We demonstrate experimentally an alternative method for the dynamic generation of atomic spin squeezing, building on the interplay between linear coupling and nonlinear phase evolution. Since the resulting quantum dynamics can be seen as rotation and shear on the generalized Bloch sphere, we call this scheme twist-and-turn. This is closely connected to an underlying instability in the classical limit of this system. The short-time evolution of the quantum state is governed by a fast initial spreading of the quantum uncertainty in one direction, accompanied by squeezing in the orthogonal axis. We find an optimal value of ${\xi }_{\mathrm{S}}^2=-7.1\left(3\right)$ dB in a single Bose-Einstein condensate and scalability of the squeezing to more than ${10}^4$ particles with ${\xi }_{\mathrm{S}}^2=-2.8\left(4\right)$ dB.

We show that two almost degenerate poles near the $\pi${}$\Delta${} threshold and the next higher mass pole in the P11 partial wave of $\pi${}N scattering evolve from a single bare state through its coupling with $\pi${}N, $\eta${}N, and $\pi${}$\pi${}N reaction channels. This finding provides new information on understanding the dynamical origins of the Roper N*(1440) and N*(1710) resonances listed by Particle Data Group. Our results for the resonance poles in other $\pi${}N partial waves are also presented.

As a first step to analyze the electromagnetic meson production reactions in the nucleon resonance region, the parameters of the hadronic interactions of a dynamical coupled-channels model, developed in Physics Reports 439, 193 (2007), are determined by fitting the $\pi N$-scattering data. The channels included in the calculations are $\pi N,\eta N$, and $\pi \pi N$, which has $\pi \Delta ,\rho N$, and $\sigma N$ resonant components. The nonresonant meson-baryon interactions of the model are derived from a set of Lagrangians by using a unitary transformation method. One or two bare excited nucleon states in each of $S,P,D$, and $F$ partial waves are included to generate the resonant amplitudes in the fits. The parameters of the model are first determined by fitting as much as possible the empirical $\pi N$ elastic-scattering amplitudes of SAID up to 2 GeV. We then refine and confirm the resulting parameters by directly comparing the predicted differential cross section and target polarization asymmetry with the original data of the elastic ${\pi }^{\pm }p\to {\pi }^{\pm }p$ and charge-exchange ${\pi }^{-}p\to {\pi }^{0}n$ processes. The predicted total cross sections of $\pi N$ reactions and $\pi N\to \eta N$ reactions are also in good agreement with the data. Applications of the constructed model in analyzing the electromagnetic meson production data as well as the future developments are discussed.

We analyze the formation of squeezed states in a condensate of ultracold bosonic atoms confined by a double-well potential. The emphasis is set on the dynamical formation of such states from initially coherent many-body quantum states. Two cases are described: the squeezing formation in the evolution of the system around the stable point, and in the short-time evolution in the vicinity of an unstable point. The latter is shown to produce highly squeezed states on very short times. On the basis of a semiclassical approximation to the Bose-Hubbard Hamiltonian, we are able to predict the amount of squeezing, its scaling with N, and the speed of coherent spin formation with simple analytical formulas which successfully describe the numerical Bose-Hubbard results. This method of producing highly squeezed spin states in systems of ultracold atoms is compared to other standard methods in the literature.

We demonstrate the existence of quantum droplets in two-component one-dimensional Bose-Hubbard chains. The droplets exist for any strength of repulsive intraspecies interactions provided they are balanced by comparable attractive interspecies interactions. The ground-state phase diagram is presented and the different phases are characterized by examining the density profile and off-diagonal one- and two-body correlation functions. A rich variety of phases is found, including atomic superfluid gases, atomic superfluid droplets, pair superfluid droplets, pair superfluid gases, and a Mott-insulator phase. A parameter region prone to be experimentally explored is identified, where the average population per site is lower than three atoms, thus avoiding three-body losses. Finally, the bipartite entanglement of the droplets is found to have a nontrivial dependence on the number of particles.

We consider a Bose-Einstein condensate in a double-well potential undergoing a dynamical transition from the regime of Josephson oscillations to the regime of self-trapping. We analyze the statistical properties of the ground state (or the highest excited state) of the Hamiltonian in these two regimes for attractive (repulsive) interactions. We demonstrate that it is impossible to describe the transition within the mean-field theory. In contrast, the transition proceeds through a strongly correlated delocalized state, with large quantum fluctuations, and spontaneous breaking of the symmetry.