Deterministic Loading of Microwaves onto an Artificial Atom Using a Time-Reversed Waveform

Abstract

Loading quantum information deterministically onto a quantum node is an important step toward a quantum network. Here, we demonstrate that coherent-state microwave photons with an optimal temporal waveform can be efficiently loaded onto a single superconducting artificial atom in a semi-infinite one-dimensional (1D) transmission-line waveguide. Using a weak coherent state (the number of photons (N) contained in the pulse ≪1) with an exponentially rising waveform, whose time constant matches the decoherence time of the artificial atom, we demonstrate a loading efficiency of 94.2% ± 0.7% from 1D semifree space to the artificial atom. The high loading efficiency is due to time-reversal symmetry: the overlap between the incoming wave and the time-reversed emitted wave is up to 97.1% ± 0.4%. Our results open up promising applications in realizing quantum networks based on waveguide quantum electrodynamics.

Keywords: Quantum network; photon loading; superconducting artificial atom; waveguide quantum electrodynamics.

Figure 1

(a) Setup sketch. A superconducting artificial atom (yellow) in a semi-infinite 1D space, terminated by a mirror. The green half-disk is the mirror image of the yellow atom, indicating that propagating microwaves can interact with the atom twice, instead of once in the open transmission line case. Here, the mirror is used to ensure that the loaded photons can only emit into a single waveguide channel and enhance the maximal loading efficiency compared to the case of a qubit along an infinite transmission line. A resonant coherent drive with voltage V_in(t) and exponentially rising waveform is sent toward the atom. After interaction with strength Γ between the atom and the input field, the atom emits an exponentially decaying output field V_out(t). (b) Photo of sample 2 showing a transmon qubit located at the end of a transmission line, terminated by an open-end capacitor, which can be seen as having a mirror at a distance equal to 0. The transmon contains a superconducting quantum interference device (SQUID, indicated by the red arrow and magnification shown on the left) loop. Therefore, the atomic resonance frequency is tunable by an external magnetic flux.

Figure 2

Loading a coherent state with exponentially rising waveforms onto a qubit (sample 1). Experimental data are shown as either square or round markers. Theoretical calculations, based on the parameters in Table 1 and the equations in the main text, are shown as curves. (a) Output magnitude for resonant input V_res, where the qubit first absorbs the input field and then emits a field when the pulse stops at t₀ = 2.63 μs (t₀^res = 2.64 μs and t₀^offres = 2.62 μs; see Section S3 in the Supporting Information). Inset: output magnitude for the off-resonant input pulse (V_offres) with four different rise times (40, 170, 230, and 600 ns) with constant N = 0.09. A magnification of (a) and the inset are provided in Figure S4 in the Supporting Information. (b) Loading efficiency (η) and (c) symmetry factor (S) as a function of τ for different input photon numbers (N) of 0.09 and 0.2. The maximum loading efficiency (symmetry) occurs around τ = T₂, consistent with the input pulse being the time-reversed version of the output. For higher input power, power broadening of the qubit line width causes the maximum loading efficiency (symmetry) to occur at an earlier time. The red dashed curve shows the analytical result from eq 8 for η and S as a function of τ assuming a weak drive, N ≪ 1. In Section S3 in the Supporting Information, we show step by step how the raw data in (a) was converted to the values in (b, c).

Figure 3

Loading a coherent state with exponentially rising waveforms onto a qubit at fixed τ ≃ T₂. (a) Loading efficiency, η, and (b) symmetry factor, S, as a function of N for samples 1 and 2. As expected, at N > 1, incoherent emission becomes dominant, leading to η → 0 and S → 0. Note that the revival for S at large N values is due to Rabi oscillations. For N ≪ 1 and τ ≃ T₂, according to eq 8, ; this expression also holds when τ = 1/γ only. Therefore, the variations of S and η are related by ΔS = Δη/2, leading to a larger fluctuation in (a) than (b). In sample 2, for N ≪ 1, η = 94.2% ± 0.7% and S = 97.1% ± 0.4%, according to eq 8. (c) Input (black) and emitted (red) voltage at low N values [the point marked by purple arrows in panels (a) and (b)] for sample 2, showing the time-reversal symmetry between the input and output fields. The time resolution for measuring samples 1 and 2 is 5 and 10 ns, respectively. The error in measurement of η and S is mainly from V_N and digitizer resolution.