Coherent interconnects between gate-defined silicon quantum processors are essential for scalable computation and long-range entanglement. We demonstrate that one-dimensional electron channels in a Si/SiGe quantum well, formed by a resistive topgate, exhibit strong Coulomb interactions, realizing Luttinger liquid physics. At low electron densities, these electrons overcome their kinetic energy to form a one-dimensional Wigner crystal—characterized by dominant 4K_F correlations.
From Bosonization we obtain the charge-sector Luttinger liquid parameter for different screening lengths and corroborate our findings through large-scale density matrix renormalization group (DMRG) simulations, revealing a density-driven crossover from Wigner to Friedel-dominated 2K_F regime for both screened and unscreened Coulomb potentials. We identify signatures of the Wigner regime, through its electronic compressibility in zero and high magnetic field limits and through charge sensing. Furthermore, we analyze effects of disorder from random alloy fluctuations and valley splitting variations, identifying thresholds below which Wigner crystal signatures remain robust against localization effects. Finally, we find that a Wigner crystal in the interconnect enables strong, long-range capacitive coupling between quantum dots across the interconnect, suggesting a route to long-range high-fidelity entangling gates. Our results position silicon interconnects as a platform for studying emergent many-body physics and for developing architectures for non-local quantum error correction and simulation.

Pizza and drinks will be served after the seminar in ATL 2117.