Impact of measurement backaction on nuclear spin qubits in silicon

S. Monir, E. N. Osika, S. K. Gorman, I. Thorvaldson, Y.-L. Hsueh, P. Macha, L. Kranz, J. Reiner, M. Y. Simmons, and R. Rahman

Phys. Rev. B 109, 035157 – Published 25 January 2024

Abstract

Phosphorus donor nuclear spins in silicon couple weakly to the environment, making them promising candidates for high-fidelity qubits. The state of a donor nuclear spin qubit can be manipulated and read out using its hyperfine interaction with the electron confined by the donor potential. Here we use a master-equation-based approach to investigate how the backaction from this electron-mediated measurement affects the lifetimes of single and multidonor qubits. We analyze this process as a function of electric and magnetic fields and hyperfine interaction strength. Apart from single nuclear spin flips, we identify an additional measurement-related mechanism, the nuclear spin flip-flop, which is specific to multidonor qubits. Although this flip-flop mechanism reduces qubit lifetimes, we show that it can be effectively suppressed by the hyperfine Stark shift. We show that using atomic precision donor placement and engineered Stark shift, we can minimize the measurement backaction in multidonor qubits, achieving larger nuclear spin lifetimes than single donor qubits.

Received 1 August 2023
Accepted 20 December 2023

DOI:https://doi.org/10.1103/PhysRevB.109.035157

Physics Subject Headings (PhySH)

Fine & hyperfine structure Spin dynamics

Quantum dots Semiconductors

Master equation

Condensed Matter, Materials & Applied PhysicsAtomic, Molecular & OpticalQuantum Information, Science & Technology

Authors & Affiliations

S. Monir ^1,2,*, E. N. Osika ^1,2, S. K. Gorman ^2,3, I. Thorvaldson ^2,3, Y.-L. Hsueh ^1,2, P. Macha ^2,3, L. Kranz^2,3, J. Reiner ^2,3, M. Y. Simmons ^2,3, and R. Rahman ^1,2

¹School of Physics, The University of New South Wales, Sydney, NSW 2052, Australia
²Silicon Quantum Computing Pty Ltd., Level 2, Newton Building, UNSW Sydney, Kensington, NSW 2052, Australia
³Centre for Quantum Computation and Communication Technology, School of Physics, University of New South Wales, Sydney, NSW 2052, Australia

^*mdserajum.monir@unsw.edu.au

Article Text (Subscription Required)

Click to Expand

Supplemental Material (Subscription Required)

Click to Expand

References (Subscription Required)

Click to Expand

Issue

Vol. 109, Iss. 3 — 15 January 2024

Reuse & Permissions

Access Options

Article part of CHORUS

Accepted manuscript will be available starting 24 January 2025.

Author publication services for translation and copyediting assistance advertisement

Images

Figure 1
Schematic of the multidonor qubit and spin readout sensor. (a) P donors can be precision placed with $\pm 0.385$ nm accuracy in Si crystal and surrounded by in-plane P-doped gate electrodes ( $G_{L}, G_{M}$ , and $G_{R}$ ), source (S), drain (D), and SET charge sensor by STM lithography [17]. The donor potential traps electrons which can tunnel to and from the SET under appropriate in-plane gate biases. (b) Effect of measurement by an SET sensor on the donor nuclear spin states. The electron nonadiabatically tunneling from the donor to the SET leaves the nuclear spins no longer in their eigenstate, resulting in a finite probability of a nuclear spin flip.
Reuse & Permissions
Figure 2
Nuclear spin flip probability in P donor qubits due to the readout pulse. (a) Electron tunneling in a 1P1e qubit during the readout pulse. Labels $| e_{1} 〉 - | e_{4} 〉$ represent eigenstates of the 1P1e system. Arrows show the nuclear-electron states forming the eigenstates, with the smaller arrows (i.e ., $⇓ ↑$ in $| e_{1} 〉$ and $⇑ ↓$ in $| e_{3} 〉$ ) representing typically very small admixtures of nuclear-electron spin configurations introduced by the hyperfine interaction. (b) Dependence of the nuclear spin flip probability on the total hyperfine interaction A of 1P1e (left panel), 2P1e (middle), and 3P1e (right) qubits at a magnetic field of 1.4 T. For each of these three cases, only the hyperfine constant of one donor ( $A_{1}$ ) is varied. The other hyperfines are fixed at $A_{2} = 50 MHz$ and $A_{3} = 20 MHz$ . (c) Dependence of the nuclear spin flip probability on the magnetic field B for 1P1e (left panel), 2P1e (middle), and 3P1e (right) qubits. The hyperfines are fixed at $A_{1} = 100 MHz, A_{2} = 50 MHz$ , and $A_{3} = 50 MHz$ . For (b)–(g), the dotted lines represent the analytical form of Eq. (8).
Reuse & Permissions
Figure 3
Nuclear spin flip-flop probabilities in multidonor dots due to the readout pulse. (a) Variation of nuclear spin flip-flop probability with $A_{1} - A_{2}$ in a 2P1e qubit for total hyperfine values of $100, 200$ and $300 MHz$ . The dotted lines represent the formula in Eq. (8). (b) Comparison between nuclear spin flip ( $⇑ ⇓ \to ⇓ ⇓$ ) and flip-flop ( $⇑ ⇓ \to ⇓ ⇑$ ) transition probabilities for a 2P1e qubit with total hyperfine $A_{total} = 117 MHz$ as a function of $A_{1} - A_{2}$ . The orange and cyan dotted lines represent formulas of Eqs. (8) and (12), respectively. The shaded region represents the Stark shift values for which the total transition probability of the first nuclear spin (flip+flip-flop) is less than the transition probability of a 1P1e qubit. The transition probability of second nuclear spin is even smaller in this region since it has a smaller hyperfine constant than the first nuclear spin. Therefore, in this region the 2P1e qubit can experience less effects from measurement backaction than a 1P1e qubit.
Reuse & Permissions

Physical Review B

covering condensed matter and materials physics