Coherent suppression of electromagnetic dissipation due to superconducting quasiparticles

Journal name:
Nature
Volume:
508,
Pages:
369–372
Date published:
DOI:
doi:10.1038/nature13017
Received
Accepted
Published online

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.

At a glance

Figures

  1. Phase-dependent quasiparticle dissipation in a Josephson junction.
    Figure 1: Phase-dependent quasiparticle dissipation in a Josephson junction.

    a, In the case of a Josephson junction biased at phase ϕ, quasiparticles (QPs) receiving a quanta of excitation from the qubit or environment can tunnel across the junction either as electrons, acquiring a phase +ϕ/2, or as holes, acquiring a phase −ϕ/2. The ϕ dependence of quasiparticle dissipation results from the interference of these two indistinguishable paths. b, Schematic representation of the fluxonium qubit: the phase-slip junction (red) is shunted by an array of bigger junctions (black) that form the superinductor. In the fluxonium qubit, the external magnetic flux, Φext, sets the average phase difference, ϕ, across the phase-slip junction. c, Flux dependence of the fluxonium relaxation time, T1, due to quasiparticle loss across the phase-slip junction. Quasiparticle loss is suppressed at Φext/Φ0 = 0.5, where the average phase difference over the small junction is π. The insets show the potential landscape (black), the qubit ground-state (|0right fence; dark red) and excited-state (|1right fence; light red) wavefunctions, and the quasiparticle dissipation operator7, sin( /2) (dashed magenta). The T1 divergence at Φext/Φ0 = 0.5 is explained by the symmetry of sin( /2) around = π, together with the respective even and odd parities of |0right fence and |1right fence, which lead to the vanishing of the quasiparticle matrix element left fence0|sin( /2)|1right fence = 0 (compare with equation(2)). Here the symbol ϕ represents the dynamical coordinate associated with the operator .

  2. Experimental set-up.
    Figure 2: Experimental set-up.

    a, Electron-beam image of fluxonium sample. The schematic diagram in the upper left corner is a three-dimensional model of the junction array. The Al/AlOx/Al junctions are made using bridge-free, double-angle evaporation30. SQUID, superconducting quantum interference device. b, Optical image of the antenna with the fluxonium qubit in the middle. c, Photograph of the sapphire chip inside the copper cavity (sample holder). d, Electrical scheme for the fluxonium qubit coupling to the input–output microwave lines.

  3. Flux dependence of the fluxonium qubit T1 measured by polarization saturation pulses.
    Figure 3: Flux dependence of the fluxonium qubit T1 measured by polarization saturation pulses.

    a, The measured values are represented by the grey circles, and the theoretical fit including all sources of dissipation is represented by the black line. The different contributions, T1X, to the total relaxation rate, 1/T1 = Σ1/T1X, are plotted as coloured dashed lines. Inductive loss does not significantly contribute to the total decay rate, and the fit lies outside the figure scale (Methods). The inset shows the measured (grey circles) and the theoretical (black line) flux dependence of the |0right fence–|1right fence qubit transition frequency. b, Time-domain measurements of qubit free decay at different flux bias points. The y axis is shown on a logarithmic scale with the traces offset for clarity. The lines represent exponential fits and the inset table lists the fitted T1 values. c, Detailed view in the vicinity of Φext/Φ0 = 0.5. The coloured lines show the calculated upper bound on T1 resulting from the sum of quasiparticle and dielectric dissipation. For this narrow flux interval, we assumed that dielectric loss limits T1 to a constant value of 8ms.

  4. Time-domain measurements of qubit relaxation after [pgr]-pulse excitation.
    Figure 4: Time-domain measurements of qubit relaxation after π-pulse excitation.

    Typical measured traces of non-exponential (a) and quasi-exponential (b) decays. The magenta curves represent theoretical fits using equation(4). For comparison, the green dashed line in b is a fit with a simple exponential decay and time constant of 720μs. The flux bias point at Φext/Φ0 = 0.48 is chosen slightly off the maximum of the T1 peak to allow faster repetition rates for the pulse calibration sequences. The data in a and b are taken several days apart; the acquisition time for data in each panel is 30min. We observe non-exponential and quasi-exponential decays with similar occurrence probabilities. The offset and amplitude of the qubit excitation are calibrated using measurements of Rabi oscillations (insets). Error bars, 1 s.d. of the qubit excitation signal.

  5. Scanning electron microscope imaging of controlled undercuts.
    Extended Data Fig. 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.

  6. Heterodyne measurement experimental set-up.
    Extended Data Fig. 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.

  7. Microwave cryogenic measurement set-up.
    Extended Data Fig. 3: Microwave cryogenic measurement set-up.
  8. Infrared shielding.
    Extended Data Fig. 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.

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

  10. Measured relaxation times near [Phi]ext/[Phi]0 = 0.5.
    Extended Data Fig. 6: Measured relaxation times near Φext/Φ0 = 0.5.

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

  11. Measured relaxation times.
    Extended Data Fig. 7: Measured relaxation times.

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

  12. Transition efficiency of the fluxonium qubit.
    Extended Data Fig. 8: Transition efficiency of the fluxonium qubit.

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

  13. Placing a bound on [epsi].
    Extended Data Fig. 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.

Tables

  1. Measured coherence times for fluxonium samples[thinsp]A and B at different bias points
    Extended Data Table 1: Measured coherence times for fluxonium samplesA and B at different bias points
  2. Expressions used to calculate the qubit energy relaxation rate
    Extended Data Table 2: Expressions used to calculate the qubit energy relaxation rate23

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Author information

  1. These authors contributed equally to this work.

    • Ioan M. Pop &
    • Kurtis Geerlings

Affiliations

  1. Department of Applied Physics, Yale University, 15 Prospect Street, New Haven, Connecticut 06511, USA

    • Ioan M. Pop,
    • Kurtis Geerlings,
    • Gianluigi Catelani,
    • Robert J. Schoelkopf,
    • Leonid I. Glazman &
    • Michel H. Devoret
  2. Forschungszentrum Jülich, Peter Grünberg Institut (PGI-2), 52425 Jülich, Germany

    • Gianluigi Catelani

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.

Competing financial interests

The authors declare no competing financial interests.

Corresponding author

Correspondence to:

Author details

Extended data figures and tables

Extended Data Figures

  1. Extended Data Figure 1: Scanning electron microscope imaging of controlled undercuts. (542 KB)

    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.

  2. Extended Data Figure 2: Heterodyne measurement experimental set-up. (104 KB)

    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.

  3. Extended Data Figure 3: Microwave cryogenic measurement set-up. (90 KB)
  4. Extended Data Figure 4: Infrared shielding. (267 KB)

    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.

  5. Extended Data Figure 5: Measured qubit frequency as a function of applied flux over the entire tunable range. (166 KB)

    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.

  6. Extended Data Figure 6: Measured relaxation times near Φext/Φ0 = 0.5. (121 KB)

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

  7. Extended Data Figure 7: Measured relaxation times. (517 KB)

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

  8. Extended Data Figure 8: Transition efficiency of the fluxonium qubit. (223 KB)

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

  9. Extended Data Figure 9: Placing a bound on ε. (491 KB)

    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 Tables

  1. Extended Data Table 1: Measured coherence times for fluxonium samplesA and B at different bias points (147 KB)
  2. Extended Data Table 2: Expressions used to calculate the qubit energy relaxation rate23 (138 KB)

Additional data