Engineering spin squeezing in a 3D optical lattice with interacting spin-orbit-coupled fermions

One of the most important tasks in modern quantum science is to coherently control and entangle many-body systems, and to subsequently use these systems to realize powerful quantum technologies such as quantum-enhanced sensors. However, many-body entangled states are difficult to prepare and preserve since internal dynamics and external noise rapidly degrade any useful entanglement. Here, we introduce a protocol that counterintuitively exploits inhomogeneities, a typical source of dephasing in a many-body system, in combination with interactions to generate metrologically useful and robust many-body entangled states. Motivated by current limitations in state-of-the-art three-dimensional (3D) optical lattice clocks (OLCs) operating at quantum degeneracy, we use local interactions in a Hubbard model with spin-orbit coupling to achieve a spin-locking effect. In addition to prolonging inter-particle spin coherence, spin-locking transforms the dephasing effect of spin-orbit coupling into a collective spin-squeezing process that can be further enhanced by applying a modulated drive. Our protocol is fully compatible with state-of-the-art 3D OLC interrogation schemes and may be used to improve their sensitivity, which is currently limited by the intrinsic quantum noise of independent atoms. We demonstrate that even with realistic experimental imperfections, our protocol may generate $\sim10$--$14$ dB of spin squeezing in $\sim1$ second with $\sim10^2$--$10^4$ atoms. This capability allows OLCs to enter a new era of quantum enhanced sensing using correlated quantum states of driven non-equilibrium systems.Comment: 20 pages, 12 figure

High-fidelity imaging of a band insulator in a three-dimensional optical lattice clock

We report on the observation of a high-density, band insulating state in a three-dimensional optical lattice clock. Filled with a nuclear-spin polarized degenerate Fermi gas of 87Sr, the 3D lattice has one atom per site in the ground motional state, thus guarding against frequency shifts due to contact interactions. At this high density where the average distance between atoms is comparable to the probe wavelength, standard imaging techniques suffer from large systematic errors. To spatially probe frequency shifts in the clock and measure thermodynamic properties of this system, accurate imaging techniques at high optical depths are required. Using a combination of highly saturated fluorescence and absorption imaging, we confirm the density distribution in our 3D optical lattice in agreement with a single spin band insulating state. Combining our clock platform with this high filling fraction opens the door to studying new classes of long-lived, many-body states arising from dipolar interactions.Comment: 10 pages, 8 figure

Cold collisions of OH and Rb. I: the free collision

We have calculated elastic and state-resolved inelastic cross sections for cold and ultracold collisions in the Rb($^1 S$) + OH($^2 \Pi_{3/2}$) system, including fine-structure and hyperfine effects. We have developed a new set of five potential energy surfaces for Rb-OH($^2 \Pi$) from high-level {\em ab initio} electronic structure calculations, which exhibit conical intersections between covalent and ion-pair states. The surfaces are transformed to a quasidiabatic representation. The collision problem is expanded in a set of channels suitable for handling the system in the presence of electric and/or magnetic fields, although we consider the zero-field limit in this work. Because of the large number of scattering channels involved, we propose and make use of suitable approximations. To account for the hyperfine structure of both collision partners in the short-range region we develop a frame-transformation procedure which includes most of the hyperfine Hamiltonian. Scattering cross sections on the order of $10^{-13}$ cm$^2$ are predicted for temperatures typical of Stark decelerators. We also conclude that spin orientation of the partners is completely disrupted during the collision. Implications for both sympathetic cooling of OH molecules in an environment of ultracold Rb atoms and experimental observability of the collisions are discussed.Comment: 20 pages, 16 figure

Finite to infinite steady state solutions, bifurcations of an integro-differential equation

We consider a bistable integral equation which governs the stationary solutions of a convolution model of solid--solid phase transitions on a circle. We study the bifurcations of the set of the stationary solutions as the diffusion coefficient is varied to examine the transition from an infinite number of steady states to three for the continuum limit of the semi--discretised system. We show how the symmetry of the problem is responsible for the generation and stabilisation of equilibria and comment on the puzzling connection between continuity and stability that exists in this problem

Long beating wavelength in the Schwarz-Hora effect

Thirty years ago, H.Schwarz has attempted to modulate an electron beam with optical frequency. When a 50-keV electron beam crossed a thin crystalline dielectric film illuminated with laser light, electrons produced the electron-diffraction pattern not only at a fluorescent target but also at a nonfluorescent target. In the latter case the pattern was of the same color as the laser light (the Schwarz-Hora effect). This effect was discussed extensively in the early 1970s. However, since 1972 no reports on the results of further attempts to repeat those experiments in other groups have appeared, while the failures of the initial such attempts have been explained by Schwarz. The analysis of the literature shows there are several unresolved up to now contradictions between the theory and the Schwarz experiments. In this work we consider the interpretation of the long-wavelength spatial beating of the Schwarz-Hora radiation. A more accurate expression for the spatial period has been obtained, taking into account the mode structure of the laser field within the dielectric film. It is shown that the discrepancy of more than 10% between the experimental and theoretical results for the spatial period cannot be reduced by using the existing quantum models that consider a collimated electron beam.Comment: 3 pages, RevTe

Inversion of Randomly Corrugated Surfaces Structure from Atom Scattering Data

The Sudden Approximation is applied to invert structural data on randomly corrugated surfaces from inert atom scattering intensities. Several expressions relating experimental observables to surface statistical features are derived. The results suggest that atom (and in particular He) scattering can be used profitably to study hitherto unexplored forms of complex surface disorder.Comment: 10 pages, no figures. Related papers available at http://neon.cchem.berkeley.edu/~dan

Existence of radial stationary solutions for a system in combustion theory

In this paper, we construct radially symmetric solutions of a nonlinear noncooperative elliptic system derived from a model for flame balls with radiation losses. This model is based on a one step kinetic reaction and our system is obtained by approximating the standard Arrehnius law by an ignition nonlinearity, and by simplifying the term that models radiation. We prove the existence of 2 solutions using degree theory