Spin squeezing can improve atomic precision measurements beyond the standard quantum limit (SQL), and unitary spin squeezing is essential for improving atomic clocks. We report substantial and nearly unitary spin squeezing in 171 Yb, an optical lattice clock atom. The collective nuclear spin of ∼ 10 3 atoms is squeezed by cavity feedback, using light detuned from the system's resonances to attain unitarity. The observed precision gain over the SQL is limited by state readout to 6.5(4) dB, while the generated states offer a gain of 12.9(6) dB, limited by the curvature of the Bloch sphere. Using a squeezed state within 30% of unitarity, we demonstrate an interferometer that improves the averaging time over the SQL by a factor of 3.7(2). In the future, the squeezing can be simply transferred onto the optical clock transition of 171 Yb.Optical lattice clocks (OLCs) employ ensembles of cold trapped atoms to reach unprecedented fractional accuracy at the level of 10 −18 [1][2][3][4][5]. Such clocks now operate near the standard quantum limit (SQL) set by quantum projection noise, where the precision of a sensor improves as √ N with the number of atoms N . Spin squeezed states (SSSs) [6-22] are many-body entangled states that can overcome the SQL [8,23]. They have simple Gaussian quasi-probability distributions with reduced (squeezed) and enhanced (antisqueezed) quantum noise, respectively, along two orthogonal directions of the collective atomic spin. While for fixed-bandwidth applications the precision depends on the squeezing alone, André et al. [24] have shown that for optimized clocks the antisqueezed direction eventually leaks into the measurement, reducing the gain in precision. In practice, the amount of antisqueezing typically far exceeds the squeezing, and this mechanism can dramatically reduce the precision gain to the point where, e.g., the state with the highest inferred squeezing of 20 dB (and an antisqueezing of 39 dB) [20] would improve the precision of a clock by a mere 2 dB [25]. Thus nearly unitary (area-preserving) squeezing is of high importance for future clock applications. Furthermore, of the most common OLC atoms, spin squeezing in Sr, Ca, Mg or Hg have not been demonstrated so far, and Yb has only been weakly squeezed by ∼ 2 dB [10].In this Letter, we demonstrate for the first time nearunitary optical spin squeezing, as well as the first substantial squeezing in an OLC atom. The observed metro-logical gain of up to 6.5(4) dB is limited by the state detection, while subtraction of the independently determined measurement noise implies that the generated SSSs offer 12.9(6) dB of metrological gain and 15.9(6) dB of spin noise suppression. Under conditions where the squeezing is unitary within 30%, and nearly optimal for clock applications, we demonstrate an interferometer with a factor of 3.7(2) reduction in averaging time over the SQL. In the future, the demonstrated squeezing between the two nuclear sublevels m = ± 1 2 of the electronic ground state 1 S 0 of 171 Yb can be directly used in the OL...

Optical cavities are widely used to enhance the interaction between atoms and light. Typical designs using a geometrically symmetric structure in the near-concentric regime face a tradeoff between mechanical stability and high single-atom cooperativity. To overcome this limitation, we design and implement a geometrically asymmetric standing-wave cavity. This structure, with mirrors of very different radii of curvature, allows strong atom-light coupling while exhibiting good stability against misalignment. We observe effective cooperativities ranging from η eff = 10 to η eff = 0.2 by shifting the location of the atoms in the cavity mode. By loading 171 Yb atoms directly from a mirror magneto-optical trap into a one-dimensional optical lattice along the cavity mode, we produce atomic ensembles with collective cooperativities up to N η = 2 × 10 4 . This system opens a way to preparing spin squeezing for an optical lattice clock and to accessing a range of nonclassical collective states. * akiok@stanford.edu; Present address: W. W. Hansen

Many-body localization (MBL), characterized by the absence of thermalization and the violation of conventional thermodynamics, has elicited much interest both as a fundamental physical phenomenon and for practical applications in quantum information. A phenomenological model, which describes the system using a complete set of local integrals of motion (LIOMs), provides a powerful tool to understand MBL, but can be usually only computed approximately. Here we explicitly compute a complete set of LIOMs with a non-perturbative approach, by maximizing the overlap between LIOMs and physical spin operators in real space. The set of LIOMs satisfies the desired exponential decay of weight of LIOMs in real-space. This LIOM construction enables a direct mapping from the real space Hamiltonian to the phenomenological model and thus enables studying the localized Hamiltonian and the system dynamics. We can thus study and compare the localization lengths extracted from the LIOM weights, their interactions, and dephasing dynamics, revealing interesting aspects of many-body localization. Our scheme is immune to accidental resonances and can be applied even at phase transition point, providing a novel tool to study the microscopic features of the phenomenological model of MBL. arXiv:1901.00034v1 [cond-mat.dis-nn]