Dynamical decoupling of a quantum dot spin in a micropillar cavity for spin-multiphoton entanglement

Technical Summary: Dynamical Decoupling of a Quantum Dot Spin in a Micropillar Cavity

Problem Statement
The generation of large-scale entangled photonic graph states, essential for scalable fault-tolerant quantum computing and networking, relies on the deterministic emission of photons entangled with a resident spin in a semiconductor quantum dot (QD). However, this approach is fundamentally limited by the short coherence time of the resident spin. In InGaAs QDs, the electron spin coherence is dominated by inhomogeneous dephasing ($T_2^*$) caused by hyperfine interactions with the nuclear spin bath, typically limiting $T_2^*$ to approximately 2 ns. While dynamical decoupling techniques like spin echo can extend coherence, previous implementations often required strong magnetic fields (>1 T) suitable only for time-bin encoding. The generation of spin-photon entanglement based on polarization (the Lindner and Rudolph scheme) requires operation in a weak transverse magnetic field regime (<100 mT), where the spin state is controlled via coherent Larmor precession. In this regime, extending coherence times sufficiently to generate complex multi-photon entangled states remains a significant challenge.

Methodology
The authors utilized a single trapped electron in an InGaAs QD positioned at the center of a micropillar cavity, which provides a high-purity, bright single-photon source. The device was operated at 4 K under a 60 mT transverse magnetic field. The experimental protocol involved:

1. Initialization and Readout: A negatively charged trion ($|X^-\rangle$) state was used, where optical selection rules map the electron spin state ($|\uparrow\rangle$ or $|\downarrow\rangle$) to the circular polarization (R or L) of emitted photons. The spin was heralded in the $|\uparrow\rangle$ state by detecting an R-polarized photon.
2. Free Induction Decay Measurement: Without intervention, the spin precesses, and its state was read out by detecting a second photon after a variable delay $\tau$. This established a baseline $T_2^* \approx 1.5$ ns.
3. Dynamical Decoupling Implementation:
   • Spin Echo (SE): An ultrafast (4 ps), red-detuned, circularly polarized pulse was applied at time $\tau/2$ to perform a $\pi$-rotation about the optical axis, refocusing the spin.
   • Carr-Purcell-Meiboom-Gill (CPMG): The spin echo technique was generalized to multiple refocusing pulses ($N$) spaced equally between excitation pulses. Pulse sequences were generated using electro-optic modulators (EOMs) to suppress specific laser pulses, allowing for precise control of delay times $\tau$ and pulse counts.
4. Entanglement Generation: The authors applied these techniques to the Lindner-Rudolph protocol to generate a three-partite Greenberger-Horne-Zeilinger (GHZ) state involving the spin and two photons. This involved sequential excitation and emission events synchronized with the spin's Larmor precession.

Key Results

• Coherence Time Extension:
  • The application of a single spin echo pulse extended the coherence time from the natural $T_2^* \approx 1.5$ ns to $T_2^{SE} \approx 27(4)$ ns, representing a more than ten-fold improvement.
  • The application of CPMG sequences further extended the coherence time to $T_2^{CPMG} \approx 298(53)$ ns, an improvement of over two orders of magnitude (more than 100 times the natural $T_2^*$).
• Entanglement Fidelity:
  • The generation of a spin-photon-photon GHZ state was demonstrated.
  • The use of spin echo between the second and third photon emissions significantly improved the purity of the conditional state of the second photon, increasing from $0.61 \pm 0.05$ (without echo) to $0.81 \pm 0.05$ (with echo).
  • Simulations based on the experimental data indicated that the three-qubit GHZ state fidelity improved from $F_{3-GHZ} = 0.63$ to $F_{3-GHZ}^{SE} = 0.76$ (a ~20% improvement) when dynamical decoupling was employed.
• Compatibility: The study confirmed that all-optical dynamical decoupling is compatible with the high-rate generation of entangled states in a weak magnetic field regime, a prerequisite for the polarization-based entanglement schemes used in scalable quantum networks.

Significance and Claims
The paper claims to present the first demonstration of optical dynamical decoupling compatible with spin-photon entangled state generation in a weak transverse magnetic field. The authors assert that these results represent the current state-of-the-art for coherence times in InGaAs QDs under such conditions.

The significance of this work is framed as a critical step toward scalable, fault-tolerant quantum computing. Specifically:

• The achieved coherence times ($T_2 \sim 300$ ns) enter the feasibility window required for hybrid spin-optical computing architectures, which demand coherence times in the hundreds of nanoseconds to microseconds relative to gate times.
• The ability to extend coherence while maintaining high generation rates enables the creation of larger and more complex entangled states (such as photonic caterpillar graph states) with lower resource overhead.
• The results suggest that fault-tolerant thresholds for gate operations can be met using QD sources with resident spins, provided dynamical decoupling is utilized to mitigate nuclear spin noise.