Hamiltonian Benchmark of a Solid-State Spin-Photon Interface for Computation

Light-matter interfaces are pivotal for quantum computation and communication. While typically analyzed using single-mode or open-quantum-system approximations, these models often neglect multi-mode field states and light-matter entanglement, hindering exact protocol modeling. Here, we solve the full Hamiltonian dynamics of a solid-state spin-photon interface for three key protocols: the generation of photon-number superpositions, a controlled photon-photon gate, and the production of photonic cluster states. By deriving exact fidelities, we identify fundamental performance limits. Our results reveal that while realistic imperfections severely limit photon-photon gates, they only slightly affect linear photonic clusters and are nearly harmless for photon-number state superpositions.

💡 Research Summary

This paper presents a comprehensive Hamiltonian‑level benchmark of a solid‑state spin‑photon interface (SPI) based on a charged quantum dot (QD) embedded in a semi‑transparent micro‑cavity that confines the electromagnetic field to a “half‑1D” geometry. The authors go beyond the usual single‑mode or open‑system master‑equation treatments by retaining the full multimode structure of the propagating field and by explicitly modeling the hyperfine interaction between the electron spin and the nuclear spin bath (the Overhauser field). The QD is described as a four‑level system: two ground spin states (|↑⟩, |↓⟩) and two trion excited states (|↑↓⇑⟩, |↑↓⇓⟩) with strict circular‑polarization selection rules. In the rotating‑wave and flat‑coupling approximations the light‑matter interaction reads
(V = i\hbar\sqrt{\gamma}\big(|\downarrow\rangle\langle\uparrow\downarrow\Downarrow|\otimes b_L^\dagger(t) + |\uparrow\rangle\langle\uparrow\downarrow\Uparrow|\otimes b_R^\dagger(t)\big) - \text{h.c.})
where (\gamma) is the spontaneous‑emission rate and (b_{L,R}(t)) are time‑localized photon annihilation operators.

Spin dynamics includes an external magnetic field in the Voigt configuration (perpendicular to the quantization axis) and a quasi‑static Overhauser field (\mathbf{B}O) that is treated as a random vector with Gaussian statistics. The total spin Hamiltonian is
(H_s = \frac{\hbar}{2}\big(\Omega_g \mathbf{n}\cdot\mathbf{s}{\text{el}} + \Omega_e s_x\big))
with (\Omega_g) set by the Overhauser field magnitude, (\Omega_e) by the external field, and (\mathbf{n}) the random unit vector describing the Overhauser direction. The authors adopt the Merkulov‑Efros‑Rosen model for the frozen‑nuclear‑spin regime (timescales of a few hundred nanoseconds), averaging over many Overhauser configurations after solving the quantum dynamics for each fixed configuration.

To solve the full dynamics, the authors employ a collision‑model approach. The continuous time axis is discretized into intervals (\Delta t\ll\gamma^{-1}), each representing a “collision unit” (a temporal mode of the field). The unitary for the nth interval is
(U_n = \exp!\big