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...

The control of internal and motional quantum degrees of freedom of laser-cooled trapped ions has been subject to intense theoretical and experimental research for about three decades. In the realm of quantum information science, the ability to deterministically prepare and measure quantum states of trapped ions is unprecedented. This expertise may be employed to investigate physical models conceived to describe systems that are not directly accessible for experimental investigations. Here, we give an overview of current theoretical proposals and experiments for such quantum simulations with trapped ions. This includes various spin models (e.g. the quantum transverse Ising model or a neural network), the Bose–Hubbard Hamiltonian, the Frenkel–Kontorova model, and quantum fields and relativistic effects.

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...