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A Superconductor Free of Quasiparticles for Seconds A superconductor free of quasiparticles for seconds 1, 2 3, 1 E. T. Mannila, ∗ P. Samuelsson, S. Simbierowicz, † J. T. Peltonen, V. Vesterinen,3 L. Gr¨onberg,3 J. Hassel,3 V. F. Maisi,2 and J. P. Pekola1 1QTF Centre of Excellence, Department of Applied Physics, Aalto University, FI-00076 Aalto, Finland 2Physics Department and NanoLund, Lund University, Box 118, 22100 Lund, Sweden 3VTT Technical Research Centre of Finland Ltd, QTF Centre of Excellence, P.O. Box 1000, FI-02044 VTT, Finland (Dated: February 2, 2021) Superconducting devices, based on the Cooper low quasiparticle densities correspond to only a few ex- pairing of electrons, are of outstanding impor- citations within the entire device [2, 12–15]. In this few- tance in existing and emergent technologies, rang- particle regime, the number of quasiparticles fluctuates ing from radiation detectors [1, 2] to quantum strongly in time [2, 6, 12, 15, 20], potentially leaving the computers [3]. Their performance is limited device free of them for certain periods. Identifying such by spurious broken Cooper pairs also known as periods would open up possibilities for operation of su- quasiparticle excitations [4–12]. In state-of-the- perconducting devices in the absence of quasiparticles. art devices, the time-averaged number of quasi- However, measuring their absolute number in real time particles can be on the order of one [2, 12–15]. is challenging, mainly because breaking of Cooper pairs However, realizing a superconductor with no ex- does not change the total charge. In fact, there are only a citations remains an outstanding challenge. Here, few time-resolved experimental investigations of the dy- we experimentally demonstrate a superconduc- namics in this few-particle regime [2, 5, 13, 15, 21, 22], tor completely free of quasiparticles up to sec- and none where quasiparticle-free periods have been iden- onds. The quasiparticle number on a mesoscopic tified. superconductor is monitored in real time by mea- Here, we show experimentally a mesoscopic supercon- suring the charge tunneling to a normal metal ducting island that is free of quasiparticles for time pe- contact. Quiet excitation-free periods are inter- riods reaching seconds, five orders of magnitude longer rupted by random-in-time events, where one or than typical operation times of superconducting qubits several Cooper pairs break, followed by a burst [3]. The instantaneous number of quasiparticles is recon- of charge tunneling within a millisecond. Our re- structed from real-time measurements of single-electron sults vindicate the opportunity to operate devices tunneling from the island to a normal metal contact, as without quasiparticles with potentially improved illustrated in Fig. 1. We observe quiet periods, with no performance. In addition, our present experi- tunneling events and no quasiparticles on the island, for ment probes the origins of nonequilibrium quasi- 99.97% of the time, interrupted by Cooper pair break- particles in it; the decay of the Cooper pair break- ing events, followed by bursts of tunneling within a mil- ing rate over several weeks following the initial lisecond. The pair breaking events occur randomly in cooldown rules out processes arising from cosmic time, with an average rate 1.5 Hz and a probability or long-lived radioactive sources [16–19]. exp( 0.9Npair) to break Npair Cooper pairs. That The Bardeen, Cooper and Schrieffer theory of super- is,∝ in 40%− of the events, more than one Cooper pair is conductivity predicts that the number of quasiparticle broken. excitations should be exponentially small at tempera- Due to the three orders of magnitude faster probing tures low compared to the superconducting gap ∆ (di- via single-electron tunneling as compared to the Cooper vided by Boltzmann’s constant kB). Nevertheless, it is pair breaking, we are able to measure the decay dynam- experimentally well established that a residual popula- ics after individual pair-breaking events, while the time- 3 tion persists down to the lowest temperatures [4–6], at- averaged density nQP 0.01 quasiparticles/µm is close tributed to Cooper pair breaking in the superconductor to the lowest reported≈ values [22]. This goes well beyond arXiv:2102.00484v1 [cond-mat.supr-con] 31 Jan 2021 due to non-thermal processes. Residual quasiparticles are previous experiments on time-resolved quasiparticle tun- detrimental to the performance of many superconducting neling in superconducting structures [2, 5, 21–24] or ex- devices, ranging from setting the fundamental limit for periments with intentional injection of a large number the sensitivity of kinetic inductance detectors [1, 6] to ar- of quasiparticles [10, 11]. The very good agreement be- guably limiting the coherence times of superconducting tween the measured dynamics and a rate equation model qubits to the millisecond range [7, 8, 16]. Correspond- for the quasiparticle number allows for an unambiguous ingly, their origins and dynamics as well as mitigation identification of the excitation-free periods. Our findings schemes have been studied extensively [9–13]. create opportunities for operating superconducting de- In several state-of-the art devices, the observed ultra- vices while simultaneously monitoring the instantaneous 2 (a) superconductor (d) N +1 normal tunnel 0 junction metal excess -1 detector electrons output (a.u.) (e) 4 charge detector (b) QP 2 N quasi- particles 0 3088.6 3089.0 3089.4 200 nm time (ms) (c) quasiparticle-free intervals N +1 0 excess -1 detector electrons output (a.u.) 0 1000 2000 3000 4000 5000 time (ms) FIG. 1. Real-time monitoring of the number of quasiparticles on a superconducting island via charge tunneling. (a) Sketch of experiment. Pair-breaking radiation (pink arrow) is absorbed in a micron-scale superconducting aluminum island (blue), breaking one or more Cooper pairs and producing quasiparticle excitations (light blue circles). The quasiparticles tunnel out to the normal metallic copper leads (orange) via a tunnel junction as either electrons or holes. The tunneling events are measured in real time with a capacitively coupled charge detector (see Methods). (b) False-color scanning electron micrograph of the device, with colors as in (a). As no voltage bias is applied across the device, the two tunnel junctions act as a single junction. (c) Time trace of charge detector output (red line) and the corresponding charge state (black line), N = 0, 1 excess electrons, of the superconducting island, measured at a refrigerator base temperature of 20 mK. On top, quasiparticle-free± periods are denoted by thick blue lines. (d) Zoom in of time trace in (c) at location indicated by arrow, showing a burst of four single-electron tunneling events (N changing by 1). (e) Number of quasiparticles NQP on the island as a function of time, inferred from (d). The initial Cooper pair breaking± event, occuring on average within 30 µs before the first tunneling event, is not directly observed (here indicated by a dashed line). quasiparticle number, allowing for identifying periods for temperature dependence of two-electron Andreev tunnel- quasiparticle-free operation. This would enable testing ing rates (supplement). Coulomb blockade limits the ob- predictions of improved device performance in the ab- served charge states to N = 0, 1 excess electrons on sence of quasiparticles [7, 8, 25]. In addition, the statis- the island. The charge detector± is a capacitively cou- tics of number of quasiparticles created might provide pled radio-frequency single-electron transistor operating additional information on the origin of the pair-breaking at 580 MHz whose output is amplified with a Joseph- processes. Here, we observe that the rate of Cooper pair son parametric amplifier with an ultralow added noise of breaking events decreased by a factor of 4 over a period about 100 mK, enabling single-shot charge readout with of weeks. This rules out commonly suggested sources of a high signal-to-noise ratio in a few µs. Details on the nonequilibrium quasiparticles, such as insufficient shield- sample fabrication, measurements and device characteri- ing against stray light [22, 26] or ionizing radiation [16– zation are given in Methods and Supplementary Material. 19]. We measure 5 s time traces of the detector output. A We monitor the charge on an aluminum superconduct- representative trace is shown in Fig. 1(c). Quiet periods ing island, sketched in Fig. 1(a) and shown in Fig. 1(b), up to seconds long, with no tunneling events and zero ex- with volume V = 2 µm 0.5 µm 35 nm, charg- cess electrons, are interrupted by bursts of two or more × × ing energy EC 90 µeV and superconducting gap ∆ one- or two-electron tunneling events between the charge 220 µeV. The≈ island is coupled to normal metal copper states N = 0, 1 within a millisecond, see Fig. 1(d). We leads≈ via an insulating aluminum oxide tunneling barrier. collect statistics± from 4.6 h of time traces, containing over Measurements were done in a dilution refrigerator with 2 104 bursts of tunneling. In Fig. 2(a) we show that a base temperature of 20 mK at a normal metal elec- the× waiting times between the bursts of tunneling fol- tron temperature T 100 mK, obtained by fitting the low an exponential distribution, characterized by a rate N ≈ 3 (a) 104 experiment (b) 104 ber of quasiparticles one by one, NQP NQP 1 as the exponential fit charge state N changes by 1. After the→ last quasiparti-− cle has tunneled out, within± a millisecond from the start 3 10 of the burst, the superconducting island is completely free 102 counts counts of quasiparticles until the next burst occurs, on average experiment for 0.4 seconds. Therefore counting the number of events 102 exponential fit changing N yields directly NQP, which also allows us to 100 infer N for each burst. 0 1 2 3 0 5 10 pair Waiting time between Broken Cooper The statistical distribution of Npair, shown in Fig.
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