Donor Spin Qubits in Ge-based Phononic Crystals

TL;DR

This paper proposes germanium donor spin qubits embedded in phononic crystals, leveraging phonon bandgap engineering to achieve long coherence times and strong, tunable qubit interactions for quantum computing.

Contribution

It introduces a novel approach to enhance donor spin qubit coherence and coupling in germanium using phononic crystal structures to suppress phonon-induced decay.

Findings

Long spin lifetimes achieved within phonon bandgaps

Strong, tunable long-range qubit coupling via virtual phonons

Viable phononic crystal geometries for quantum applications

Abstract

We propose qubits based on shallow donor electron spins in germanium. Spin-orbit interaction for donor spins in germanium is in many orders of magnitude stronger than in silicon. In a uniform bulk material it leads to very short spin lifetimes. However the lifetime increases dramatically when the donor is placed into a quasi-2D phononic crystal and the energy of the Zeeman splitting is tuned to lie within a phonon bandgap. In this situation single phonon processes are suppressed by energy conservation. The remaining two-phonon decay channel is very slow. The Zeeman splitting within the gap can be fine tuned to induce a strong, long-range coupling between the spins of remote donors via exchange by virtual phonons. This, in turn, opens a very efficient way to manipulate the quits. We explore various geometries of phononic crystals in order to maximize the coherent qubit-qubit coupling while keeping the decay rate minimal. We find that phononic crystals with unit cell sizes of 100-150 nm are viable candidates for quantum computing applications and suggest several spin-resonance experiments to verify our theoretical predictions.