We study spin relaxation and diffusion in an electron-spin ensemble of nitrogen impurities in diamond at low temperature (0.25-1.2 K) and polarizing magnetic field (80-300 mT). Measurements exploit mode-and temperature-dependent coupling of hyperfine-split sub-ensembles to the resonator. Temperature-independent spin linewidth and relaxation time suggest that spin diffusion limits spin relaxation. Depolarization of one sub-ensemble by resonant pumping of another indicates fast cross-relaxation compared to spin diffusion, with implications on use of sub-ensembles as independent quantum memories.PACS numbers: 42.50.Pq, 03.67.Lx The study of spin ensembles coupled to superconducting integrated circuits is of both technological and fundamental interest. An eventual quantum computer may involve a hybrid architecture [1-4] combining superconducting qubits for processing of information, solid-state spins for storage, and superconducting resonators for interconversion. Additionally, superconducting resonators allow the study of spin ensembles at low temperatures with ultra-low excitation powers and high spectral resolution [5,6]. While one spin couples to one microwave photon with strength g/2π ∼ 10 Hz, an ensemble of N spins collectively couples with g ens = g √ N [7,8], reaching the strong-coupling regime g ens > κ, γ at N 10 12 [8][9][10], where κ and γ are the circuit damping and spin dephasing rates, respectively.Among the solid-state spin ensembles under consideration, nitrogen defects in diamond (P1 centers) [11] are excellent candidates for quantum information processing. Diamond samples can be synthesized with P1 centers as only paramagnetic impurities. Additionally, samples with spin densities ranging from highly dense (> 200 ppm) to very dilute (< 5 ppb) are commercially available, allowing the tailoring of spin linewidth (γ ∝ N [12]) and collective strength (g ens ∝ √ N ). In contrast to nitrogen-vacancy centers in diamond [13] and rare-earth ions in Y 2 SiO 5 [14, 15], P1 centers are optically inactive, making a coupled microwave resonator an ideal probe for their study. However, the magnetic fields 100 mT needed to polarize the ensemble at the few-GHz transition frequencies of circuits [16] must not compromise superconductivity. The freezing of all spin dynamics in a high-purity P1 ensemble by the field would allow quenching spin decoherence [17] through dynamical decoupling [18], realizing a useful quantum memory. * These authors contributed equally to this work.Here, we investigate the dynamics of a P1 electron-spin ensemble probed by controlled coupling to two modes of a coplanar waveguide (CPW) resonator. The resonator is patterned on a NbTiN film [19] withstanding applied magnetic fields beyond 300 mT. Three hyperfine-split spin sub-ensembles are clearly resolved over the temperature range 0.25-1.2 K. The collective coupling of each arXiv:1208.5473v1 [cond-mat.mes-hall]

Recent experimental work on superconducting transmon qubits in three-dimensional (3D) cavities shows that their coherence times are increased by an order of magnitude compared to their two-dimensional cavity counterparts. However, to take advantage of these coherence times while scaling up the number of qubits it is advantageous to address individual qubits which are all coupled to the same 3D cavity fields. The challenge in controlling this system comes from spectral crowding, where the leakage transition of qubits is close to computational transitions in other qubits. Here, it is shown that fast pulses are possible which address single qubits using two-quadrature control of the pulse envelope, while the derivative removal by adiabatic gate method of Motzoi et al. [Phys. Rev. Lett. 103, 110501 (2009)] alone only gives marginal improvements over the conventional Gaussian pulse shape. On the other hand, a first-order result using the Magnus expansion gives a fast analytical pulse shape which gives a high-fidelity gate for a specific gate time, up to a phase factor on the second qubit. Further numerical analysis corroborates these results and yields to even faster gates, showing that leakage-state anharmonicity does not provide a fundamental quantum speed limit.

We propose a scheme for the ultrafast control of the emitter-field coupling rate in cavity quantum electrodynamics. This is achieved by the control of the vacuum field seen by the emitter through a modulation of the optical modes in a coupled-cavity structure. The scheme allows the on-off switching of the coupling rate without perturbing the emitter and without introducing frequency chirps on the emitted photons. It can be used to control the shape of single-photon pulses for high-fidelity quantum state transfer, to control Rabi oscillations, and as a gain-modulation method in lasers. We discuss two possible experimental implementations based on photonic crystal cavities and on microwave circuits.

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