We found that self-determining collimated light is generated in a photonic crystal fabricated on silicon. The divergence of the collimated beam is insensitive to that of the incident beam and much smaller than the divergence that would be generated in conventional Gaussian optics. The incident-angle dependence of the self-collimated light propagation including lens-like divergent propagation was interpreted in terms of the highly modulated dispersion surfaces with inflection points, where the curvature changes from downward to upward corresponding to respectively a concave/convex-lens case. This demonstration is an important step towards controlling beam profile in photonic crystal integrated light circuits and towards developing “photonic crystalline optics.”

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2Optical fibers have been enabling numerous distinguished applications involving the operation and generation of light, such as soliton transmission 1 , light amplification 2 , alloptical switching 3 and supercontinuum generation 4 . The active function of optical fibers in the quantum regime is expected to be applicable to ultralow-power all-optical signal processing 5 and quantum information processing 6 . Here we demonstrate the first experimental observation of optical nonlinearity at the single-photon level in an optical fiber. Taking advantage of large nonlinearity and managed dispersion of a photonic crystal fiber 7,8 , we have successfully measured very small (10 -7 ~ 10 -8 ) conditional phase shifts induced by weak coherent pulses that contain one or less than one photon per pulse on average. In spite of its tininess, the phase shift was measurable using much (~10 6 times) stronger coherent probe pulses than the pump pulses. We discuss the feasibility of quantum information processing using optical fibers, taking into account the observed Kerr nonlinearity accompanied by ultrafast response time and low induced loss.A photon, the light quantum having much less interaction with its environment than do other quanta (e.g., electron spin, superconducting current), is an outstanding carrier of information for quantum communication and thus is called a 'flying qubit.' This also means that photons may not be suited for computations that require strong unitary interaction between qubits. Hence, fabrication of optical nonlinear media that intermediate sufficiently strong interaction between photons has been under intense study. Cavity quantum electrodynamics-based devices have performed nonlinear Kerr phase shifts of a few ten degrees at the single-photon level 9,10 . Another approach to quantum-optical information processing (QOIP) is to apply weak nonlinearity inherent in currently existing media. Recent proposals 11,12 indicated that such moderately weak nonlinearity can mediate the interaction between photons or other qubits through a strong coherent light (known as a qubus).Exploring the availability of single-photon-level nonlinearity in various media is thus an important challenge that provides a test bed for nonlinear optical phenomena that may emerge in the quantum regime of light 13 .In the present experiment, we used a photonic crystal fiber (PCF) as a Kerr medium. PCF has a high capacity for confining light in its silica core by a large core-cladding index 3 contrast 7,8 . Taking advantage of this feature incorporated with its controlled dispersion property, PCF is widely applied in various applications such as supercontinuum generation 4 , entangled photon generation 14 , squeezing light 15 and a test of the event horizon 16 . To measure the expected ultrasmall phase shift at the single-photon level, we adopted a polarizationdivision Sagnac interferometer (SI) 17 . The SI has the advantage of inherent stability; two interfering beams counter-propagate through the same path in the interferometer so tha...

Realization of fast fault-tolerant quantum gates on a single spin is the core requirement for solid-state quantum-information processing. As polarized light shows geometric interference, spin coherence is also geometrically controlled with light via the spin-orbit interaction. Here, we show that a geometric spin in a degenerate subspace of a spin-1 electronic system under a zero field in a nitrogen vacancy center in diamond allows implementation of optical non-adiabatic holonomic quantum gates. The geometric spin under quasi-resonant light exposure undergoes a cyclic evolution in the spin-orbit space, and acquires a geometric phase or holonomy that results in rotations about an arbitrary axis by any angle defined by the light polarization and detuning. This enables universal holonomic quantum gates with a single operation. We demonstrate a complete set of Pauli quantum gates using the geometric spin preparation and readout techniques. The new scheme opens a path to holonomic quantum computers and repeaters.3 Main textA quantum bit or qubit must be capable of being precisely and quickly manipulated, as well as robust against noise. These criteria pose a dilemma in that the qubit must be open for a driving field but not for a noise field. It has been demonstrated that the degenerate subspace of a spin-1 electronic system under a zero field, which we call a geometric spin, can serve as a promising memory qubit that is robust against environmental noise 1 . The challenge is to manipulate the degenerate qubit with the help of a geometric phase. The concept of the geometric phase was first proposed by Pancharatnam in 1956 2 in reference to light polarization. Since then, two kinds of geometric phase have been discussed. Adiabatic geometric phases were first proposed by Berry in 1984 3 , and nonadiabatic non-Abelian geometric phases were proposed by Anandan in 1988 4 . Holonomic quantum computation (HQC) based on the adiabatic geometric phase was then proposed for fault-tolerant quantum gates by Zanardi and Rasetti in 1999 5 , and generalized to non-adiabatic HQC by Wang and Matsumoto in 2001 6,7 and Zhu and Wang in 2002 8 . The geometric phase has been experimentally demonstrated in molecular ensembles 8,9 , in a superconducting qubit 10 , in trapped ions 11,12 , in a quantum dot 13,14 , and in a single nitrogen-vacancy (NV) center in diamond 15-17 .

§ These authors contributed equally to this work Building a quantum repeater network for long distance quantum communication requires photons and quantum registers that comprise qubits for interaction with light, good memory capabilities and processing qubits for storage and manipulation of photons. Here we demonstrate a key step, the coherent transfer of a photon in a single solid-state nuclear spin qubit with an average fidelity of 98% and storage over 10 seconds. The storage process is achieved by coherently transferring a photon to an entangled electron-nuclear spin state of a nitrogen vacancy centre in diamond, confirmed by heralding through high fidelity single-shot readout of the electronic spin states. Stored photon states are robust against repetitive optical writing operations, required for repeater nodes. The photon-electron spin interface and the nuclear spin memory demonstrated here constitutes a major step towards practical quantum networks, and surprisingly also paves the way towards a novel entangled photon source for photonic quantum computing.A quantum repeater network is intended to distribute entanglement between distant nodes realizing an elementary quantum network [1]. Building up such a network requires photon sources (single or entangled pairs), processing nodes with the ability to make (i) optical or spin Bell-state measurements, (ii) long coherence times and (iii) ability for entanglement purification or quantumerror correction [2,3] . With such strong requirements it is hard to find physical systems meeting all of the above criteria. In this regard ensembles of atomic gases, trapped ions and solid state systems are intensively studied [1,2,[4][5][6][7]. While e.g., atomic systems provide high interaction efficiency with photons, rare earth systems on the other hand show long coherence times, all are required for processing the absorbed/emitted photons. As opposed to ensembles, single particles though typically have a significantly less interaction efficiency with photons, however are useful for quantum networks due to their ability for in situ information processing [8][9][10][11], like entanglement purification [12,13].For this reason solid state devices with well controllable spins are recently proposed to be promising candidates for quantum repeater networks [15,16]. The nitrogenvacancy (NV) defect centre in diamond does show significant potential in this respect. It provides a hybrid spin system in which electron spins are used for fast [17], high-fidelity control [18] and readout [19,20], and nuclear spins which are well-isolated from their environment yielding ultra-long coherence time [21]. Electron and nuclear spins could form a small-scale quantum register allowing for e.g. necessary high-fidelity quantum error correction. Furthermore, the NV electron spin can be entangled with an emitted optical photon [22,23]. Quantum entanglement and quantum teleportation between two remote NV centres have already been experimentally demonstrated [24,25]. A further and significant step towa...

We have demonstrated 1.55 μm wavelength lightwave propagation through a 120° sharply bent waveguide formed in a triangular-lattice two-dimensional photonic crystal (2D PC). Such propagation has not previously been experimentally confirmed. The photonic crystal was fabricated in a silicon-on-insulator (SOI) wafer with the top silicon layer of the wafer used as a core layer. A 877-μm-long single-line-defect waveguide was formed in the PC with a sharp 120° bend near the middle of the waveguide. A tapered-hemispherical-end fiber was coupled to the input end of the waveguide for the light input, and the output from the other end of the waveguide was directly observed by scanning its near-field profile with another tapered-hemispherical-end fiber.

We demonstrate that the superposition of light polarization states is coherently transferred to electron spins in a semiconductor quantum well. By using time-resolved Kerr rotation, we observe the initial phase of Larmor precession of electron spins whose coherence is transferred from light. To break the electron-hole spin entanglement, we utilized the big discrepancy between the transverse g factors of electrons and light-holes. The result encourages us to make a quantum media converter between flying photon qubits and stationary electron-spin qubits in semiconductors.