Novel control of the Schrödinger cat state in high-spin nuclei in silicon

We present the experimental demonstration of a quantum control scheme to leverage the full Hilbert space of high-spin (I=7/2) ¹²³Sb donor nucleus implanted in silicon. The scheme is based on defining a generalized rotating frame [1] consisting of 7 “clocks”, each corresponding to one of the NMR frequencies of the ¹²³Sb nucleus. We can implement SU(8) operation by driving individual transitions, or “global” SU(2) rotations by driving all 7 NMR frequencies at the same time, and virtual phase gates by shifting the relative phase of the clocks in software. This method enables the efficient initialization and manipulation of spin qudit states of interest, including spin coherent states, Schrödinger cat states [2], and logic-encoded qubit states [3]. It also allows to reconstruct the Husimi-Q distribution and the Wigner functions, to verify the generation of interesting nonclassical spin states. We measured the decoherence time for Schrödinger cat states along different axes and of varying sizes, with potential applications in quantum sensing. This powerful qudit platform will enable interesting new experiment in quantum information processing, quantum metrology, and foundations of quantum mechanics.

[1] M. Leuenberger and D. Loss, Phys. Rev. B 68, 165317 (2003)

[2] P. Gupta et al., arXiv:2304.13813

[3] J.A. Gross, Phys. Rev. Lett. 127(1), 010504 (2021)