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 investigate dissipative phase transitions in an open central spin system. In our model the central spin interacts coherently with the surrounding many-particle spin environment and is subject to coherent driving and dissipation. We develop analytical tools based on a self-consistent Holstein-Primakoff approximation that enable us to determine the complete phase diagram associated with the steady states of this system. It includes first and second-order phase transitions, as well as regions of bistability, spin squeezing and altered spin pumping dynamics. Prospects of observing these phenomena in systems such as electron spins in quantum dots or NV centers coupled to lattice nuclear spins are briefly discussed.

We propose and analyze a new approach based on quantum error correction (QEC) to improve quantum metrology in the presence of noise. We identify the conditions under which QEC allows one to improve the signal-to-noise ratio in quantum-limited measurements, and we demonstrate that it enables, in certain situations, Heisenberg-limited sensitivity. We discuss specific applications to nanoscale sensing using nitrogen-vacancy centers in diamond in which QEC can significantly improve the measurement sensitivity and bandwidth under realistic experimental conditions.

We propose a universal, on-chip quantum transducer based on surface acoustic waves in piezoactive materials. Because of the intrinsic piezoelectric (and/or magnetostrictive) properties of the material, our approach provides a universal platform capable of coherently linking a broad array of qubits, including quantum dots, trapped ions, nitrogen-vacancy centers, or superconducting qubits. The quantized modes of surface acoustic waves lie in the gigahertz range and can be strongly confined close to the surface in phononic cavities and guided in acoustic waveguides. We show that this type of surface acoustic excitation can be utilized efficiently as a quantum bus, serving as an on-chip, mechanical cavity-QED equivalent of microwave photons and enabling long-range coupling of a wide range of qubits.