Integrable and Chaotic Dynamics of Spins Coupled to an Optical Cavity

We show that a class of random all-to-all spin models, realizable in systems of atoms coupled to an optical cavity, gives rise to a rich dynamical phase diagram due to the pairwise separable nature of the couplings. By controlling the experimental parameters, one can tune between integrable and chaotic dynamics on the one hand and between classical and quantum regimes on the other hand. For two special values of a spin-anisotropy parameter, the model exhibits rational Gaudin-type integrability, and it is characterized by an extensive set of spin-bilinear integrals of motion, independent of the spin size. More generically, we find a novel integrable structure with conserved charges that are not purely bilinear. Instead, they develop "dressing tails" of higher-body terms, reminiscent of the dressed local integrals of motion found in many-body localized phases. Surprisingly, this new type of integrable dynamics found in finite-size spin-1/2 systems disappears in the large-S limit, giving way to classical chaos. We identify parameter regimes for characterizing these different dynamical behaviors in realistic experiments, in view of the limitations set by cavity dissipation

Atom chip based generation of entanglement for quantum metrology

Atom chips provide a versatile `quantum laboratory on a microchip' for experiments with ultracold atomic gases. They have been used in experiments on diverse topics such as low-dimensional quantum gases, cavity quantum electrodynamics, atom-surface interactions, and chip-based atomic clocks and interferometers. A severe limitation of atom chips, however, is that techniques to control atomic interactions and to generate entanglement have not been experimentally available so far. Such techniques enable chip-based studies of entangled many-body systems and are a key prerequisite for atom chip applications in quantum simulations, quantum information processing, and quantum metrology. Here we report experiments where we generate multi-particle entanglement on an atom chip by controlling elastic collisional interactions with a state-dependent potential. We employ this technique to generate spin-squeezed states of a two-component Bose-Einstein condensate and show that they are useful for quantum metrology. The observed 3.7 dB reduction in spin noise combined with the spin coherence imply four-partite entanglement between the condensate atoms and could be used to improve an interferometric measurement by 2.5 dB over the standard quantum limit. Our data show good agreement with a dynamical multi-mode simulation and allow us to reconstruct the Wigner function of the spin-squeezed condensate. The techniques demonstrated here could be directly applied in chip-based atomic clocks which are currently being set up