In 2012, Sato and co-workers demonstrated strong (Rabi-like) coupling between two ultrahigh-Q photonic-crystal nanocavities separated by more than 100 wavelengths on a silicon chip, mediated by a bounded line-defect waveguide, and showed that a picosecond free-carrier control pulse can stop the photon exchange on demand and freeze the photon state. The authors explicitly identified what remained unresolved: the demonstration was classical and only indirectly supported at the single-photon level because detector timing jitter exceeded the 54 ps oscillation period; the optical control pulse absorbs photons when it strikes an occupied cavity (photon lifetime reduced to about one sixth); the decoupled state persists only about 1 ns, set by the silicon carrier lifetime; and the tolerance of the scheme to non-unity reflector reflectivity, fabrication disorder, and full three-dimensional radiation loss was not quantified. The objective is to extend the dynamically controlled, waveguide-mediated coupling of distant on-chip nanocavities to genuine quantum-regime operation — direct time-resolved observation of single-photon coherent exchange and its on-demand control — together with fast, absorption-free, rapidly recoverable tuning mechanisms. Later literature has largely resolved the classical control engineering (absorption-free transfer via a third nonresonant cavity, ~90% efficiency; short-carrier-lifetime GaAs dynamic-Q control; electrical carrier-injection control at 76% efficiency), while the single-photon/quantum-regime core remains open in the optical platform.

Background

Photonic-crystal nanocavities are wavelength-scale optical resonators formed by introducing a line or point defect into a periodic dielectric lattice; the surrounding photonic bandgap (a frequency range in which the periodic lattice forbids light propagation) confines light so strongly that quality factors (Q, the resonance frequency divided by its linewidth; equivalently, the photon storage time measured in radians of the optical cycle, so higher Q means longer photon storage) above 400,000 can coexist with a mode volume on the order of one cubic wavelength in the material. Two such cavities are normally coupled only when they sit within a few wavelengths of each other, so that their evanescent fields overlap; this proximity requirement prevents placing coupled cavities at arbitrary positions on a chip and hampers independent control of each element. Connecting distant cavities through an ordinary open waveguide fails because the waveguide provides a continuum of states into which cavity photons leak, destroying coherent two-mode exchange.

Sato, Tanaka, Upham, Takahashi, Asano and Noda (Nature Photonics 6, 56–61, 2012) overcame this by bounding the connecting waveguide with partial reflectors, which discretize its mode spectrum (Fabry–Pérot modes with a free spectral range ΔFP\Delta_{\rm FP}, the frequency spacing between adjacent waveguide resonances), and choosing the cavity–waveguide coupling bandwidth δin\delta_{\rm in} to satisfy δin≪ΔFP\delta_{\rm in} \ll \Delta_{\rm FP} together with a propagation-phase mismatch 2θc≈(2m+1)π2\theta_{\rm c} \approx (2m+1)\pi at the cavity frequency, with mm an integer labeling the waveguide mode order. Under these mode-mismatch conditions the waveguide modes are barely excited, and two nanocavities separated by 83 µm (>100 wavelengths) form a split pair of symmetric/antisymmetric eigenmodes with Q ≈ 460,000. Exciting this pair produces Rabi oscillation — the periodic coherent exchange of energy (photons) back and forth between the two cavities, here with a period of 54 ps — while the photon population stays in the cavities, not the waveguide. A quantum-mechanical diagonalization of the cavity-plus-bounded-waveguide Hamiltonian showed that the many discrete waveguide modes renormalize into an effective direct two-cavity coupling, so the same dynamics should persist for single photons.

Dynamic control was demonstrated optically: a 4 ps pulse at 770 nm generates free carriers in one cavity (the free-carrier plasma effect — the refractive-index decrease caused by photoexcited electrons and holes), shifting its resonance by more than the coupling splitting and abruptly detuning that cavity, which stops the Rabi oscillation and freezes the photon population. At an average of roughly 0.02 photons per cavity, a superconducting single-photon detector (SSPD, a cryogenic nanowire detector) with 100 ps timing jitter could not resolve the 54 ps oscillation directly, but the timing of the remote control pulse modulated the late-time photon counts, indirect evidence that the single-photon-level exchange responds to control. The finite-difference time-domain (FDTD) simulations supporting the design were two-dimensional, neglecting out-of-plane radiation, and non-unity reflectivity of the end reflectors was known to degrade the coupled-mode Q. These limitations — the quantum-regime demonstration, control-induced absorption (photon lifetime cut to about one sixth when the control pulse hits an occupied cavity), the roughly 1 ns limit on the frozen state set by the silicon carrier lifetime, and the unquantified tolerances to partial reflectors and fabrication disorder — were stated by the authors as what remains to be addressed to turn the effect into a usable building block for quantum photonic circuits and lossless dynamic control of light.

Problem Statement

In the system of Sato et al. (2012) — two ultrahigh-Q photonic-crystal nanocavities (wavelength-scale optical resonators in a periodic dielectric lattice) coupled indirectly through a bounded, reflector-terminated line-defect waveguide whose cavity–waveguide coupling bandwidth δin\delta_{\rm in} is much smaller than the waveguide's Fabry–Pérot mode spacing (free spectral range) ΔFP\Delta_{\rm FP} and whose round-trip propagation phase 2θc2\theta_{\rm c} at the cavity frequency is an odd multiple of π\pi (both being the mode-mismatch conditions that keep the photons in the two cavities rather than the waveguide), with coherent photon exchange (Rabi oscillation, period ~54 ps) dynamically stoppable by a free-carrier control pulse — extend the demonstrated strong coupling and its dynamic control to the regime and performance needed for quantum photonic circuits. Specifically: (1) demonstrate the quantum regime of the coupled system directly, i.e. time-resolved observation of coherent photon exchange at the single-photon level (single-photon Rabi oscillation, or equivalent phase-coherent transfer and freezing of a single-photon state between the two cavities) and controlled manipulation of single-photon-level states, including entanglement between the two distant cavity modes; (2) implement, at the single-photon level and jointly with item (1), dynamic control of the coupling that is fast compared with the Rabi period, essentially free of control-induced absorption even when the control acts on an occupied cavity, and recoverable on timescales well below the ~1 ns silicon carrier lifetime; and (3) establish the design tolerances — partial-reflector reflectivity, fabrication disorder, and full three-dimensional radiation and material-absorption losses — within which the quantum-regime coherent exchange and its control remain usable. The unifying objective is a distant-cavity coupled system whose coherent single-photon dynamics can be created, frozen, and released on demand with negligible loss, as a building block for on-chip quantum state storage, transfer, and entanglement; the three items are jointly the completion boundary stated by the source's own limitations.

References

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