Generating spatially entangled itinerant photons with waveguide quantum electrodynamics

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Science Advances  07 Oct 2020:
Vol. 6, no. 41, eabb8780
DOI: 10.1126/sciadv.abb8780
  • Fig. 1 Generating spatially correlated itinerant photons in wQED.

    (A) False-colored micrograph of the device. The device consists of three independently flux-tunable transmon qubits that are capacitively coupled to a common waveguide. (B) Schematic diagram of three qubits that are coupled to a common waveguide with equal strength γ. Qubits Q1 and Q3 are initially excited and placed on resonance at ω/2π = 4.85 GHz such that their spatial separation along the waveguide is Δx = 3λ/4. Qubit Q2 is detuned far away ∣ω − ω ∣ ≫ γ such that it can be ignored and is left in the ground state. The four possible coherent pathways for the photons emitted by the qubits into the left and right traveling modes of the waveguide are shown below. The state of the emitted photons is a two-photon N00N state due to destructive interference between the single-photon pathways ∣11〉. (C) Same setup as (B) except Q1 and Q2 are now placed on resonance ω/2π = 6.45 GHz such that Δx = λ/2 and Q3 is now detuned far away. The ∣11〉 states constructively interfere for this choice of Δx.

  • Fig. 2 Measurement setup and procedure.

    (A) Schematic setup of the dual-sided control and measurement chain. The signal from the photons emitted by the qubits is amplified and downconverted to an intermediary frequency fd before digitization. The digitized signal is then further demodulated and integrated using custom field-programmable gate array (FPGA) code to obtain a pair of complex numbers SL = XL + iPL and SR = XR + iPR. Single-shot measurements of these values are then binned into a histogram to construct a 4D probability distribution. The mode of interest, âL(R), and noise mode, ĥL(R), of the left (right) measurement chain are indicated directly before amplification. (B) Representative time trace of the digitized and averaged voltage from the emission of a single qubit initialized to (g+e)/2. The exponential temporal envelope of the emission is superimposed with oscillations at the downconverted frequency fd = 40 MHz. (C) Voltage from the emission of a qubit initialized to ∣e〉. The photon is emitted with a random phase such that the voltage averages to zero.

  • Fig. 3 Photon state tomography.

    (A) Real (blue) and imaginary (orange) parts of the measured normally ordered moments of the left and right propagating photonic fields âLwâLxâRyâRz up to fourth order (w, x, y, z ∈ {0,1,2}) for Δx = 3λ/4. The moments are separated according to their corresponding channel or correlations. The ideal values for the moments are given by the box frames around the measured values. (B) Measured and ideal moments for Δx = λ/2.

  • Fig. 4 Density matrix reconstruction of photonic states.

    Real part of the density matrix in the Fock basis of the left and right propagating modes compared with the expected state (wire frames) for (A) (2002)/2 at Δx = 3λ/4 and (B) (20+02)/2+11/2 at Δx = λ/2. Density matrices are obtained via maximum likelihood estimation on measured photonic moments with fidelities of 84 and 87%, respectively. The matrix elements that are ideally nonzero are shaded in blue. The predominant source of infidelity is given by the finite population of 0.09 (A) and 0.11 (B) in the ∣00〉〈00∣ state.

Supplementary Materials

  • Supplementary Materials

    Generating spatially entangled itinerant photons with waveguide quantum electrodynamics

    B. Kannan, D. L. Campbell, F. Vasconcelos, R. Winik, D. K. Kim, M. Kjaergaard, P. Krantz, A. Melville, B. M. Niedzielski, J. L. Yoder, T. P. Orlando, S. Gustavsson, W. D. Oliver

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    • Experimental Setup
    • Spectroscopic Measurements
    • Figs. S1 and S2
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