Abstract: Fully controlled coherent coupling of arbitrary harmonic oscillators is an important tool for processing quantum information. Coupling between quantum harmonic oscillators has previously been demonstrated in several physical systems using a two-level system as a mediating element. Direct interaction at the quantum level has only recently been realized by means of resonant coupling between trapped ions. Here we implement a tunable direct coupling between the microwave harmonics of a superconducting resonator by means of parametric frequency conversion. We accomplish this by coupling the mode currents of two harmonics through a superconducting quantum interference device (SQUID) and modulating its flux at the difference (~7GHz) of the harmonic frequencies. We deterministically prepare a single-photon Fock state and coherently manipulate it between multiple modes, effectively controlling it in a superposition of two different 'colours'. This parametric interaction can be described as a beamsplitter-like operation that couples different frequency modes. As such, it could be used to implement linear optical quantum computing protocols on-chip.

Abstract: Quantum entanglement plays a vital role in many quantum-information and communication tasks. Entangled states of higher-dimensional systems are of great interest owing to the extended possibilities they provide. For example, they enable the realization of new types of quantum information scheme that can offer higher-information-density coding and greater resilience to errors than can be achieved with entangled two-dimensional systems (see ref. and references therein). Closing the detection loophole in Bell test experiments is also more experimentally feasible when higher-dimensional entangled systems are used. We have measured previously untested correlations between two photons to experimentally demonstrate high-dimensional entangled states. We obtain violations of Bell-type inequalities generalized to d-dimensional systems up to d=12. Furthermore, the violations are strong enough to indicate genuine 11-dimensional entanglement. Our experiments use photons entangled in orbital angular momentum, generated through spontaneous parametric down-conversion, and manipulated using computer-controlled holograms.

Abstract: Quantum control of individual spins in condensed-matter systems is an emerging field with wide-ranging applications in spintronics, quantum computation and sensitive magnetometry. Recent experiments have demonstrated the ability to address and manipulate single electron spins through either optical or electrical techniques. However, it is a challenge to extend individual-spin control to nanometre-scale multi-electron systems, as individual spins are often irresolvable with existing methods. Here we demonstrate that coherent individual-spin control can be achieved with few- nanometre resolution for proximal electron spins by carrying out single-spin magnetic resonance imaging (MRI), which is realized using a scanning-magnetic-field gradient that is both strong enough to achieve nanometre spatial resolution and sufficiently stable for coherent spin manipulations. We apply this scanning-field-gradient MRI technique to electronic spins in nitrogen-vacancy (NV) centres in diamond and achieve nanometre resolution in imaging, characterization and manipulation of individual spins. For NV centres, our results in individual-spin control demonstrate an improvement of nearly two orders of magnitude in spatial resolution when compared with conventional optical diffraction-limited techniques. This scanning-field-gradient microscope enables a wide range of applications including materials characterization, spin entanglement and nanoscale magnetometry.