Engineering coherent systems is a central goal of quantum science. Color centers in diamond are a promising approach, with the potential to combine the coherence of atoms with the scalability of a solid-state platform. We report a color center that shows insensitivity to environmental decoherence caused by phonons and electric field noise: the neutral charge state of silicon vacancy (SiV). Through careful materials engineering, we achieved >80% conversion of implanted silicon to SiV SiV exhibits spin-lattice relaxation times approaching 1 minute and coherence times approaching 1 second. Its optical properties are very favorable, with ~90% of its emission into the zero-phonon line and near-transform-limited optical linewidths. These combined properties make SiV a promising defect for quantum network applications.

Atomic and atom-like defects in the solid-state are widely explored for quantum computers, networks and sensors. Rare earth ions are an attractive class of atomic defects that feature narrow spin and optical transitions that are isolated from the host crystal, allowing incorporation into a wide range of materials. However, the realization of long electronic spin coherence times is hampered by magnetic noise from abundant nuclear spins in the most widely studied host crystals. Here, we demonstrate that Er 3+ ions can be introduced via ion implantation into TiO2, a host crystal that has not been studied extensively for rare earth ions and has a low natural abundance of nuclear spins. We observe efficient incorporation of the implanted Er 3+ into the Ti 4+ site (40% yield), and measure narrow inhomogeneous spin and optical linewidths (20 and 460 MHz, respectively) that are comparable to bulk-doped crystalline hosts for Er 3+ . This work demonstrates that ion implantation is a viable path to studying rare earth ions in new hosts, and is a significant step towards realizing individually addressed rare earth ions with long spin coherence times for quantum technologies. *

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We achieve the strong-coupling regime between an ensemble of phosphorus donor spins in a highly enriched 28 Si crystal and a 3D dielectric resonator. Spins are polarized beyond Boltzmann equilibrium using spin-selective optical excitation of the no-phonon bound exciton transition resulting in N ¼ 3.6 × 10 13 unpaired spins in the ensemble. We observe a normal mode splitting of the spin-ensemble-cavity polariton resonances of 2g ffiffiffiffi N p ¼ 580 kHz (where each spin is coupled with strength g) in a cavity with a quality factor of 75 000 ( γ ≪ κ ≈ 60 kHz, where γ and κ are the spin dephasing and cavity loss rates, respectively). The spin ensemble has a long dephasing time (T Ã 2 ¼ 9 μs) providing a wide window for viewing the dynamics of the coupled spin-ensemble-cavity system. The free-induction decay shows up to a dozen collapses and revivals revealing a coherent exchange of excitations between the superradiant state of the spin ensemble and the cavity at the rate g ffiffiffiffi N p. The ensemble is found to evolve as a single large pseudospin according to the Tavis-Cummings model due to minimal inhomogeneous broadening and uniform spin-cavity coupling. We demonstrate independent control of the total spin and the initial Z projection of the psuedospin using optical excitation and microwave manipulation, respectively. We vary the microwave excitation power to rotate the pseudospin on the Bloch sphere and observe a long delay in the onset of the superradiant emission as the pseudospin approaches full inversion. This delay is accompanied by an abrupt π-phase shift in the peusdospin microwave emission. The scaling of this delay with the initial angle and the sudden phase shift are explained by the Tavis-Cummings model.

Color centers in diamond are a promising platform for quantum technologies, and understanding their interactions with the environment is crucial for these applications. We report a study of spinlattice relaxation (T1) of the neutral charge state of the silicon vacancy center in diamond. Above 20 K, T1 decreases rapidly with a temperature dependence characteristic of an Orbach process, and is strongly anisotropic with respect to magnetic field orientation. As the angle of the magnetic field is rotated relative to the symmetry axis of the defect, T1 is reduced by over three orders of magnitude. The electron spin coherence time (T2) follows the same temperature dependence but is drastically shorter than T1. We propose that these observations result from phonon-mediated transitions to a low lying excited state that are spin conserving when the magnetic field is aligned with the defect axis, and we discuss likely candidates for this excited state.

Coherence times of electron spins bound to phosphorus donors have been measured, using a standard Hahn echo technique, to be up to 20 ms in isotopically pure silicon with [P] = 10 14 cm −3 and at temperatures ≤ 4 K. Although such times are exceptionally long for electron spins in the solid state, they are nevertheless limited by donor electron spin-spin interactions. Suppressing such interactions requires even lower donor concentrations, which lie below the detection limit for typical ESR spectrometers. Here we describe an alternative method for phosphorus donor ESR detection, exploiting the spin-to-charge conversion provided by the optical donor-bound-exciton transition. We characterize the method and its dependence on laser power and use it to measure a coherence time of T 2 = 130 ms for one of the purest silicon samples grown to date ([P] = 5 × 10 11 cm −3 ). We then benchmark this result using an alternative application of the donor-bound-exciton transition: optically polarizing the donor spins before using conventional ESR detection at 1.7 K for a sample with [P] = 4 × 10 12 cm −3 , and measuring in this case a T 2 of 350 ms. In both cases, T 2 is obtained after accounting for the effects of magnetic field noise, and the use of more stable (e.g., permanent) magnets could yield even longer coherence times.

Over the past decade donor spin qubits in isotopically enriched 28 Si have been intensely studied due to their exceptionally long coherence times. More recently bismuth donor electron spins have become popular because Bi has a large nuclear spin which gives rise to clock transitions (first-order insensitive to magnetic field noise). At every clock transition there are two nearly degenerate transitions between four distinct states which can be used as a pair of qubits. Here it is experimentally demonstrated that these transitions are excited by microwaves of opposite helicity such that they can be selectively driven by varying microwave polarization. This work uses a combination of a superconducting coplanar waveguide (CPW) microresonator and a dielectric resonator to flexibly generate arbitrary elliptical polarizations while retaining the high sensitivity of the CPW.Donors spins in Si are among the most promising quantum bits owing to their long coherence times (T 2 ) which exceed seconds in isotopically enriched 28 Si 1-4 . Bismuth donor electrons are particularly attractive because they have clock transitions which are first order insensitive to magnetic field noise [5][6][7][8][9] . This means that even in natural Si, electron spins can have long coherence times 5 . In Bi doped Si clock transitions come in pairs of nearly degenerate transitions separated by ∼1 MHz. These are predicted to be excited by microwaves of opposite circular polarization 7,10 . In this work we combine a coplanar waveguide microresonator (CPW) with a dielectric resonator to generate microwaves with tunable polarization. By varying this polarization, we demonstrate the selective addressability of the 7.03 GHz clock transitions. This will be important for hybrid donor-dot quantum computing schemes since the 5 GHz clock transition was recently predicted to form an avoided crossing with silicon based quantum dots 10 . This was discussed in the donor-dot surface code proposal by Pica et al 10 which also suggested addressing the clock transitions using microwave polarization.Bismuth donors in Si have a large hyperfine coupling which not only gives rise to a large zero field splitting, but also allows for rapid manipulation of both the electronic and nuclear spin states when operating in the intermediate field regime where the hyperfine coupling is comparable to the Zeeman splitting 8,[11][12][13] . In this regime we describe the states using the total spin, F , and its projection, m F 6 . The total spin is given by F = I ± S where I is the nuclear spin and S is the electron spin. At the 7.03 GHz clock transition the two nearly degenerate transitions are described in the |F, m F basis by |5, −1 ⇔ |4, −2 and |5, −2 ⇔ |4, −1 . In the high field limit the second transition is forbidden since it involves a nuclear spin flip, but due to strong mixing, both transitions are accessible near the clock transition. By convention we will still refer to the |5, −1 ⇔ |4, −2 transition as allowed and the |5, −2 ⇔ |4, −1 transition as forbidden. These transi...

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