Trapped atomic ions have been successfully used for demonstrating basic elements of universal quantum information processing (QIP) [1]. Nevertheless, scaling up of these methods and techniques to achieve large scale universal QIP, or more specialized quantum simulations [2][3][4][5] remains challenging. The use of easily controllable and stable microwave sources instead of complex laser systems [6,7] on the other hand promises to remove obstacles to scalability. Important remaining drawbacks in this approach are the use of magnetic field sensitive states, which shorten coherence times considerably, and the requirement to create large stable magnetic field gradients. Here, we present theoretically a novel approach based on dressing magnetic field sensitive states with microwave fields which addresses both issues and permits fast quantum logic. We experimentally demonstrate basic building blocks of this scheme to show that these dressed states are long-lived and coherence times are increased by more than two orders of magnitude compared to bare magnetic field sensitive states. This changes decisively the prospect of microwave-driven ion trap QIP and offers a new route to extend coherence times for all systems that suffer from magnetic noise such as neutral atoms, NV-centres, quantum dots, or circuit-QED systems. arXiv:1105.1146v1 [quant-ph] 5 May 20112 Introduction -Using laser light for coherent manipulation of qubits gives rise to fundamental issues, notably, unavoidable spontaneous emission which destroys quantum coherence [8,9]. The difficulty in cooling a collection of ions to their motional ground state and the time needed for such a process in the presence of spurious heating of Coulomb crystals limits the fidelity of quantum logic operations in laser-based quantum gates, and thus hampers scalability. This limitation is only partially removed by the use of 'hot' gates [10,11]. Technical challenges in accurately controlling the frequency and intensity of laser light as well as delivering a large number of laser beams of high intensity to trapped ions are further obstacles for scalability.These issues associated with the use of laser light for scalable QIP have lead to the development of novel concepts for performing conditional quantum dynamics with trapped ions that rely on radio frequency (rf) or microwave (mw) radiation instead of laser light [6,7,[12][13][14][15]. Rf or mw radiation can be employed for quantum gates through the use of magnetic gradient induced coupling (MAGIC) between spin states of ions [16], thus averting technical and fundamental issues of scalability that were described above. Furthermore, the sensitivity to motional excitation of ions is reduced in such schemes. A drawback of MAGIC is the necessity to use magnetic field sensitive states for conditional quantum dynamics, thus making qubits susceptible to ambient field noise and shortening their coherence time. This issue is shared with some optical ion trap schemes for QIP that usually rely on magnetic field sensitive states for cond...

Long-lived quantum memories are essential components of a long-standing goal of remote distribution of entanglement in quantum networks. These can be realized by storing the quantum states of light as single-spin excitations in atomic ensembles. However, spin states are often subjected to different dephasing processes that limit the storage time, which in principle could be overcome using spin-echo techniques. Theoretical studies suggest this to be challenging due to unavoidable spontaneous emission noise in ensemble-based quantum memories. Here, we demonstrate spin-echo manipulation of a mean spin excitation of 1 in a large solid-state ensemble, generated through storage of a weak optical pulse. After a storage time of about 1 ms we optically read-out the spin excitation with a high signal-to-noise ratio. Our results pave the way for long-duration optical quantum storage using spin-echo techniques for any ensemble-based memory.

Individual electrodynamically trapped and laser cooled ions are addressed in frequency space using radio-frequency radiation in the presence of a static magnetic field gradient. In addition, an interaction between motional and spin states induced by an rf field is demonstrated employing rfoptical double resonance spectroscopy. These are two essential experimental steps towards realizing a novel concept for implementing quantum simulations and quantum computing with trapped ions.PACS numbers: 37.10. Vz, 37.10.Ty, 32.60.+i Quantum simulations addressing a specific scientific problem and universal quantum computation are expected to yield new insight into as of yet unsolved physical problems that withstand efficient treatment on a classical computer (e.g., [1]). Already a small number of qubits (i.e., a few tens) used for quantum simulations could solve problems even beyond the realm of quantum information science. Creating and investigating entanglement in large physical systems is a related important experimental challenge with implications for our understanding of the transition between the elusive quantum regime and the classical world [2].Laser cooled atomic ions confined in an electrodynamic cage have successfully been used for quantum information processing (QIP) [3] and advantages and difficulties associated with this system have been and still are subject to detailed investigations. The electromagnetic radiation used to coherently drive ionic resonances that serve as qubits needs to be stable against variations in frequency, phase, and amplitude over the course of a quantum computation or simulation. Experimentally this is particularly challenging when laser light is used for realizing quantum gates. When employing laser light additional issues need to be dealt with to allow for accurate qubit manipulation such as the intensity profile of the laser beam, its pointing stability, and diffraction effects. Furthermore, the motional state of the ion chain strongly affects the gate fidelity which requires ground state cooling and low heating rates during the gate operation [4]. Also, spontaneous scattering of laser light off excited electronic states may pose a limit for the coherence time of a quantum many-body state. The probability for scattering can be reduced by increasing the detuning from excited states (when two laser light fields are used that drive a Raman transition between hyperfine or Zeeman states) which, however, leads to an increasing demand for laser power [5].For generating Raman laser beams with a desired frequency difference, first a radio-frequency (rf) or microwave signal at this difference frequency has to be generated that is then "imprinted" on the laser light and send to the ions. Using rf or microwave radiation directly for coherent driving of qubit transitions is impeded in usual ion trap schemes, since, (i) individual addressing of qubits by focusing radiation on just one ion is difficult due to the long wavelength of rf radiation, and (ii) the required coupling between qubit stat...

We report on the experimental demonstration of an optical spin-wave memory, based on the atomic frequency comb (AFC) scheme, where the storage efficiency is strongly enhanced by an optical cavity. The cavity is of low finesse, but operated in an impedance matching regime to achieve high absorption in our intrinsically low-absorbing Eu 3+ :Y 2 SiO 5 crystal. For storage of optical pulses as an optical excitation (AFC echoes), we reach efficiencies of 53% and 28% for 2 μs and 10 μs delays, respectively. For a complete AFC spin-wave memory we reach an efficiency of 12%, including spin-wave dephasing, which is a 12-fold increase with respect to previous results in this material. This result is an important step towards the goal of making efficient and long-lived quantum memories based on spin waves, in the context of quantum repeaters and quantum networks.

Long-distance quantum communication through optical fibers is currently limited to a few hundreds of kilometres due to fiber losses. Quantum repeaters could extend this limit to continental distances. Most approaches to quantum repeaters require highly multimode quantum memories in order to reach high communication rates. The atomic frequency comb memory scheme can in principle achieve high temporal multimode storage, without sacrificing memory efficiency. However, previous demonstrations have been hampered by the difficulty of creating high-resolution atomic combs, which reduces the efficiency for multimode storage. In this article we present a comb preparation method that allows one to increase the multimode capacity for a fixed memory bandwidth. We apply the method to a 151 Eu 3+ -doped Y 2 SiO 5 crystal, in which we demonstrate storage of 100 modes for 51 μs using the AFC echo scheme (a delay-line memory) and storage of 50 modes for 0.541 ms using the AFC spin-wave memory (an on-demand memory). We also briefly discuss the ultimate multimode limit imposed by the optical decoherence rate, for a fixed memory bandwidth.

Rare-earth-ion-doped solids are promising materials as light-matter interfaces for quantum applications. Europium doped into an yttrium orthosilicate crystal in particular has interesting coherence properties and a suitable ground-state energy-level structure for a quantum memory for light. In this paper we report on spectroscopic investigations of this material from the perspective of implementing an atomic frequency comb (AFC)-type quantum memory with spin-wave storage. For this goal we determine the order of the hyperfine levels in the 7 F 0 ground state and 5 D 0 excited state, and we measure the relative strengths of the optical transitions between these levels. We also apply spectral hole burning techniques in order to prepare the system as a well-defined system, as required for further quantum memory experiments. Furthermore, we measure the optical Rabi frequency on one of the strongest hyperfine transitions, a crucial experimental parameter for the AFC protocol. From this we also obtain a value for the transition dipole moment which is consistent with that obtained from absorption measurements.

Coherent operations constitutive for the implementation of single and multi-qubit quantum gates with trapped ions are demonstrated that are robust against variations in experimental parameters and intrinsically indeterministic system parameters. In particular, pulses developed using optimal control theory are demonstrated for the first time with trapped ions. Their performance as a function of error parameters is systematically investigated and compared to composite pulses.In order to experimentally implement a device capable of performing fault-tolerant universal quantum computation (QC), quantum gate operations involving one or multiple qubits have to be carried out with demandingly high accuracy (see, for instance, [1,2]). According to recent theoretical investigations, the experimentally required accuracy of quantum gates for fault-tolerant universal quantum computation no longer seems daunting or even prohibitive [2]. But still, the desired error probability per gate (EPG) should be as small as possible in order to keep the experimental overhead necessary for quantum computation within a feasible limit. Thus a low error probability is prerequisite for scalable fault-tolerant QC.Any quantum algorithm can be decomposed into a sequence of unitary operations applied to individual qubits (single-qubit gate) and conditional quantum dynamics with at least two qubits [3]. Multi-qubit gates (involving two or more qubits) are synthesized by applying a sequence of elementary unitary operations on a collection of qubits. Each of these elementary operations is often similar, or identical, to what is needed for singlequbit gates, and therefore each operation has to be implemented with an error probability well below the tolerable EPG characterizing the full gate operation.If electrodynamically trapped ions are used as qubits, then a unitary operation amounts to letting ions interact with electromagnetic radiation with prescribed frequency, phase, amplitude, and duration of interaction in order to implement quantum gates. Recently, impressive experimental progress was demonstrated in entangling up to eight ions, and performing 2-qubit quantum gates [4,5,6]. Architectures allowing for scalable QC with trapped ions have been proposed (e.g., [7]), and building blocks necessary for achieving this ambitious goal are currently being investigated using various types of ions.The error budget, for instance, of the geometrical phase gate demonstrated in [6] is dominated by the frequency and amplitude uncertainty of the laser light field. These errors are also responsible for a part of the EPG of the controlled-NOT gate reported in [5]. If an "ion spin molecule", that is, trapped ions coupled via a long range spin-spin interaction, is to be used for quantum information processing, then the exact transition frequency of a particular ionic qubit depends on the internal state of other ions [8]. Therefore, here too, it is important to have quantum gates at hand that are insensitive to the detuning of the radiation driving the qubit tran...

A long-lived quantum memory is a firm requirement for implementing a quantum repeater scheme. Recent progress in solid-state rare-earth-ion-doped systems justifies their status as very strong candidates for such systems. Nonetheless an optical memory based on spin-wave storage at the single-photon level has not been shown in such a system to date, which is crucial for achieving the long storage times required for quantum repeaters. In this paper we show that it is possible to execute a complete atomic frequency comb (AFC) scheme, including spin-wave storage, with weak coherent pulses ofn = 2.5 ± 0.6 photons per pulse. We discuss in detail the experimental steps required to obtain this result and demonstrate the coherence of a stored time-bin pulse. We show a noise level of (7.1 ± 2.3) × 10 −3 photons per mode during storage, and this relatively low noise level paves the way for future quantum optics experiments using spin waves in rare-earth-doped crystals.