Interaction of Strain and Nuclear Spins in Silicon: Quadrupolar Effects on Ionized Donors

Abstract

The nuclear spins of ionized donors in silicon have become an interesting quantum resource due to their very long coherence times. Their perfect isolation, however, comes at a price, since the absence of the donor electron makes the nuclear spin difficult to control. We demonstrate that the quadrupolar interaction allows us to effectively tune the nuclear magnetic resonance of ionized arsenic donors in silicon via strain and determine the two nonzero elements of the S tensor linking strain and electric field gradients in this material to S(11)=1.5×10(22) V/m2 and S(44)=6×10(22) V/m2. We find a stronger benefit of dynamical decoupling on the coherence properties of transitions subject to first-order quadrupole shifts than on those subject to only second-order shifts and discuss applications of quadrupole physics including mechanical driving of magnetic resonance, cooling of mechanical resonators, and strain-mediated spin coupling.

Optical Dependence of Electrically Detected Magnetic Resonance in Lightly Doped Si:P Devices

“…Isolated semiconductor dopants and defects offer long coherence times, robust and accurate quantum control and can be integrated into realistic device geometries. Some of the more intensively studied systems are nitrogen-and silicon-vacancy centers in diamond [1][2][3], various defects in silicon carbide [4,5], as well as group V donors in silicon such as phosphorus [6][7][8], arsenic [9] and bismuth [10].…”

Multiple-Quantum Transitions and Charge-Induced Decoherence of Donor Nuclear Spins in Silicon

“…Due to different interaction strengths with their surroundings, they form a powerful combination of a fast, but more volatile electron spin and a slower, but very coherent nuclear spin qubit [9][10][11]. This nuclear spin is I = 1/2 for phosphorus, but systems with a higher nuclear spin can be realized by simply replacing phosphorus by the other hydrogenic donors As (I = 3/2) [12,13], Sb (5/2 and 7/2) [14,15], and Bi (9/2) [16][17][18]. Several advantages of the d-dimensional Hilbert spaces of such systems, sometimes called qudits, have been proposed, such as the realization of simpler and more efficient gates [19,20] or more secure quantum cryptography [21].…”

“…Following NMR literature, we will call coherences of order |p| = 1, 2, and 3 single, double, and triple quantum transitions (SQTs, DQTs, and TQTs), respectively [27]. To characterize them, we will follow two different approaches: First, we will study the SQTs in a strained Si sample, where ν Q is large compared to the linewidth of the resonance signal [13]. In this case, the resonances corresponding to the three SQTs do not overlap (cf.…”

“…These concepts usually require coherent superpositions of higher orders, which show specific interactions with their surroundings that can be reflected in the observed coherence times. In particular, the additional quadrupole interaction with electric field gradients arising from strain [13,23,24] or defect states [25], has to be considered for heavier dopants. In this work, we study first-and higher-order coherences of ionized As donors in silicon.…”

“…The [111]-oriented sample was thinned and cemented to a sapphire substrate, which at low temperatures generates a compressive strain due to the different thermal extension coefficients of the materials [13]. Nuclear spin transitions and echoes are measured by electrically detected electron nuclear double resonance (EN-DOR) which is described in detail in Refs.…”