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...

There is a growing interest in bismuth-doped silicon (Si:Bi) as an alternative to the well-studied proposals for silicon-based quantum information processing (QIP) using phosphorus-doped silicon (Si:P). We focus here on the implications of its anomalously strong hyperfine coupling. In particular, we analyze in detail the regime where recent pulsed magnetic resonance experiments have demonstrated the potential for orders of magnitude speedup in quantum gates by exploiting transitions that are electron paramagnetic resonance (EPR) forbidden at high fields. We also present calculations using a phenomenological Markovian master equation, which models the decoherence of the electron spin due to Gaussian temporal magnetic field perturbations. The model quantifies the advantages of certain "optimal working points" identified as the df /dB = 0 regions, where f is the transition frequency, which come in the form of frequency minima and maxima. We show that at such regions, dephasing due to the interaction of the electron spin with a fluctuating magnetic field in the z direction (usually adiabatic) is completely removed.

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Pulsed magnetic resonance allows the quantum state of electronic and nuclear spins to be controlled on the timescale of nanoseconds and microseconds respectively. The time required to flip dilute spins is orders of magnitude shorter than their coherence times, leading to several schemes for quantum information processing with spin qubits. Instead, we investigate 'hybrid nuclear-electronic' qubits consisting of near 50:50 superpositions of the electronic and nuclear spin states. Using bismuth-doped silicon, we demonstrate quantum control over these states in 32 ns, which is orders of magnitude faster than previous experiments using pure nuclear states. The coherence times of up to 4 ms are five orders of magnitude longer than the manipulation times, and are limited only by naturally occurring (29)Si nuclear spin impurities. We find a quantitative agreement between our experiments and an analytical theory for the resonance positions, as well as their relative intensities and Rabi oscillation frequencies. These results bring spins in a solid material a step closer to research on ion-trap qubits.