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State-of-the-art atomic clocks are based on the precise detection of the energy difference between two atomic levels, measured as a quantum phase accumulated in a given time interval. Optical-lattice clocks (OLCs) now operate at or near the standard quantum limit (SQL) that arises from the quantum noise associated with discrete measurement outcomes. While performance beyond the SQL has been achieved in microwave clocks and other atomic sensors by engineering quantum correlations (entanglement) between the atoms, the generation of entanglement on an optical-clock transition and operation of such a clock beyond the SQL represent major goals in quantum metrology that have never been demonstrated. Here we report creation of a many-atom entangled state on an optical transition, and demonstrate an OLC with an Allan deviation below the SQL. We report a metrological gain of $4.4^{+0.6}_{-0.4}$ dB over the SQL using an ensemble consisting of a few hundred 171Yb atoms, allowing us to reach a given stability $2.8{pm}0.3$ times faster than the same clock operated at the SQL. Our results should be readily applicable to other systems, thus enabling further advances in timekeeping precision and accuracy. Entanglement-enhanced OLCs will have many scientific and technological applications, including precision tests of the fundamental laws of physics, geodesy, or gravitational wave detection.
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Over the last decade, optical atomic clocks have surpassed their microwave counterparts and now offer the ability to measure time with an increase in precision of two orders of magnitude or more. This performance increase is compelling not only for enabling new science, such as geodetic measurements of the earth, searches for dark matter, and investigations into possible long-term variations of fundamental physics constants but also for revolutionizing existing technology, such as the global positioning system (GPS). A significant remaining challenge is to transition these optical clocks to non-laboratory environments, which requires the ruggedization and miniaturization of the atomic reference and clock laser along with their supporting lasers and electronics. Here, using a compact stimulated Brillouin scattering (SBS) laser to interrogate a $^8$$^8$Sr$^+$ ion, we demonstrate a promising component of a portable optical atomic clock architecture. In order to bring the stability of the SBS laser to a level suitable for clock operation, we utilize a self-referencing technique to compensate for temperature drift of the laser to within $170$ nK. Our SBS optical clock achieves a short-term stability of $3.9 times 10^{-14}$ at $1$ s---an order of magnitude improvement over state-of-the-art microwave clocks. Based on this technology, a future GPS employing portable SBS clocks offers the potential for distance measurements with a 100-fold increase in resolution.
Laboratory optical atomic clocks achieve remarkable accuracy (now counted to 18 digits or more), opening possibilities to explore fundamental physics and enable new measurements. However, their size and use of bulk components prevent them from being more widely adopted in applications that require precision timing. By leveraging silicon-chip photonics for integration and to reduce component size and complexity, we demonstrate a compact optical-clock architecture. Here a semiconductor laser is stabilized to an optical transition in a microfabricated rubidium vapor cell, and a pair of interlocked Kerr-microresonator frequency combs provide fully coherent optical division of the clock laser to generate an electronic 22 GHz clock signal with a fractional frequency instability of one part in 10^13. These results demonstrate key concepts of how to use silicon-chip devices in future portable and ultraprecise optical clocks.
Entanglement measures quantify nonclassical correlations present in a quantum system, but can be extremely difficult to calculate, even more so, when information on its state is limited. Here, we consider broad families of entanglement criteria that are based on variances of arbitrary operators and analytically derive the lower bounds these criteria provide for two relevant entanglement measures: the best separable approximation (BSA) and the generalized robustness (GR). This yields a practical method for quantifying entanglement in realistic experimental situations, in particular, when only few measurements of simple observables are available. As a concrete application of this method, we quantify bipartite and multipartite entanglement in spin-squeezed Bose-Einstein condensates of $sim 500$ atoms, by lower bounding the BSA and the GR only from measurements of first and second moments of the collective spin operator.
Fiber optic gyroscopes (FOG) based on the Sagnac effect are a valuable tool in sensing and navigation and enable accurate measurements in applications ranging from spacecraft and aircraft to self-driving vehicles such as autonomous cars. As with any classical optical sensors, the ultimate performance of these devices is bounded by the standard quantum limit (SQL). Quantum-enhanced interferometry allows us to overcome this limit using non-classical states of light. Here, we report on an entangled-photon gyroscope that uses path-entangled NOON-states (N=2) to provide phase supersensitivity beyond the standard-quantum-limit.
Spin squeezing is a form of entanglement that can improve the stability of quantum sensors operating with multiple particles, by inducing inter-particle correlations that redistribute the quantum projection noise. Previous analyses of potential metrological gain when using spin squeezing were performed on theoretically ideal states, without incorporating experimental imperfections or inherent limitations which result in non-unitary quantum state evolution. Here, we show that potential gains in clock stability are substantially reduced when the spin squeezing is non-unitary, and derive analytic formulas for the clock performance as a function of squeezing, excess spin noise, and interferometer contrast. Our results highlight the importance of creating and employing nearly pure entangled states for improving atomic clocks.
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