Phase-Tuned Entangled State Generation between Distant Spin Qubits

Quantum entanglement between distant qubits is an important feature of quantum networks. Distribution of entanglement over long distances can be enabled through coherently interfacing qubit pairs via photonic channels. Here, we report the realization of optically generated quantum entanglement between electron spin qubits confined in two distant semiconductor quantum dots. The protocol relies on spin-photon entanglement in the trionic $\mathrm{\Lambda }$ system and quantum erasure of the Raman-photon path information. The measurement of a single Raman photon is used to project the spin qubits into a joint quantum state with an interferometrically stabilized and tunable relative phase. We report an average Bell-state fidelity for $|{\psi }^{(+)}⟩$ and $|{\psi }^{(-)}⟩$ states of $61.6\pm 2.3\%$ and a record-high entanglement generation rate of 7.3 kHz between distant qubits.

Figure 1

Experimental setup and sequence for detecting entanglement between distant spin qubits. (a) Sketch of the optical interferometer with the QD nodes. Optical pulses, labeled entanglement, read-out and initialization, and spin control are used, together with a continuous-wave phase reference laser. Active phase stabilization utilizes a retroreflector on a piezo stack and a phase electro-optic modulator. (b) Entanglement verification sequence. The spins are initialized in the $|{\downarrow }_{\mathit{A}}{\downarrow }_{\mathit{B}}⟩$ state. The entanglement creation pulse is followed by coherent rotations of both qubits when measuring in an arbitrary basis. Further $\pi$ rotations of the qubits are added to cycle through the four two-spin combinations in a given basis. Resonant excitation of the blue transition is used for spin read-out.

Figure 2

Overlap of the optical and spin properties. (a) Ramsey interference fringes for both QDs (the data and curves have been offset for clarity). Sinusoidal fits to the data show electron spin splittings of $2\pi \times 25.2\pm 0.1\mathrm{GHz}$ for ${\mathrm{QD}}_{\mathit{A}}$ and $2\pi \times 25.1\pm 0.1\mathrm{GHz}$ for ${\mathrm{QD}}_{\mathit{B}}$. (b) Two-photon correlation measurements of the Raman emission generated by the entanglement pulse for each QD, with 0.78% average background. (c) Radiative decay measurements of the Raman transitions (offset for clarity). (d) Raman two-photon indistinguishability measurement with the same count rate from each QD. The five peaks closest to zero-time delay are displayed; the indistinguishability is $93\pm 1\%$.

Figure 3

Joint spin-state reconstruction through three-photon coincidence events. (a) Joint spin-state population conditional on a single Raman photon detection event. An antisymmetric population is retrieved with a probability of $85.7\pm 3.8\%$. The error bars represent the statistical uncertainty drawn from the 603 three-photon events that were used to reconstruct the population. (b),(c) Spin correlations in the transverse basis for projection of $|{\psi }^{(+)}⟩$ (b) or $|{\psi }^{(-)}⟩$ (c). (d) Visibility in the transverse basis for varying optical phase between the interfering paths. A positive visibility corresponds to a correlated phase and negative to an anticorrelated phase. The curves are sinusoidal fits to the data. (e) Normalized coincidence events for a Raman photon detected on beam splitter output 1 (red histograms) or output 2 (blue histograms) for five different set points of the interferometer phase.

Figure 4

Comparison of the measured fidelity and entanglement-generation rate (a) or generation probability (b) between the electron spins in this Letter and other physical systems. The indices denote the reference of the work from which the figures were extracted. The shaded regions mark the distribution protocol used, either single- or two-photon detection state projection (yellow and blue, respectively). We note our quoted fidelity is not corrected for our imperfect state retrieval.