Quantum acoustics with superconducting qubits

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Science  13 Oct 2017:
Vol. 358, Issue 6360, pp. 199-202
DOI: 10.1126/science.aao1511
  • Fig. 1 Qubit with piezoelectric transducer.

    (A) False-color scanning electron microscopy image of a transmon qubit on a sapphire substrate with one electrode covering an AlN transducer, which is ~900 nm thick and d = 200 μm in diameter. (B). Schematic of piezoelectric coupling to the modes of a HBAR (not to scale). The longitudinal part of the wave function is illustrated by a sinusoidal profile with wavelength λ = 2h/l on the cylindrical mode volume defined by the AlN disk and the sapphire substrate underneath. The transverse energy density profile of Embedded Image is plotted in 3D, showing the effective confinement of energy inside the mode volume, while some energy leaks out due to diffraction. This also illustrates that the Embedded Image mode corresponds to the Embedded Image mode of a larger volume with diameter a.

  • Fig. 2 Spectroscopy of qubit-phonon coupling.

    (A) Qubit spectroscopy as a function of current applied to flux tuning coil. White dashed lines indicate anticrossings for different longitudinal wave numbers. The highest accessible longitudinal mode is lmax = 505, assuming vl is constant with frequency. (Inset) Detailed spectroscopy around the l = 503 anticrossing, which is also used in (B) and (C), along with Figs. 3 and 4. The blue dash-dot line shows the frequency of the uncoupled qubit. Dashed white lines indicate anticrossings for m = 0,1,2, whose transverse mode profiles are plotted to the left. The frequencies of these modes are given relative to v0 = 6.65235 GHz. The faint feature indicated by a yellow arrow is due to multiphoton transitions to higher states of the Jaynes-Cummings level structure (30). (B and C) Spectroscopy and qubit dynamics. Vertical arrows indicate locations of prominent subfeatures. Horizontal arrows in (B) indicate frequencies used for Stark shift control, as described in the text. In (C), the qubit excitation pulse is 20 ns long, which ensures that the bandwidth is large enough to excite the hybridized qubit-phonon states.

  • Fig. 3 Quantum control of the qubit-phonon system.

    (A) Vacuum Rabi oscillations measured by varying the amplitude and duration of the Stark drive pulse after exciting the qubit while it is off-resonant from the phonons, as shown in the inset. The pulse is a decrease in the Stark drive amplitude with a rise time of 50 ns. Except for Fig. 3B, axes labeled “Population” in Figs. 3 and 4 correspond to all populations not in the g state. (B) Measurement of the excited state populations of the qubit and phonon. We plot measured Rabi oscillations between the e state and the transmon’s third energy level f, normalized using the same experiment with a preceding g-e π pulse [see (19, 31) for details]. The amplitude of oscillations gives the population in the n = 1 Fock state of the phonon or the e state of the qubit, depending on whether or not a swap operation is performed at the beginning. Black lines show sinusoidal fits to the data. (C) Rabi oscillations between the g and e qubit states, with and without a preceding swap operation. We use the former to calibrate the qubit population measurements in Figs. 3 and 4.

  • Fig. 4 Phonon coherence properties.

    (A) Phonon T1 measurement. The black line is a fit to an exponential decay plus a decaying sinusoid. (B) Phonon T2 measurement. The phase of the second π/2 pulse is set to be (ω0 + Ω)t, where t is the delay, ω0 is the detuning between the qubit and phonon during the delay, and Ω provides an additional artificial detuning. The black line is a fit to an exponentially decaying sinusoid with frequency Ω.

Supplementary Materials

  • Quantum acoustics with superconducting qubits

    Yiwen Chu, Prashanta Kharel, William H. Renninger, Luke D. Burkhart, Luigi Frunzio, Peter T. Rakich, Robert J. Schoelkopf

    Materials/Methods, Supplementary Text, Tables, Figures, and/or References

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    • Materials and Methods
    • Supplementary Text
    • Figs. S1 to S8
    • Table S1
    • References

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