Exchange in multi-defect semiconductor clusters: assessment of `control-qubit' architectures

TL;DR

This paper develops a variational method to analyze exchange interactions in multi-defect semiconductor clusters, crucial for quantum control architectures, revealing how control states influence the magnitude and sign of exchange couplings.

Contribution

It introduces a novel variational approach combining effective-mass and quantum defect methods to calculate exchange interactions in complex donor clusters with delocalized control electrons.

Findings

Exchange interactions can be switched on and off by the control state.

Both the magnitude and sign of exchange interactions are affected by the control state.

Excitation of the control electron narrows the distribution of coupling strengths and can change the coupling from anti-ferromagnetic to ferromagnetic.

Abstract

We present a variational method to calculate the exchange interactions among donor clusters in a semiconductor. Such clusters are candidates for a so-called control-qubit architecture for quantum information, where the effective exchange coupling between two atoms is controlled by the electronic state of a third. We use a combination of the effective-mass approximation and the quantum defect method; our variational ansatz is particularly suited to cases where an excited state of one of the donors (control) is partially delocalised over several different centres, forming an analogue of an extended molecular orbital. Our method allows calculations of the "on/off" ratios of exchange interactions in such cases. We compare exchange interactions when the control is in the "on" and "off" states, and find that both the magnitude and sign of the exchange interactions may be changed. To rationalize the sign-change, we carry out a simple Green's function perturbation-theory calculation. This simple model qualitatively explains the sign change and illustrates its origins both in ring-exchange processes and in the delocalization of the control electron. We also compute probability distributions for the coupling strengths over the ensemble of clusters, and show that excitation of the control causes narrowing of the distributions along with shifts to larger magnitudes and from anti-ferromagnetic to ferromagnetic coupling.