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Coherent suppression of electromagnetic dissipation due to superconducting quasiparticles

Abstract

Owing to the low-loss propagation of electromagnetic signals in superconductors, Josephson junctions constitute ideal building blocks for quantum memories, amplifiers, detectors and high-speed processing units, operating over a wide band of microwave frequencies. Nevertheless, although transport in superconducting wires is perfectly lossless for direct current, transport of radio-frequency signals can be dissipative in the presence of quasiparticle excitations above the superconducting gap1. Moreover, the exact mechanism of this dissipation in Josephson junctions has never been fully resolved experimentally. In particular, Josephson’s key theoretical prediction that quasiparticle dissipation should vanish in transport through a junction when the phase difference across the junction is π (ref. 2) has never been observed3. This subtle effect can be understood as resulting from the destructive interference of two separate dissipative channels involving electron-like and hole-like quasiparticles. Here we report the experimental observation of this quantum coherent suppression of quasiparticle dissipation across a Josephson junction. As the average phase bias across the junction is swept through π, we measure an increase of more than one order of magnitude in the energy relaxation time of a superconducting artificial atom. This striking suppression of dissipation, despite the presence of lossy quasiparticle excitations above the superconducting gap, provides a powerful tool for minimizing decoherence in quantum electronic systems and could be directly exploited in quantum information experiments with superconducting quantum bits.

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Figure 1: Phase-dependent quasiparticle dissipation in a Josephson junction.
Figure 2: Experimental set-up.
Figure 3: Flux dependence of the fluxonium qubit T1 measured by polarization saturation pulses.
Figure 4: Time-domain measurements of qubit relaxation after π-pulse excitation.

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Acknowledgements

We acknowledge discussions with L. Frunzio, A. Kamal, N. Masluk and U. Vool. Facilities use was supported by YINQE and NSF MRSEC DMR 1119826. This research was supported by IARPA under grant no. W911NF-09-1-0369, ARO under grant no. W911NF-09-1-0514, the NSF under grants nos DMR-1006060 and DMR-0653377, DOE contract no. DE-FG02-08ER46482 (L.I.G.), and the EU under REA grant agreement CIG-618258 (G.C.).

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Authors

Contributions

I.M.P. and K.G. performed the experiment and analysed the data, under the guidance of M.H.D. Theoretical support was provided by G.C. and L.I.G. The experimental design was proposed by I.M.P., K.G., R.J.S. and M.H.D. I.M.P. and M.H.D. led the writing of the manuscript. All authors provided suggestions for the experiment, discussed the results and contributed to the manuscript.

Corresponding author

Correspondence to Ioan M. Pop.

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The authors declare no competing financial interests.

Extended data figures and tables

Extended Data Figure 1 Scanning electron microscope imaging of controlled undercuts.

a, 500-nm-deep cut; b, 900-nm-deep cut. For the purpose of scanning electron microscope imaging, the entire structure is covered with a 10-nm layer of sputtered gold. Notice that the residual undercut on the right-hand side of the trenches is at least an order of magnitude smaller than the designed undercut.

Extended Data Figure 2 Heterodyne measurement experimental set-up.

Schematic diagram of experimental set-up to perform heterodyne measurement, involving an interferometric measurement, which compares a microwave signal going through the device under test with a signal bypassing the device. Two microwave generators (cavity and LO) are mixed together to produce a lower frequency tone at the difference frequency, ωIF, that can be digitized in the computer. The additional (qubit) microwave generator can be used to stimulate the device and the effect on the cavity transmission can be measured.

Extended Data Figure 3 Microwave cryogenic measurement set-up.

Extended Data Figure 4 Infrared shielding.

a, Top plate of the infrared shield and the attached samples connected by microwave coaxial lines. The hermetic seal is on the top side of the plate. The top half of the cryoperm shield is also visible. b, Inside of the infrared shield can. An infrared absorbent coating was applied to a thin copper sheet and placed on the walls and bottom of the can. c, Closed infrared shield, completely enclosing the experimental area.

Extended Data Figure 5 Measured qubit frequency as a function of applied flux over the entire tunable range.

Fits of the expected frequency dependence from theory match well with the measured data and yield parameters as listed for each fluxonium sample. The flux dependence of fluxonium B was sampled more sparsely than that of fluxonium A.

Extended Data Figure 6 Measured relaxation times near Φext/Φ0 = 0.5.

Data are fitted to a single exponential and reveal that lifetimes are 1 ms for fluxonium sample A at f01 = 640 MHz (a) and fluxonium sample B at f01 = 750 MHz (b). The presence of single exponentials as shown here fluctuates in time, as shown in Fig. 4.

Extended Data Figure 7 Measured relaxation times.

Measured T1 values and theoretical bounds for capacitive (a), inductive (b), quasiparticle (c) and radiation (d) loss.

Extended Data Figure 8 Transition efficiency of the fluxonium qubit.

Shown as a function of applied magnetic flux for capacitive (red), inductive (blue) and quasiparticle (green) loss.

Extended Data Figure 9 Placing a bound on ε.

The lines represent T1 values calculated from equation (11) for ε = 0.9, 0.991 (the fitted value), 0.999 and 0.9999, respectively. The green line (ε = 0.991) bounds all measured points (grey circles), giving a conservative bound of ε 0.99.

Extended Data Table 1 Measured coherence times for fluxonium samples A and B at different bias points
Extended Data Table 2 Expressions used to calculate the qubit energy relaxation rate23

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Pop, I., Geerlings, K., Catelani, G. et al. Coherent suppression of electromagnetic dissipation due to superconducting quasiparticles. Nature 508, 369–372 (2014). https://doi.org/10.1038/nature13017

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