We describe how strong resonant interactions in multimode optomechanical systems can be used to induce controlled nonlinear couplings between single photons and phonons. Combined with linear mapping schemes between photons and phonons, these techniques provide a universal building block for various classical and quantum information processing applications. Our approach is especially suited for nano-optomechanical devices, where strong optomechanical interactions on a single photon level are within experimental reach.

The development of precise atomic clocks has led to many scientific and technological advances that play an increasingly important role in modern society. Shared timing information constitutes a key resource for positioning and navigation with a direct correspondence between timing accuracy and precision in applications such as the Global Positioning System (GPS). By combining precision metrology and quantum networks, we propose here a quantum, cooperative protocol for the operation of a network consisting of geographically remote optical atomic clocks. Using nonlocal entangled states, we demonstrate an optimal utilization of the global network resources, and show that such a network can be operated near the fundamental limit set by quantum theory yielding an ultra-precise clock signal. Furthermore, the internal structure of the network, combined with basic techniques from quantum communication, guarantees security both from internal and external threats. Realization of such a global quantum network of clocks may allow construction of a real-time single international time scale (world clock) with unprecedented stability and accuracy.With the advances of highly phase coherent lasers, optical atomic clocks containing multiple atoms have demonstrated stability that reaches the standard quantum limit (SQL) set by the available atom number within a clock [1,2]. Reaching beyond SQL, we stand to gain a significant improvement of clock performance by preparing atoms in quantum correlated states (e.g., spin squeezed states [3]). Here we describe a new approach to maximize the performance of a network composed of multiple clocks allowing to gain advantage of all rescources available at each node. Several recent advances in precision metrology and quantum science make this approach realistic. On the one hand, capabilities to maintain phase coherent optical links spanning the entire visible spectrum and over macroscopic distances have been demonstrated, with the capability of delivering the most stable optical oscillator from one color or location to another [4,5]. On the other hand, quantum communications and * These authors contributed equally to this work FIG. 1.The concept of world-wide quantum clock network. a) Illustration of a cooperative clock operation protocol in which individual parties (e.g., satellite based atomic clocks from different countries) jointly allocate their respective resources in a global network involving entangled quantum states. This guarantees an optimal use of the global resources, achieving an ultra-precise clock signal limited only by the fundamental bounds of quantum metrology and, in addition, guaranteeing secure distribution of the clock signal. b) In addition to locally operating the individual clocks, the different nodes (i.e., satellites) employ network-wide entangled states to interrogate their respective local oscillators (LOs). The acquired information is sent to a particular node serving as a center where it is used to stabilize a center of mass mode of the different LOs. This yiel...

We present a quantum-enhanced atomic clock protocol based on groups of sequentially larger Greenberger-Horne-Zeilinger (GHZ) states that achieves the best clock stability allowed by quantum theory up to a logarithmic correction. Importantly the protocol is designed to work under realistic conditions where the drift of the phase of the laser interrogating the atoms is the main source of decoherence. The simultaneous interrogation of the laser phase with a cascade of GHZ states realizes an incoherent version of the phase estimation algorithm that enables Heisenberg-limited operation while extending the coherent interrogation time beyond the laser noise limit. We compare and merge the new protocol with existing state of the art interrogation schemes, and identify the precise conditions under which entanglement provides an advantage for clock stabilization: it allows a significant gain in the stability for short averaging time.

We present a detailed theoretical analysis of a weakly driven, multimode optomechanical system, in which two optical modes are strongly and near-resonantly coupled to a single mechanical mode via a three-wave mixing interaction. We calculate one-and two-time intensity correlations of the two optical fields and compare them to analogous correlations in atom-cavity systems. Nonclassical photon correlations arise when the optomechanical coupling g exceeds the cavity decay rate κ, and we discuss signatures of one-and two-photon resonances as well as quantum interference. We also find a long-lived correlation that decays slowly with the mechanical decay rate γ , reflecting the heralded preparation of a single-phonon state after detection of a photon. Our results provide insight into the quantum regime of multimode optomechanics, with potential applications for quantum information processing with photons and phonons.

We propose and analyze heralded quantum gates between qubits in optical cavities. They employ an auxiliary qubit to report if a successful gate occurred. In this manner, the errors, which would have corrupted a deterministic gate, are converted into a non-unity probability of success: once successful the gate has a much higher fidelity than a similar deterministic gate. Specifically, we describe that a heralded , near-deterministic controlled phase gate (CZ-gate) with the conditional error arbitrarily close to zero and the success probability that approaches unity as the cooperativity of the system, C, becomes large. Furthermore, we describe an extension to near-deterministic Nqubit Toffoli gate with a favorable error scaling. These gates can be directly employed in quantum repeater networks to facilitate near-ideal entanglement swapping, thus greatly speeding up the entanglement distribution.