantized changes of sA products in steps of ~0.06 cm^{2} s^{−1} consistent between all three systematically measured type B devices with up to 50% difference in device areas (Fig. 3c). In Fig. 3c, we have subtracted a relatively small (zerovortex) background trapping rate that varies from device to device (zero field s<0.05 ms^{−1} for B1 but ~0.18 ms^{−1} for B3), whose origin remains to be explored in future studies. Assuming each step corresponds to the entry of one vortex (which is stochastically most probable and also suggested by the widths of the steps), and adjusting for the finite speed of QP diffusion (Supplementary Note 5), we determine trapping power P=(6.7±0.5) × 10^{−2}cm^{2} s^{−1} as an intrinsic property of each individual vortex in our superconducting film.
The reduced step heights and the eventual saturation of s at higher magnetic field can be fully explained by QP diffusion using realistic geometric parameters of our device (Supplementary Note 5). When there are a large number of vortices in the pads, the apparent trapping rate s is limited by the diffusion time for QPs to reach the trapping pad from other regions of the device (Fig. 3e). The saturated trapping rate is higher for B2 because of the smaller volume of its gap capacitor. By fitting s as a function of B over a large range (Fig. 3b) for both devices, we determine the diffusion constant D=18±2 cm^{2} s^{−1} for our Al film at 20 mK, consistent with the values measured in Xray singlephoton spectrometers adjusted for different temperature^{25}.
QP recombination constant
Across seven devices (Supplementary Table 1), we measure recombination constants r in the range of 1/(170 ns) to 1/(80 ns), consistent with the theoretical electron–phonon coupling time of aluminium τ_{0}=438 ns (ref. 22) adjusting for the phonontrapping effect^{39}. Recombinationgenerated phonons can rebreak Cooper pairs before escaping into the substrate, reducing the effective recombination constant by a factor F, giving . For our 80nm bilayer Al film on sapphire, the best estimate of F is in the range of 5–10 considering the strong acoustic mismatch at the interface^{40}. The reported values of r for Al in the literature range from 1/(120 ns) to 1/(8 ns)^{14,18,19,28,41}. The recombination constant we measured directly from the powerlaw decay characteristics is near the low end. It is comparable to r=1/(120 ns) extracted from DC steadystate injection measurements in extended Al films with similar thickness on sapphire^{14}.
Our measured value of r suggests the effect of recombination is extremely weak for the sparse QP background in typical superconducting qubits (recombinationresulted τ_{ss}~50 ms for x_{qp}~10^{−6}). Even one single vortex (occupying less than onemillionth of the total area of a type B device) can eliminate QPs much faster than the intrinsic recombination process, as demonstrated by the drastically different QP decay curves for 0 (red), 1 (orange) and 2 (green) vortices in Fig. 3a.
Improved qubit coherence by vortices
In strong correlation with the reduced QP lifetime because of vortex trapping, we observe dramatic improvement of qubit coherence as a result of the suppressed background QP density. Improved qubit T_{1} is already demonstrated by the lower background Γ_{0} in Fig. 3a at higher cooling field. This ‘steadystate’ T_{1} of the qubit can also be measured separately without QP injection, which more than doubled from its zerofield value over a wide range of cooling magnetic field for both Devices B1 (Fig. 4a) and B2 (Fig. 4b). The coherence time with Hahn echo, T_{2E}, shows similar relative improvement because it is close to the limit of 2T_{1}.
We can separate qubit loss mechanisms based on the linear relation between 1/T_{1} and τ_{ss} (noting x_{0}≈gτ_{ss}),
where the intercept equals the qubit relaxation rate because of other loss mechanisms, and the slope reveals the stray QP generation rate g (Fig. 4c,d). In both B1 and B2, Γ_{ex} is likely dominated by dielectric loss at the Al/Al_{2}O_{3} interface under the gap capacitor^{42}. We find QP generation rate g≈0.7–1.3 × 10^{−4} s^{−1} in the two devices over several thermal cycles, or 0.3–0.6 QPs created per ms for every μm^{3} of volume.
Vortex flow dissipation
The eventual decrease of T_{1} and T_{2E} at highmagnetic field (B≳200 mG) can be attributed to vortices entering the gap capacitors where current density is high. Such dissipation due to vortex flow resistance has been wellknown to degrade the quality factor of superconducting resonators and qubits^{43,44}. Therefore, precautions such as multilayer magnetic shielding, specialized nonmagnetic hardware and honeycombstyle device designs have been widely employed in the community to avoid vortices. However, here we have shown that the benefit of vortices in suppressing nonequilibrium QPs is not only relevant to practical devices, but can also significantly outweigh its negative impact if the locations of the vortices are optimized.
In device A1 (or most type A devices, see Supplementary Table 1), our measured τ_{ss} at nominally zero field implies the presence of about 20 vortices based on our measured singlevortex trapping power, consistent with its geometry assuming a residue magnetic field of 1–2 mG. Introducing more vortices to type A devices by cooling in an applied magnetic field can further reduce τ_{ss}, but no clear improvement of qubit T_{1} is observed. We attribute it to the limited range that τ_{ss} can be varied (from its already small value at nominally zero field) and the vortex flow dissipation, which clearly reduces T_{1} at B≳30 mG (Supplementary Note 7). Assuming both types of devices have similar g as they are shielded and measured in the same setup, it is plausible to infer that the long coherence times of the widely adopted type A 3D transmons would have been limited to much lower values without the assistance from QP trapping by unintentional vortices.
Discussion
In our work, for the first time, the interaction between QPs and a single vortex is measured. The singlevortex trapping power (P) is an intrinsic property of an aluminium film, and has the same dimension as the diffusion constant (D). The fact that we measure P/D≈10^{−2} implies that a QP can diffuse through a vortex with only a small (~1%) probability to be trapped. Despite a vortex being a topological defect with Δ=0 at its core, the spatial distribution of QP density is barely perturbed by the presence of a vortex, just like a small ‘ripple’ on the order of 1% deep in a flat ‘sea’ (Fig. 3d, see Supplementary Note 8 for calculation). For a uniform film extended in 2D space, this relatively homogeneous QP distribution holds for all practical length scales at any density of vortices, so the trapping rate s can be simply computed from the total trapping power. In the highmagnetic field limit, this leads to s∝B with a linear coefficient P/φ_{0}=0.3 μs^{−1} G^{−1} based on our measured P, close to the fitted value of 0.5 μs^{−1} G^{−1} in ref. 28.
Understanding and controlling the steadystate QP lifetime (τ_{ss}) may be important for a variety of superconducting devices. For superconducting qubits and resonators, achieving short τ_{ss} (either with vortices or potentially more efficient methods such as bandgap engineering or normal metal traps) to suppress the background QP density is desirable. In other devices such as kinetic inductance detectors^{9,10}, it may be desirable to obtain a long QP lifetime. Our measured τ_{ss} of 18 ms in a type B device is so far the longest reported in aluminium. Previous experiments in aluminium films showed that the expected exponential increase of τ_{ss} with lower temperature saturates below 200 mK (refs 14, 15, 18) to about 3 ms at most^{10}.
To shed light on the mechanisms limiting τ_{ss} in this regime of extremely low QP density (without intentional QP traps), our technique allows quantitative separation between QP recombination and any residual trapping effects. Our quantification of the weak recombination of background QPs and the singlevortex trapping extends our understanding of QP dynamics into the 10’s of millisecond regime, and thus sets a more stringent bound on possible additional mechanisms in limiting the QP lifetimes.
To distinguish between recombination and trapping of QPs, our analysis relies critically on large dynamic range in x_{qp} to achieve sufficient contrast between the functional forms of QP decay. A measurement near a steady state would observe the exponential tail of the decay, giving τ_{ss}=1/(s+2rx_{0}) without distinguishing between the two mechanisms. Such analysis of linear response has been traditionally carried out in timedomain measurements after photon pulses^{15,19,23,25}. Noise spectroscopy measurements^{15,19} by design are also limited to measuring the single timescale of τ_{ss}. The experiment of Lenander et al.^{20} introduced the use of qubit T_{1} to probe QP dynamics, but the achieved dynamic range was below a factor of 4. The dynamic range of 2–3 orders of magnitude in our experiment has been made possible by a long T_{1} time in 3D transmons, the effectiveness of our microwave injection technique and the geometric simplicity of an isolated aluminium island to eliminate outdiffusion.
A significant stray QP generation rate of about 1 × 10^{−4} s^{−1} has been measured in our study. Owing to the large device volume and relatively long integration time, our measured g should be considered a spatialtemporal average of QP generation rate. Quite remarkably, it agrees within a factor of 3 with the average QP generation rate in a much smaller fluxonium qubit^{35} with a much shorter τ_{ss} where there is evidence for the discreteness of QP numbers and QP generation events. This magnitude of QP generation rate, together with the weakness of recombination at low QP density, strongly suggests QP trapping should be an important ingredient for suppressing nonequilibrium x_{qp} in superconducting qubits and other devices to further improve performance. Our method of extracting g utilizing the sensitivity of type B devices to QP generation should facilitate future identification of the QP generation source. The injection and measurement technique introduced in this work can be readily applied to nearly all cQED implementations without any modification to device structure or measurement circuit, and can play a crucial role in the future development of quantum circuits as a powerful probe of QP dynamics.
Additional information
How to cite this article: Wang, C. et al. Measurement and control of quasiparticle dynamics in a superconducting qubit. Nat. Commun. 5:5836 doi: 10.1038/ncomms6836 (2014).
References
Devoret, M. H. & Schoelkopf, R. J. Superconducting circuits for quantum information: an outlook. Science 339, 1169–1174 (2013).
Hofheinz, M. et al. Synthesizing arbitrary quantum states in a superconducting resonator. Nature 459, 546–549 (2009).
Vlastakis, B. et al. Deterministically encoding quantum information using 100photon Schrödinger cat states. Science 342, 607–610 (2013).
Steffen, L. et al. Deterministic quantum teleportation with feedforward in a solid state system. Nature 500, 319–322 (2013).
Chow, J. M. et al. Implementing a strand of a scalable faulttolerant quantum computing fabric. Nat. Commun. 5, 4015 (2014).
Catelani, G., Schoelkopf, R. J., Devoret, M. H. & Glazman, L. I. Relaxation and frequency shifts induced by quasiparticles in superconducting qubits. Phys. Rev. B 84, 064517 (2011).
Knowles, H. S., Maisi, V. F. & Pekola, J. P. Efficiency of quasiparticle evacuation in superconducting devices. Appl. Phys. Lett. 100, 262601 (2012).
Aumentado, J., Keller, M. W., Martinis, J. M. & Devoret, M. H. Nonequilibrium quasiparticles and 2e periodicity in singleCooperpair transistors. Phys. Rev. Lett. 92, 066802 (2004).
Day, P. K., LeDuc, H. G., Mazin, B. A., Vayonakis, A. & Zmuidzinas, J. A. broadband superconducting detector suitable for use in large arrays. Nature 425, 817–821 (2003).
de Visser, P. J., Baselmans, J. J. A., Bueno, J., Llombart, N. & Klapwijk, T. M. Fluctuations in the electron system of a superconductor exposed to a photon flux. Nat. Commun. 5, 4130 (2014).
Sun, L. et al. Measurements of quasiparticle tunneling dynamics in a bandgapengineered Transmon Qubit. Phys. Rev. Lett. 108, 230509 (2012).
Ristè, D. et al. Millisecond chargeparity fluctuations and induced decoherence in a superconducting transmon qubit. Nat. Commun. 4, 1913 (2013).
Pop, I. M. et al. Coherent suppression of electromagnetic dissipation due to superconducting quasiparticles. Nature 508, 369–372 (2014).
Gray, K. E. Steady state measurements of the quasiparticle lifetime in superconducting aluminium. J. Phys. F Met. Phys. 1, 290–308 (1971).
Wilson, C. M., Frunzio, L. & Prober, D. E. Timeresolved measurements of thermodynamic fluctuations of the particle number in a nondegenerate Fermi gas. Phys. Rev. Lett. 87, 067004 (2001).
Ullom, J. N., Fisher, P. A. & Nahum, M. Measurements of quasiparticle thermalization in a normal metal. Phys. Rev. B 61, 14839 (2000).
Rajauria, R. et al. Quasiparticlediffusionbased heating in superconductor tunneling microcoolers. Phys. Rev. B 85, 020505 (2012).
Barends, R. et al. Quasiparticle relaxation in optically excited highQ superconducting resonators. Phys. Rev. Lett. 100, 257002 (2008).
de Visser, P. J. et al. Number fluctuations of sparse quasiparticles in a superconductor. Phys. Rev. Lett. 106, 167004 (2011).
Lenander, M. et al. Measurement of energy decay in superconducting qubits from nonequilibrium quasiparticles. Phys. Rev. B 84, 024501 (2011).
Wenner, J. et al. Excitation of superconducting qubits from hot nonequilibrium quasiparticles. Phys. Rev. Lett. 110, 150502 (2013).
Kaplan, S. B. et al. Quasiparticle and phonon lifetimes in superconductors. Phys. Rev. B 14, 4854–4873 (1976).
Goldie, D. J., Booth, N. E., Patel, C. & Salmon, G. L. Quasiparticle trapping from a singlecrystal superconductor into a normalmetal film via the proximity effect. Phys. Rev. Lett. 64, 954–957 (1990).
Joyez, P., Lafarge, P., Filipe, A., Esteve, D. & Devoret, M. H. Observation of parityinduced suppression of Josephson tunneling in the superconducting single electron transistor. Phys. Rev. Lett. 72, 2458–2461 (1994).
Friedrich, S. et al. Experimental quasiparticle dynamics in a superconducting, imaging Xray spectrometer. Appl. Phys. Lett. 71, 3901–3903 (1997).
Court, N. A., Ferguson, A. J., Lutchyn, R. & Clark, R. G. Quantitative study of quasiparticle traps using the singleCooperpair transistor. Phys. Rev. B 77, 100501 (2008).
LevensonFalk, E. M., Kos, F., Vijay, R., Glazman, L. I. & Siddiqi, I. Singlequasiparticle trapping in aluminum nanobridge Josephson junctions. Phys. Rev. Lett. 112, 047002 (2014).
Ullom, J. N., Fisher, P. A. & Nahum, M. Magnetic field dependence of quasiparticle losses in a superconductor. Appl. Phys. Lett. 73, 2494–2496 (1998).
Peltonen, J. T., Muhonen, J. T., Meschke, M., Kopnin, N. B. & Pekola, J. P. Magneticfieldinduced stabilization of nonequilibrium superconductivity in a normalmetal/insulator/superconductor junction. Phys. Rev. B 84, 220502 (2011).
Bardeen, J. & Stephen, M. J. Theory of the motion of vortices in superconductors. Phys. Rev. 140, A1197–A1207 (1965).
Paik, H. et al. Observation of high coherence in Josephson junction qubits measured in a threedimensional circuit QED architecture. Phys. Rev. Lett. 107, 240501 (2011).
Sears, A. P. et al. Photon shot noise dephasing in the strongdispersive limit of circuit QED. Phys. Rev. B 86, 180504 (2012).
Vijay, R. et al. Stabilizing Rabi oscillations in a superconducting qubit using quantum feedback. Nature 490, 77–80 (2012).
Nsanzineza, I. & Plourde, B. L. T. Trapping a single vortex and reducing quasiparticles in a superconducting resonator. Phys. Rev. Lett. 113, 117002 (2014).
Vool, U. et al. NonPoissonian quantum jumps of a fluxonium qubit due to quasiparticle excitations. Preprint at http://arxiv.org/abs/1406.1769 (2014).
Martinis, J. M., Ansmann, M. & Aumentado, J. Energy decay in superconducting Josephsonjunction qubits from nonequilibrium quasiparticle excitations. Phys. Rev. Lett. 103, 097002 (2009).
Kogan, V. G., Clem, J. R. & Mints, R. G. Properties of mesoscopic superconducting thinfilm rings: London approach. Phys. Rev. B 69, 064516 (2004).
Kuit, K. H. et al. Vortex trapping and expulsion in thinfilm YBa2Cu3O7−δ strips. Phys. Rev. B 77, 134504 (2008).
Rothwarf, A. & Taylor, B. N. Measurement of recombination lifetimes in superconductors. Phys. Rev. Lett. 19, 27–30 (1967).
Kaplan, S. B. Acoustic matching of superconducting films to substrates. J. Low Temp. Phys. 37, 343–365 (1979).
Wilson, C. M. & Prober, D. E. Quasiparticle number fluctuations in superconductors. Phys. Rev. B 69, 094524 (2004).
Wenner, J. et al. Surface loss simulations of superconducting coplanar waveguide resonators. Appl. Phys. Lett. 99, 113513 (2011).
Wang, H. et al. Improving the coherence time of superconducting coplanar resonators. Appl. Phys. Lett. 95, 233508 (2009).
Song, C. et al. Microwave response of vortices in superconducting thin films of Re and Al. Phys. Rev. B 79, 174512 (2009).
Acknowledgements
We acknowledge helpful discussions with D.E. Prober and B.L.T. Plourde. Facilities use was supported by YINQE and NSF MRSEC DMR 1119826. This research was supported by IARPA under Grant No. W911NF0910369, ARO under Grant No. W911NF0910514, DOE Contract No. DEFG0208ER46482 (L.I.G.), and the EU under REA grant agreement CIG618258 (G.C.). Y.Y.G. acknowledges support from an A*STAR NSS Fellowship.
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C.W. and Y.Y.G. carried out the experiment and performed data analysis based on the model developed by C.W., G.C. and L.I.G. The experimental method was conceived and developed by I.M.P., U.V., C.W., Y.Y.G., M.H.D. and R.J.S. C.A., T.B. and R.W.H. provided further experimental contributions. Devices are fabricated by C.W. and L.F. C.W. and R.J.S. led the writing of the manuscript. All authors provided suggestions for the experiment, discussed the results and contributed to the manuscript.
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Wang, C., Gao, Y., Pop, I. et al. Measurement and control of quasiparticle dynamics in a superconducting qubit. Nat Commun 5, 5836 (2014). https://doi.org/10.1038/ncomms6836
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DOI: https://doi.org/10.1038/ncomms6836
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