Bell's inequality violation with spins in silicon

Abstract

Bell's theorem proves the existence of entangled quantum states with no classical counterpart. An experimental violation of Bell's inequality demands simultaneously high fidelities in the preparation, manipulation and measurement of multipartite quantum entangled states, and provides a single-number benchmark for the performance of devices that use such states for quantum computing. We demonstrate a Bell/ Clauser-Horne-Shimony-Holt inequality violation with Bell signals up to 2.70(9), using the electron and the nuclear spins of a single phosphorus atom embedded in a silicon nanoelectronic device. Two-qubit state tomography reveals that our prepared states match the target maximally entangled Bell states with >96% fidelity. These experiments demonstrate complete control of the two-qubit Hilbert space of a phosphorus atom and highlight the important function of the nuclear qubit to expand the computational basis and maximize the readout fidelity.

Radii of Rydberg states of isolated silicon donors

“…Equation (1) has cylindrical symmetry about z so the azimuthal dependence of the wave-function envelope is e imφ , which is an eigenfunction of the LZE term with quantum number m, the magnetic quantum number. For our field direction (B z)Ĥ 1 commutes withĤ 0z andĤ 2 so there are no off-diagonal matrix elements ofĤ 1 , and the magnetic quantum number m is conserved for all B. The LZE energy E 1 = μ * B mB is, therefore, well defined for all B.Ĥ 0z andĤ 2 do not commute, but for sufficiently small field we can treat H 2 by perturbation theory which produces…”

“…Knowledge of the wave-function extent is needed for prediction of the interaction between donors and their neighbors for tests of physics [1][2][3][4], device transport [5] and entanglement/gating [6][7][8][9]. With knowledge of the extent, the atoms may be appropriately placed to optimize these interactions [10,11].…”

Coherent superpositions of three states for phosphorous donors in silicon prepared using THz radiation

“…Similar experiments have been carried out on optical transitions in semiconductors13, but it is known that in free space atoms one is able to gain better control by including many orbital eigenstates in the wavepacket1013. The importance of control over neighbouring qubit interactions in silicon has been shown separately67913, and it is also appreciated that control over interactions is important for the implementation of surface code error quantum correction14151617. A convenient radiation source for coherent studies in the THz spectral region is the free-electron laser.…”

“…There is a long history of incoherent spectroscopy of shallow impurities (P, Bi and so on) in silicon, normally utilizing the Fourier Transform Infrared technique (FTIR) (Si:Bi2; Si:P2; and more recently our own high field (30 T) work4 in Si:P). Si:P can now be positioned and detected with atomic precision5 to make devices that demonstrate control over coherent quantum interactions between neighbouring donors67 and semiclassical interaction with contacts8. Optical control of Rydberg orbits of trapped atoms in vacuum has provided high-fidelity gate interactions9 and fine control over the electron trajectory10, with applications in atomic clocks and quantum computing1112.…”

Delayed entanglement echo for individual control of a large number of nuclear spins

“…As a consequence, our work is expected to find applications as well in traditional fields of NMR and ENDOR, for example, in analysis of chemical shifts. Finally, the method has a general character being equally applicable to other electron-nuclear spin systems4344.…”