Research ArticlePHYSICS

Superadiabatic population transfer in a three-level superconducting circuit

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Science Advances  08 Feb 2019:
Vol. 5, no. 2, eaau5999
DOI: 10.1126/sciadv.aau5999
  • Fig. 1 Schematic of the experiment.

    (A) Loop driving for saSTIRAP: A counterdiabatic drive with effective Rabi frequency Ω02 (dashed purple arrow) is applied in parallel with a STIRAP sequence consisting of pulses Ω01 and Ω12, which are resonant with the respective transitions 0–1 and 1–2. The counterdiabatic drive is a two-photon process realized by an off-resonant pulse (detuning Δ with respect to the first transition), which couples with strengths Ω2ph and Embedded Image into the corresponding transitions. (B) Schematic of the timings and shapes of the pulses. The last pulse is the measurement pulse applied to the resonator. (C) Schematic (including the IQ mixers used for driving and measurement) and optical image of the transmon. (D) Geometric representation of the Hamiltonian on a three-site plaquette with Peierls hopping and resulting gauge-invariant phase Φ = ϕ01 + ϕ12 + ϕ20.

  • Fig. 2 Comparison between STIRAP and saSTIRAP.

    Time evolution of the populations p0, p1, and p2 during STIRAP (diamonds) and saSTIRAP (circles). The solid lines show the corresponding simulation, which includes decoherence. A simulation for the ideal case without decoherence is presented with dashed lines. The experiment was performed with the parameters Ω01 = Ω12 = 25.5 MHz, ts/σ = − 1.5, and σ = 20 ns.

  • Fig. 3 Correction of the nonadiabatic losses with the saSTIRAP protocol.

    (A) Population p2 in the state |2〉 for the STIRAP process with Ω01/(2π) = Ω12/(2π) = 25.5 MHz as a function of the pulse width σ and the normalized pulse separation |ts|/σ. (B) Population p2 for the corresponding saSTIRAP process. The left plots are experiments, while the right ones are the corresponding simulation results. The solid black lines show the transfer time Embedded Image in nanoseconds to achieve the population p2 = 0.9 in saSTIRAP.

  • Fig. 4 Control of the system dynamics with the gauge-invariant phase.

    Under loop driving, the phase Φ is a gauge-invariant quantity, in analogy with lattice gauge theories, where it is typically produced by an applied magnetic field. The three-dimensional plot shows lines of constant population p2 in the state |2〉, in the orthogonal planes (ϕ12, ϕ2ph) (with ϕ01 constant), (ϕ01, ϕ2ph) (with ϕ12 constant), and (ϕ12, ϕ01) (with ϕ2ph constant). The gauge-invariance relation ϕ01 + ϕ12 − 2ϕ2ph − π = Φ corresponds to tilted planes that intersect the axes. Note also that the periodicity along the ϕ2ph axis is twice that of the periodicity along the axes ϕ01 and ϕ12 as a result of two-photon driving. In the experiment, we had Ω01/(2π) = Ω12/(2π) = 25.5 MHz, ts = −30 ns, and σ = 20 ns.

  • Fig. 5 Robustness of saSTIRAP against variations in the counterdiabatic pulse parameters.

    Population p2 in the state |2〉 as a function of the area of the counterdiabatic pulse and the gauge-invariant phase. The experimental result is shown in the left panel with the corresponding simulation in the right panel. The parameters used in the experiment are ts = −30 ns, σ = 20 ns, and Embedded Image. Note that Embedded Image corresponds to pure STIRAP. The blue dashed-line ellipses represent the areas where saSTIRAP is robust against changes in parameters Embedded Image and ϕ2ph.

  • Fig. 6 Comparison between saSTIRAP and nonadiabatic population transfer.

    Transferred population p2 (experiment) as a function of the STIRAP pulse area A defined in Eq. 8 and the two-photon pulse area Embedded Image from Eq. 7. We also show isopopulation lines (from 0.1 to 0.8 in steps of 0.1 and from 0.8 to 1.0 in steps of 0.01) obtained from the simulations, showing agreement with the data and delineating the same region of high transfer as that obtained from the experiment. In this experiment, the peak STIRAP Rabi frequencies were increased from zero to Ω01/(2π) = Ω12/(2π) = 40 MHz. Similarly, the two-photon pulse amplitude was varied from zero to Ω2ph/(2π) = 77 MHz. The horizontal axis with Embedded Image corresponds to two-photon Rabi driving, whereas the vertical axis with Embedded Image corresponds to standard STIRAP. In the experiment, the STIRAP pulse separation was ts = −30 ns and the pulse width was σ = 20 ns.

Supplementary Materials

  • Supplementary material for this article is available at http://advances.sciencemag.org/cgi/content/full/5/2/eaau5999/DC1

    Experimental setup and sample

    Reverse engineering of the counteradiabatic drive

    Synthetic Peierls couplings on the triangular plaquette

    Fig. S1. Electronics, cryogenics, and sample schematic.

    Fig. S2. Pulse sequence for saSTIRAP.

    References (4547)

  • Supplementary Materials

    This PDF file includes:

    • Experimental setup and sample
    • Reverse engineering of the counteradiabatic drive
    • Synthetic Peierls couplings on the triangular plaquette
    • Fig. S1. Electronics, cryogenics, and sample schematic.
    • Fig. S2. Pulse sequence for saSTIRAP.
    • References (4547)

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