The representation of information within the spins of electrons and nuclei has been powerful in the ongoing development of quantum computers 1, 2 . Although nuclear spins are advantageous as quantum bits (qubits) due to their long coherence lifetimes (exceeding seconds 3, 4 ), they exhibit very slow spin interactions and have weak polarisation. A coupled electron spin can be used to polarise the nuclear spin 5-7 and create fast single-qubit gates 8, 9 , however, the permanent presence of electron spins is a source of nuclear decoherence. Here we show how a transient electron spin, arising from the optically excited triplet state of C60, can be used to hyperpolarise, manipulate and measure two nearby nuclear spins. Implementing a scheme which uses the spinor nature of the electron 10 , we performed an entangling gate in hundreds of nanoseconds: five orders of magnitude faster than the liquid-state J coupling. This approach can be widely applied to systems comprising an electron spin coupled to multiple nuclear spins, such as NV centres 11 , while the successful use of a transient electron spin motivates the design of new molecules able to exploit photo-excited triplet states.

Molecular nanostructures may constitute the fabric of future quantum technologies, if their degrees of freedom can be fully harnessed. Ideally one might use nuclear spins as low-decoherence qubits and optical excitations for fast controllable interactions. Here, we present a method for entangling two nuclear spins through their mutual coupling to a transient optically excited electron spin, and investigate its feasibility through density-functional theory and experiments on a test molecule. From our calculations we identify the specific molecular properties that permit high entangling power gates under simple optical and microwave pulses; synthesis of such molecules is possible with established techniques. DOI: 10.1103/PhysRevLett.104.200501 PACS numbers: 03.67.Bg, 03.67.Lx, 31.15.EÀ, 33.40.+f Molecules are promising building blocks for quantum technologies, due to their reproducible nature and ability to self-assemble into complex structures. However, the need to control interactions between adjacent qubits represents a key challenge [1][2][3][4]. We here describe a method for optical control of a nuclear spin-spin interaction that presents several advantages over conventional NMR quantum processors: the spin-spin interaction can be switched, the gates are faster, and the larger energy transitions facilitate polarization transfer onto the nuclear spins. After explaining the theory behind our method, we present an experimental study of a test molecule, and show with density-functional theory that an entangling gate could be achieved.We consider two nuclear spin qubits labeled n and n 0 and one mediator e. The mediator possesses a paramagnetic excited state jei with spin one character and a diamagnetic, spinless ground state j0i. The two nuclear qubits do not interact with each other directly, but both couple to the excitation via an isotropic hyperfine (HF) coupling with generally unequal strengths A and A 0 , see Fig. 1(a). The Hamiltonian in a magnetic field is given by (@ ¼ 1):where S z;i and S i are the Pauli spin operators and ! i denotes the respective Zeeman splittings (i ¼ n, n 0 , e). D is the zero-field-splitting (ZFS). ! 0 denotes the optical frequency corresponding to the creation energy of the excitation. Let us first analyze the case of a symmetric (homonuclear) system with ! n ¼ ! n 0 and A ¼ A 0 . Using degenerate perturbation theory and assuming that the electronic Zeeman splitting is much larger than that of the nuclei, ! n ( ! e and the ZFS, D ( ! e , we obtain an effective Hamiltonian by approximating H sym : ¼ hejHjei; thus,where V ¼ ðjc 1 ijc 2 i Á Á Á jc 12 iÞ is the matrix of the approximate eigenvectors up to first order and the E i (i ¼ 1; . . . ; 12) are the eigenenergies up to second order. This reveals that the time evolution of the entire system can be

Pulsed electron paramagnetic resonance spectroscopy of the photoexcited, metastable triplet state of the oxygen-vacancy center in silicon reveals that the lifetime of the ms=±1 sub-levels differ significantly from that of the ms=0 state. We exploit this significant difference in decay rates to the ground singlet state to achieve nearly ∼100% electron spin polarization within the triplet. We further demonstrate the transfer of a coherent state of the triplet electron spin to, and from, a hyperfine-coupled, nearest-neighbor 29 Si nuclear spin. We measure the coherence time of the 29 Si nuclear spin employed in this operation and find it to be unaffected by the presence of the triplet electron spin and equal to the bulk value measured by nuclear magnetic resonance.PACS numbers: 71.55.Cn, 76.70.Dx, 03.67.Lx Nuclear spins in solids are promising candidates for quantum bits (qubits) as their weak coupling to the environment often leads to very long spin coherence times [1][2][3][4]. However, performing fast manipulation and controlling interaction between nuclear spin qubits is often more challenging than in other, more engineered, quantum systems [5][6][7]. The use of an optically driven mediator spin has been suggested as a way to control coupling between donor electron spins in silicon: the donor spins exhibit weak direct coupling, but mutually couple through the optically excited state of the mediator [8]. Such ideas could similarly be applied to couple nuclear spins, and, if the mediator spin is a photo-excited triplet with a spinzero single ground state, it would have the added advantage that it avoids long-term impact on the nuclear spin coherence [9][10][11].Photoexcited triplets are optically-generated electron spins (S = 1) which often exhibit large (positive or negative) spin polarization, thanks to preferential population of each of the triplet sub-levels following intersystem crossing and/or the differing decay rates of these sublevels to the ground singlet state [12,13]. Nuclear spins, in contrast, have weak thermal spin polarization at experimentally accessible conditions, due to its small magnetic moment. Highly polarized electron spin triplets can be used to polarize surrounding nuclear spins, through continuous wave microwave illumination (under processes termed dynamic nuclear polarization) [14,15], or using microwave pulses [16]. Triplet states can also be used to mediate entanglement between mutually-coupled nuclear spins [9], on timescales much faster than their intrinsic dipolar coupling [17].Oxygen-vacancy (O-V ) complexes can be formed in silicon by electron beam or γ-ray irradiation of oxygen-rich silicon crystals [18,19], and can be excited to the triplet state (termed an SL1 center,) using illumination of above band gap light [20]. Magnetic resonance studies including electron paramagnetic resonance (EPR), electrically or optically detected magnetic resonance, spin dependent recombination and electrically-detected cross relaxation [20][21][22][23][24][25] have revealed that the SL1 has ...

The study of hyperfine interactions in optically excited fullerenes has recently acquired importance within the context of nuclear spin entanglement for quantum information technology. We here report a first-principles pseudopotential study of the hyperfine coupling parameters of optically excited fullerene derivatives as well as small organic radicals. The calculations are performed within the gauge-invariant projector-augmented wave method [C. Pickard and F. Mauri, Phys. Rev. B. 63, 245101 (2001)]. In order to establish the accuracy of this methodology we compare our results with all-electron calculations and with experiment. In the case of fullerene derivatives we study the hyperfine coupling in the spin-triplet exciton state and compare our calculations with recent electron paramagnetic resonance measurements [M. Schaffry et al., Phys. Rev. Lett. 104, 200501 (2010)]. We discuss our results in light of a recent proposal for entangling remote nuclear spins in photo-excited chromophores.

We report on a pulsed electron paramagnetic resonance (EPR) study of the photoexcited triplet state (S = 1) of oxygen-vacancy centers in silicon. Rabi oscillations between the triplet sublevels are observed using coherent manipulation with a resonant microwave pulse. The Hahn echo and stimulated echo decay profiles are superimposed with strong modulations known as electron-spin-echo envelope modulation (ESEEM). The ESEEM spectra reveal a weak but anisotropic hyperfine coupling between the triplet electron spin and a 29 Si nuclear spin (I = 1/2) residing at a nearby lattice site, that cannot be resolved in conventional field-swept EPR spectra.