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

Abstract

We study single-and multi-quantum transitions of the nuclear spins of ionized arsenic donors in silicon and find quadrupolar effects on the coherence times, which we link to fluctuating electrical field gradients present after the application of light and bias voltage pulses. To determine the coherence times of superpositions of all orders in the 4-dimensional Hilbert space, we use a phasecycling technique and find that, when electrical effects were allowed to decay, these times scale as expected for a field-like decoherence mechanism such as the interaction with surrounding 29 Si nuclear spins.Aiming for the realization of a scalable quantum technology, the electron and nuclear spins of phosphorus donors in silicon have been studied extensively [1][2][3][4][5][6][7][8]. 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]. In addition, one higher order system can replace several qubits, simplifying their physical implementation [22]. 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. By including light and voltage pulses in the experiment, we are able to link the additional quadrupolar decoherence effect to the electrical environment of the nucleus and show that it vanishes, when the sample is allowed to relax electrically. In addition, we use a phase cycling technique to study superpositions of all orders and find that the coherence times scale inversely proportional to the coherence order, as expected for a field-like decoherence mechanism such as the interaction with surrounding 29 Si nuclear spins. The Hamiltonian H characterizing ionized arsenic donors with nuclear spin I = {I x , I y , I z } in a magnetic field B z can be written as where ν 0 = γ n B z with the nuclear gyromagnetic ratio γ n and h is Planck's constant. The second term on the right hand side of (1) describes the nuclear quadrupole interaction with an effective electric field gradient V 33 , here approximated to first order [26], withwhere Q is the nuclear quadrupole moment, e is the elementary charge, and ϑ describes the angle between B z and...

Coherent electrical control of a single high-spin nucleus in silicon

“…Both values, while extremely long in absolute terms, are noticeably shorter than the T * 2n+ ≈ 250 − 600 ms measured on the 31 P nucleus in two other similar devices [16], fabricated on the same 28 Si wafer. Since the 31 P nucleus has zero quadrupole moment, this suggests that the 123 Sb coherence may be affected by electrical noise [23], in a way that the 31 P is not. Therefore, the 123 Sb nucleus could become a useful tool for spectroscopy of very slow electrical noise.…”

Navigating the 16-dimensional Hilbert space of a high-spin donor qudit with electric and magnetic fields

“…This is intuitively expected because the Ramsey experiment probes the free evolution of the spin, in the absence of drives. However, this result indicates that the application of strong AC electric fields needed to drive NER does not destabilise the electrical environment of the nucleus in a noticeable way 46 .…”

Atomic-Scale Patterning of Arsenic in Silicon by Scanning Tunneling Microscopy

“…20,21,22 Arsenic donors in silicon are particularly interesting, since they have a lower diffusivity and a higher solid solubility in bulk silicon than phosphorus, 23 as well as a higher ionization energy in silicon (53.76 meV, compared to 45.59 meV for phosphorus), 24 a larger atomic radius (rAs =115 pm, rP = 100 pm), 25 larger atomic spin-orbit interaction (ZAs = 33, ZP = 15), and a higher nuclear spin value (IAs = 3/2, IP = ½) than phosphorus. These differing properties present opportunities for atomic-scale device designs with advanced functionality, such as nuclear spin qudits (where a qudit is a generalized quantum information object with n > 2 quantum states), 26,27 and silicon photonic crystal cavity based quantum computation schemes. 28 Furthermore, the ability to position multiple dopant species in silicon with atomic-scale precision would allow independent addressing of each donor species, and will enable new principles of device operation, such as implementations of quantum error correction codes, 29 and optically driven silicon-based quantum gates.…”

“…Arsenic donors in silicon are particularly interesting, since they have a lower diffusivity and a higher solid solubility in bulk silicon than phosphorus, as well as a higher ionization energy in silicon (53.76 meV, compared to 45.59 meV for phosphorus), a larger atomic radius ( r As = 115 pm, r P = 100 pm), larger atomic spin–orbit interaction ( Z As = 33, Z P = 15), and a higher nuclear spin value ( I As = 3/2, I P = 1/2) than phosphorus. These differing properties present opportunities for atomic-scale device designs with advanced functionality, including quantum computation schemes based on silicon photonic crystal cavities, which would exploit the larger spin–orbit interaction of arsenic, and schemes employing qudits (generalized d -dimensional quantum information units) where the 4-state Zeeman splitting of the arsenic 3/2 nuclear spin could be utilized as a d = 4 qudit. , In this latter case, while arsenic nuclear spins can in principle also be operated as 2-state qubits with some added complexities, accessing the higher dimensionality provided by the 3/2 spin could offer advantages over qubit based quantum computation, including simplifications in physical implementations of quantum gate structures, and greater efficiency and breadth of quantum simulations . Furthermore, the ability to position multiple dopant species in silicon with atomic-scale precision should allow independent addressing of each donor species by exploiting the different orbital excitation energies, and could thus enable principles of device operation such as optically driven silicon-based quantum gates .…”