Quantum control of donor electrons for Si-based quantum computing

Quantum control of donor electrons at the Si-SiO₂ interface
M.J. Calderón, Belita Koiller, Xuedong Hu and S. Das Sarma, Phys. Rev. Lett. 96, 096802 (2006). cond-mat/0508647.

Prospects for the quantum control of electrons in the silicon quantum computer architecture are considered theoretically. In particular, we investigate the feasibility of shuttling donor-bound electrons between the impurity in the bulk and the Si-SiO₂ interface by tuning an external electric field. We calculate the shuttling time to range from sub-picoseconds to nanoseconds depending on the distance (~ 10-50 nm) of the donor from the interface. Our results establish that quantum control in such nanostructure architectures should be achievable.

Magnetic field-assisted manipulation and entanglement of Si spin qubits .
M.J. Calderón, Belita Koiller, and S. Das Sarma, Phys. Rev. B 74, 081302(R) (2006). cond-mat/0602597.

Architectures of donor-electron based qubits in silicon near an oxide interface are considered theoretically. We find that the precondition for reliable logic and read-out operations, namely the individual identification of each donor-bound electron near the interface, may be accomplished by fine-tuning electric and magnetic fields, both applied perpendicularly to the interface. We argue that such magnetic fields may also be valuable in controlling two-qubit entanglement via donor electron pairs near the interface.

External field control of donor electron exchange at the Si/SiO₂ interface .
M.J. Calderón, Belita Koiller, and S. Das Sarma, Phys. Rev. B 75, 125311 (2007). cond-mat/0612093 .

We analyze several important issues for the single- and two-qubit operations in Si quantum computer architectures involving P donors close to a SiO₂ interface. For a single donor, we investigate the donor-bound electron manipulation (i.e. 1-qubit operation) between the donor and the interface by electric and magnetic fields. We establish conditions to keep a donor-bound state at the interface in the absence of local surface gates, and estimate the maximum planar density of donors allowed to avoid the formation of a 2-dimensional electron gas at the interface. We also calculate the times involved in single electron shuttling between the donor and the interface. For a donor pair, we find that under certain conditions the exchange coupling (i.e. 2-qubit operation) between the respective electron pair at the interface may be of the same order of magnitude as the coupling in GaAs-based two-electron double quantum dots where coherent spin manipulation and control has been recently demonstrated (for example for donors ~10 nm below the interface and ~40 nm apart, J~10^-4 meV), opening the perspective for similar experiments to be performed in Si.

donors

Proposal for electron spin relaxation measurement using double-donor excited states in Si quantum computer architectures .
M.J. Calderón, Belita Koiller, and S. Das Sarma, Phys. Rev. B 75, 161304(R) (2007). cond-mat/0610089 .

The possibility of performing single spin measurements in Si-based quantum computers through electric field control of electrons bound to double donors near a barrier interface is assessed. We find that both the required electric fields and the tunneling times involved are probably too large for practical implementations. On the other hand, operations with double donors in their first excited state require smaller fields and faster tunneling times, and are therefore suitable for spin-to-charge conversion measurements. We also propose a measurement scheme that would render statistical (ensemble) estimates of the spin coherence at the Si/SiO₂ interface.

Valley interference effects on a donor electron close to a Si/SiO₂ interface.
M.J. Calderón, B. Koiller, and S. Das Sarma. Phys. Rev. B 77, 155302 (2008). arXiv:0712.1823.

We analyze the effects of valley interference on the quantum control and manipulation of an electron bound to a donor close to a Si/SiO₂ interface as a function of the valley-orbit coupling at the interface. We find that, for finite valley-orbit coupling, the tunneling times involved in shuttling the electron between the donor and the interface oscillate with the interface/donor distance in much the same way as the exchange coupling oscillates with the interdonor distance. These oscillations disappear when the ground state at the interface is degenerate (corresponding to zero valley-orbit coupling).

Physical mechanisms of interface-mediated intervalley coupling in Si.
A.L. Saraiva, M.J. Calderón, X. Hu, S. Das Sarma, and B. Koiller. Phys. Rev. B 80, 081305 (2009). arXiv:0901.4702.

The conduction band degeneracy in Si (valley-degeneracy) is known to be detrimental for quantum computing, for which nondegenerate ground and first excited states are required. This degeneracy is lifted at an interface with an insulator. We present an effective mass study of the interface induced valley splitting in Si that provides simple criteria for optimal fabrication related conditions to maximize this splitting. Our work emphasizes the specific role played by the interface width in the quantitative determination of the valley splitting.

Heterointerface effects on the charging energy of shallow D- ground state in silicon: the role of dielectric mismatch.
M.J. Calderón, J. Verduijn, G.P. Lansbergen, G.C. Tettamanzi, S. Rogge, B. Koiller. Phys. Rev. B 82, 075317 (2010). arXiv:1005.1237

Donor states in Si nanodevices can be strongly modified by nearby insulating barriers and metallic gates. Experimental results indicate a strong reduction in the charging energy of isolated As dopants in Si nonplanar field effect transistors relative to the bulk value. By studying the problem of two electrons bound to a shallow donor within the effective mass approach, we find that the measured reduction in the charging energy (measurements also presented here) may be due to a combined effect of the insulator screening and the proximity of metallic gates.

Intervalley Coupling for Silicon Electronic Spin Qubits: Insights from an Effective Mass Study.
A.L. Saraiva, M.J. Calderón, X. Hu, S. Das Sarma, and B. Koiller. arXiv:1006.3338

Orbital degeneracy of the electronic conduction band edge in silicon is a potential source of problems for the storage and manipulation of quantum information involving the electronic spin degree of freedom in this host material. This difficulty may be mitigated near an interface between Si and some barrier material, where intervalley scattering may couple states in the conduction ground state, leading to non-degenerate orbital ground and first excited states. The level splitting is experimentally found to have a strong sample dependence, varying by orders of magnitude for different interfaces and samples. The basic physical mechanisms leading to such coupling in different systems are addressed here. We expand here our recent study based on an effective mass approach, bringing new insights from a simple Si/barrier model. In particular, we present a clear comparison between ours and different approximations and formalisms adopted in the literature, and establish the applicability of these approximations in different physical scenarios.

Heitler-London calculations of exchange in semiconductor nanostructures

Exchange coupling in semiconductor nanostructures: Validity and limitations of the Heitler-London approach .
M.J. Calderón, Belita Koiller, and S. Das Sarma, Phys. Rev. B 74, 045310 (2006). cond-mat/0512321.

The exchange coupling of the spins of two electrons in double well potentials in a semiconductor background is calculated within the Heitler-London (HL) approximation. Atomic and quantum dot types of confining potentials are considered, and a systematic analysis for the source of inaccuracies in the HL approach is presented. For the strongly confining coulombic atomic potentials in the H₂ molecule, the most dramatic failure occurs at very large interatomic distances, where HL predicts a triplet ground state, both in 3D and in 2D, coming from the absence of electron-electron correlation effects in this approach. For a 2D double well potential, failures are identified at relatively smaller interdot distances, and may be attributed to the less confining nature of the potential, leading to larger overlap and consequently an inadequate representation of the two-particle states written, within HL, in terms of the ground state orbital at each isolated well. We find that in the double dot case, the range of validity of HL is improved (restricted) in a related 3D (1D) model, and that results always tend to become more reliable as the interdot distance increases. Our calculated exchange coupling is of relevance to the exchange gate quantum computer architectures in semiconductors.

Reliability of the Heitler-London approach for the exchange coupling between electrons in semiconductor nanostructures .
A.L. Saraiva, M.J. Calderón, and Belita Koiller. Phys. Rev. B 76, 233302 (2007). arXiv:0706.3354.

We calculate the exchange coupling J between electrons in a double-well potential in a two-dimensional semiconductor environment within the Heitler-London approach. The adopted single-well potential may model a gated quantum dot or the potential created by an out-of-plane donor in a two-dimensional system. We show that, by choosing an appropriate and relatively simple single-electron variational wave function, it is possible to significantly improve the HL estimates for J. The present scheme overcomes previously reported HL limitations at short interdot distances, where unphysical triplet ground states have been found, and leads to good agreement with analytic interpolated expressions for J obtained for the same form of the potential.