A light-storage experiment with a total (storage and retrieval) efficiency η=56% is carried out by enclosing a sample, with a single-pass absorption of 10%, in an impedance-matched cavity. The experiment is carried out using the atomic frequency comb (AFC) technique in a praseodymium-doped crystal (0.05%Pr(3+):Y2SiO5) and the cavity is created by depositing reflection coatings directly onto the crystal surfaces. The AFC technique has previously by far demonstrated the highest multimode capacity of all quantum memory concepts tested experimentally. We claim that the present work shows that it is realistic to create efficient, on-demand, long storage time AFC memories.

In optically controlled quantum computers it may be favorable to address different qubits using light with different frequencies, since the optical diffraction does not then limit the distance between qubits. Using qubits that are close to each other enables qubit-qubit interactions and gate operations that are strong and fast in comparison to qubit-environment interactions and decoherence rates. However, as qubits are addressed in frequency space, great care has to be taken when designing the laser pulses, so that they perform the desired operation on one qubit, without affecting other qubits. Complex hyperbolic secant pulses have theoretically been shown to be excellent for such frequency-addressed quantum computing ͓I. Roos and K. Molmer, Phys. Rev. A 69, 022321 ͑2004͔͒-e.g., for use in quantum computers based on optical interactions in rare-earthmetal-ion-doped crystals. The optical transition lines of the rare-earth-metal-ions are inhomogeneously broadened and therefore the frequency of the excitation pulses can be used to selectively address qubit ions that are spatially separated by a distance much less than a wavelength. Here, frequency-selective transfer of qubit ions between qubit states using complex hyperbolic secant pulses is experimentally demonstrated. Transfer efficiencies better than 90% were obtained. Using the complex hyperbolic secant pulses it was also possible to create two groups of ions, absorbing at specific frequencies, where 85% of the ions at one of the frequencies was shifted out of resonance with the field when ions in the other frequency group were excited. This procedure of selecting interacting ions, called qubit distillation, was carried out in preparation for two-qubit gate operations in the rare-earth-metal-ion-doped crystals. The techniques for frequency-selective state-to-state transfer developed here may be also useful also for other quantum optics and quantum information experiments in these long-coherence-time solid-state systems.

We demonstrate two-stage laser stabilization based on a combination of FabryPérot and spectral-hole burning techniques. The laser is first pre-stabilized by the Fabry-Pérot cavity to a fractional-frequency stability of σ y (τ ) < 10 −13 . A pattern of spectral holes written in the absorption spectrum of Eu 3+ :Y 2 SiO 5 serves to further stabilize the laser to σ y (τ ) = 6 × 10 −16 for 2 s ≤ τ ≤ 8 s. Measurements characterizing the frequency sensitivity of Eu 3+ :Y 2 SiO 5 spectral holes to environmental perturbations suggest that they can be more frequencystable than Fabry-Pérot cavities.

Due to inhomogeneous broadening, the absorption lines of rare-earth-ion dopands in crystals are many order of magnitudes wider than the homogeneous linewidths. Several ways have been proposed to use ions with different inhomogeneous shifts as qubit registers, and to perform gate operations between such registers by means of the static dipole coupling between the ions.In this paper we show that in order to implement high-fidelity quantum gate operations by means of the static dipole interaction, we require the participating ions to be strongly coupled, and that the density of such strongly coupled registers in general scales poorly with register size. Although this is critical to previous proposals which rely on a high density of functional registers, we describe architectures and preparation strategies that will allow scalable quantum computers based on rareearth-ion doped crystals.

Due to their narrow homogeneous linewidths, rare-earth ions in inorganic crystals at low temperatures have recently been given considerable attention as test materials for experiments in coherent quantum optics. Because these narrow linewidth transitions have been buried in a wide inhomogeneous line, the scope of experiments that could be carried out in these materials has been limited. However, here we present spectroscopic techniques, based on spectral hole burning and optical pumping, which allow hyperfine transitions that are initially buried within an inhomogeneously broadened absorption line to be studied with no background absorption from other transitions. A sequence of hole-burning pulses is used to isolate selected transitions between hyperfine levels, which makes it possible to directly study properties of the transitions, e.g., transition strengths, and gives access to information that is difficult to obtain in standard hole-burning spectroscopy, such as the ordering of hyperfine levels. The techniques introduced are applicable to absorbers in a solid with long-lived sublevels in the ground state and where the homogeneous linewidth and sublevel separations are smaller than the inhomogeneous broadening of the optical transition. In particular, this includes rare-earth ions doped into inorganic crystals and in the present work the techniques are demonstrated in spectroscopy of Pr

Full quantum state tomography is used to characterize the state of an ensemble based qubit implemented through two hyperfine levels in Pr 3+ ions, doped into a Y2SiO5 crystal. We experimentally verify that single-qubit rotation errors due to inhomogeneities of the ensemble can be suppressed using the Roos-Mølmer dark state scheme [1]. Fidelities above > 90%, presumably limited by excited state decoherence, were achieved. Although not explicitly taken care of in the Roos-Mølmer scheme, it appears that also decoherence due to inhomogeneous broadening on the hyperfine transition is largely suppressed.A large variety of systems are presently investigated in order to find out whether they can be used as hardware for quantum computers. The present work is carried out on a solid state based system, rare earth ions doped into inorganic crystals. As in several other solid state systems the qubits are encoded in nuclear spin states, which for rare earths can have coherence times of seconds and where much longer coherence times are predicted [2]. For being a solid state system the rare earth ions are unusual because their optical transitions can have coherence times as long as several ms [3,4]. Quantum state tomography have previously been carried out to characterize the fidelity by which superpositions on an optical transition can be manipulated [5]. However, since coherence times for the hyperfine states are several orders of magnitude longer, it is highly relevant to also investigate the fidelity of arbitrary qubit rotations using hyperfine qubits. Multi-qubit gate operations can readily be implemented in the system, because optical excitation of an ion will induce frequency shifts >100 MHz (>10 4 line widths) of the optical transitions of nearby ions [6]. The large frequency shift of the optical transition makes it possible to entangle two nearby ions using operations with a duration of just a few ns [7]. A scalable implementation of the rare earth ion scheme can e.g. be achieved using a short lifetime readout ion, acting as a state sensitive probe for the local environment [7] in a manner similar to how the electronic spin of an NV center can probe the nuclear spin states of surrounding C 13 ions [8]. However, because of the hour-long lifetimes of the rare earth spin states [9,10], it is possible to also create qubits consisting of an ensemble of ions, all in a specific quantum state. Each such qubit can be selectively manipulated by optical pulses [6,11,12]. These ensemble qubits, which give strong readout signals, can be used to investigate general properties of the system. In this work ensemble qubits * present address: Research Center COM, DTU, DK-2800, Lyngby, Denmark are used to experimentally carry out arbitrary rotations on the qubit Bloch sphere and the results are characterized by full quantum state tomography. The relevant part of the Pr 3+ :Y 2 SiO 5 energy level diay z x 1 0 B D (b) 17.3 MHz 10.2 MHz 4.6 MHz 4.8 MHz (a) 0 0 , 1 1 , aux 0 e z x y 1 2 (c) B e 1 FIG. 1: (color online) a) energy level diagram,...

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