In this Letter, we provide a general methodology to directly measure topological order in cold atom systems. As an application, we propose the realization of a characteristic topological model, introduced by Haldane, using optical lattices loaded with fermionic atoms in two internal states. We demonstrate that time-of-flight measurements directly reveal the topological order of the system in the form of momentumspace Skyrmions. DOI: 10.1103/PhysRevLett.107.235301 PACS numbers: 67.85.Àd, 03.65.Vf Different phases of matter can be distinguished by their symmetries. This information is usually captured by locally measurable order parameters that summarize the essential properties of the phase. Topological insulators are materials with symmetries that depend on the topology of the energy eigenstates of the system [1]. These materials are of interest because they give rise to robust spin transport effects with potential applications ranging from sensitive detectors to quantum computation [2,3]. However, direct observation and measurement of topological order has been up to now impossible due to its nonlocal character. Instead, experiments have relied so far on indirect manifestations of this order, such as edge states and the quantization of conductivity.Ultracold atoms facilitate the implementation of artificial gauge fields [4]. Here, we distinguish proposals that generate continuous fields [5], such as the recent experiment by Lin et al. [6], from those that rely on optical lattices and engineering of hopping [7]. We will concentrate on the latter, introducing a method based on standard time-of-flight (TOF) measurements that can identify a topological character in the quantum state of the system. Our starting point is a possible implementation of Haldane's model using fermionic atoms in two internal states. The topological nature of its ground state is witnessed by the Chern number. This number counts the times the ground state, written as a spinor, wraps around the sphere, as a function of momentum. We demonstrate that TOF measurements reconstruct the Chern number in a way which is robust against the presence of external perturbations or state preparation. Our method can be adapted to other quantum simulations of topological order in optical lattices [8][9][10][11][12][13][14][15][16][17], as many already use internal degrees of freedom of the atoms to encode the order.One common mechanism for the appearance of topological order is based on the topology of the eigenstate manifolds. Consider a real-space lattice whose unit cell has d quantum degrees of freedom-position of the particle, spin, etc. In the case of the quantum Hall effect, the energy bands are separated from each other and the material becomes an insulator for appropriate Fermi energies, E F . In a real setup, with finite boundaries, the sample can have a quantized nonzero conductivity given by the topological invariant m xy ¼ e 2 =h P E m

The ability to convert quantum states from microwave photons to optical photons is important for hybrid system approaches to quantum information processing. In this paper we report the upconversion of a microwave signal into the optical telecommunications wavelength band using erbium dopants in a yttrium orthosilicate crystal via stimulated Raman scattering. The microwaves were applied to the sample using a 3D copper loop-gap resonator and the coupling and signal optical fields were single passed. The conversion efficiency was low, in agreement with a theoretical analysis, but can be significantly enhanced with an optical resonator.

Coherently converting the frequency and temporal waveform of single and entangled photons will be crucial to interconnect the various elements of future quantum information networks. Of particular importance is the quantum frequency conversion of photons emitted by material systems able to store quantum information, so-called quantum memories. There have been significant efforts to implement quantum frequency conversion using nonlinear crystals, with non-classical light from broadband photon-pair sources and solid-state emitters. However, solid state quantum frequency conversion has not yet been achieved with long-lived optical quantum memories. Here we demonstrate an ultra-low-noise solid state photonic quantum interface suitable for connecting quantum memories based on atomic ensembles to the telecommunication fibre network. The interface is based on an integrated-waveguide nonlinear device. We convert heralded single photons at 780 nm from a rubidium-based quantum memory to the telecommunication wavelength of 1,552 nm, showing significant non-classical correlations between the converted photon and the heralding signal.