Bismuth Qubits in Silicon: The Role of EPR Cancellation Resonances

Abstract

We investigate electron paramagnetic resonance spectra of bismuth-doped silicon, at intermediate magnetic fields B ' 0:1-0:6 T, theoretically and experimentally (with 9.7 GHz X-band spectra). We identify a previously unexplored regime of ''cancellation resonances,'' where a component of the hyperfine coupling is resonant with the external field. We show that this regime has experimentally accessible consequences for quantum information applications, such as reduction of decoherence, fast manipulation of the coupled electron-nuclear qubits, and spectral line narrowing. DOI: 10.1103/PhysRevLett.105.067602 PACS numbers: 76.30.Àv, 03.67.Lx, 71.55.Cn, 76.90.+d Following Kane's suggestion [1] for using phosphorusdoped silicon as a source of qubits for quantum computing, there has been intense interest in such systems [2]. The phosphorus system ( 31 P) is appealing in its simplicity: It represents a simple electron-spin qubit S ¼ 1 2 coupled to a nuclear-spin qubit I ¼ 1 2 via an isotropic hyperfine interaction AI:S of moderate strength ( A 2 ¼ 117:5 MHz). However, recent developments [3-5] point to Si:Bi (bismuth-doped silicon) as a very promising new alternative. Two recent studies measured spin-dephasing times of over 1 ms at 10 K, which is longer than comparable (nonisotopically purified) materials, including Si:P [3,4]. Another group implemented a scheme for rapid (on a time scale of $100 s) and efficient (of order 90%) hyperpolarization of Si:Bi into a single spin state [5].Bismuth has an atypically large hyperfine constant A 2 ¼ 1:4754 GHz and nuclear spin I ¼ 9 2 . This makes its EPR spectra somewhat more complex than for phosphorus, and there is strong mixing of the eigenstates for external field B & 0:6 T. Mixing of Si:P states was studied experimentally in Ref. [6], by means of electrically detected magnetic resonance, but at much lower fields B & 0:02 T. Residual mixing in Si:Bi for B ¼ 2-6 T, where the eigenstates are *99:9% pure uncoupled eigenstates of bothÎ z andŜ z , was also proposed as important for the hyperpolarization mechanism of illuminated Si:Bi [5]. In Ref.[4] it was found that even a $30% reduction in the effective paramagnetic ratio df dB (where f is the transition frequency) leads to a detectable reduction in decoherence rates.Below, we present an analysis of EPR spectra for Si:Bi, testing this against experimental spectra. We identify the points for which df dB ¼ 0, explaining them in a unified manner in terms of a series of EPR ''cancellation resonances''; some are associated with avoided level crossings while others, such as a maximum shown in ENDOR [7] spectra at B % 0:37 T in Ref.[4], are of a quite different origin. These cancellation resonances represent, to the best of our knowledge, an unexplored regime in EPR spectroscopy, arising in systems with exceptionally high A and I. They are somewhat reminiscent of the so-called ''exact cancellation'' regime, widely used in ESEEM spectroscopy [7,8] but differ in essential ways: For instance, they affect both electronic and nuclear freq...

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

“…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. The coherence times of donor electron spins in natural silicon are typically limited to a few hundred microseconds by the 5% naturally abundant 29 Si nuclear spins.…”

Electrical activation and electron spin resonance measurements of implanted bismuth in isotopically enriched silicon-28

“…The small Bohr radius and bismuth's reduced effective gyromagnetic ratio [7] can make it less susceptible to interface noise at a given implant depth and make bismuth very desirable for quantum logic implementation via magnetic dipolar coupling [11]. Furthermore, bismuth is also the heaviest donor in silicon and thus shows the least ion range straggling during ion implantation, which enables for donor qubit placement with high spatial resolution [12,13].To date, studies of spin resonance properties of bismuth in silicon have been performed with bulk doped natural silicon [7,8,[14][15][16] whereas silicon-28 material is preferable for improved spin coherence properties. Electrical activation of implanted bismuth via thermal anneals has been studied for relatively high implant doses [17][18][19][20][21], and concentrations close to the the metalinsulator transition (N c = 1.7 × 10 19 cm −3 ) [18].…”

“…To date, studies of spin resonance properties of bismuth in silicon have been performed with bulk doped natural silicon [7,8,[14][15][16] whereas silicon-28 material is preferable for improved spin coherence properties. Electrical activation of implanted bismuth via thermal anneals has been studied for relatively high implant doses [17][18][19][20][21], and concentrations close to the the metalinsulator transition (N c = 1.7 × 10 19 cm −3 ) [18].…”

Probing a single nuclear spin in a silicon single electron transistor

“…In the q = 1 state, the electron and the nuclear spin are hyperfine coupled. The Hamiltonian that describes both states reads [20][21][22]24 where ǫ d is the donor energy level with respect to the Fermi energy, which we take as E F = 0, and V G denotes an external gate voltage. We assume that valley degeneracies of the donor level are split-off and neglect the valley degree of freedom.…”

“…In the q = 1 state, the electron and the nuclear spin are hyperfine coupled. The Hamiltonian that describes both states reads [20][21][22]24 …”