Decoherence mechanisms of209Bi donor electron spins in isotopically pure28Si

Abstract

Bismuth (209 Bi) is the deepest Group V donor in silicon and possesses the most extreme characteristics such as a 9/2 nuclear spin and a 1.5 GHz hyperfine coupling. These lead to several potential advantages for a Si:Bi donor electron spin qubit compared to the more common phosphorus donor. Previous studies on Si:Bi have been performed using natural silicon where linewidths and electron spin coherence times are limited by the presence of 29 Si impurities. Here we describe electron spin resonance (ESR) and electron nuclear double resonance (ENDOR) studies on 209 Bi in isotopically pure 28 Si. ESR and ENDOR linewidths, transition probabilities and coherence times are understood in terms of the spin Hamiltonian parameters showing a dependence on field and mI of the 209 Bi nuclear spin. We explore various decoherence mechanisms applicable to the donor electron spin, measuring coherence times up to 700 ms at 1.7 K at X-band, comparable with 28 Si:P. The coherence times we measure follow closely the calculated field-sensitivity of the transition frequency, providing a strong motivation to explore 'clock' transitions where coherence lifetimes could be further enhanced.Amongst the first proposals for quantum information processing (QIP) in solid state devices was that by Kane in 1998, using phosphorus (P) dopants in silicon, the first of the group V donors [1]. The choice of the P-dopant in particular can be attributed to its use in classical silicon technology as donors, in addition to the simplicity of the spin system which consists of an electron and nuclear spin 1/2. Si:P has been extensively studied as a potential qubit [2,3] and is more than ever one of the leading candidates in the quest for a solid-state quantum computer [4,5]. It begs the question, however, of whether other donors of the same group, i.e. arsenic (As), antimony (Sb) and bismuth (Bi), could have the same if not better properties than P. As the deepest group V donor, Bi has the largest nuclear spin (9/2) and the largest hyperfine coupling (1.4754 GHz) [6], and has received increasing attention over the past two years [7][8][9][10][11]. A single donor has a 20 dimensional Hilbert space, allowing either more storage space or a more robust encoding of information. The large hyperfine coupling enables shorter nuclear manipulation times and a zero field splitting of 7.3 GHz, making Si:Bi useful as memory for hybrid superconducting circuits [8,12,13]. At low magnetic fields, the spin Hamiltonian provides so-called 'clock' transitions for the electron spin, where the transition frequency between two states is insensitive to first order in magnetic field fluctuations of the environment [14][15][16]. On the other hand, high vapour pressure and low solubility of the donor in silicon complicates the doping process during growth [17], while the high atomic weight (209) increases defect density during ion implantation [11].Previous works [7-10] on bismuth were realized using doped natural silicon crystals where the presence of other silicon isotopes, in partic...

Isotope engineering of silicon and diamond for quantum computing and sensing applications

“…[65,66] The coherence times of the bismuth electron spins were as long as those of the phosphorus atoms. [65] The existence of the optimal magnetic field (atomic clock transition), at which the electron decoherence was suppressed by its insensitivity to the external magnetic field perturbation was demonstrated.…”

“…[65,66] The coherence times of the bismuth electron spins were as long as those of the phosphorus atoms. [65] The existence of the optimal magnetic field (atomic clock transition), at which the electron decoherence was suppressed by its insensitivity to the external magnetic field perturbation was demonstrated. [66] The Keio University group investigated the hyperfine clock transition of bismuth using the magnetic field at which the resonant frequency was insensitive to fluctuations in the hyperfine constant in isotopically enriched 28 Si [67] using the spin-dependent-recombination EPR technique developed especially for this purpose.…”

Quantum-bath-driven decoherence of mixed spin systems

“…A large number of important defects in the solid state possess such mixing, including donors in silicon, [18][19][20] NV centres in diamond, 21 transition metals in II-VI materials 22 and rare-earth dopants in silicates.…”

Classical nature of nuclear spin noise near clock transitions of Bi donors in silicon

“…Therefore, examining the conditions for the validity of a classical Gaussian noise model is not only of fundamental interest but also highly desirable for accurate quantum control under realistic conditions. Bismuth donors in silicon (Si:Bi) have recently attracted much attention in spin-based quantum computation due to a number of favorable properties [18][19][20][21]. These include long electron spin coherence times of up to 3 s [22] observed for Bi donors (in isotopically enriched silicon-28) tuned to so-called clock transitions (CTs)-also known as optimal working points [23] or zero first-order Zeeman transitions)-whose frequency is insensitive, to first order, to magnetic field fluctuations.…”