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We study systematically the period-doubled Bloch states for a weakly interacting Bose-Einstein condensate in a one-dimensional optical lattice. This kind of state is of form $psi_k=e^{ikx}phi_k(x)$, where $phi_k(x)$ is of period twice the optical lattice constant. Our numerical results show how these nonlinear period-doubled states grow out of linear period-doubled states at a quarter away from the Brillouin zone center as the repulsive interatomic interaction increases. This is corroborated by our analytical results. We find that all nonlinear period-doubled Bloch states have both Landau instability and dynamical instability.
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Mobile impurities in a Bose-Einstein condensate form quasiparticles called polarons. Here, we show that two such polarons can bind to form a bound bipolaron state. Its emergence is caused by an induced nonlocal interaction mediated by density oscillations in the condensate, and we derive using field theory an effective Schrodinger equation describing this for arbitrarily strong impurity-boson interaction. We furthermore compare with Quantum Monte Carlo simulations finding remarkable agreement, which underlines the predictive power of the developed theory. It is found that bipolaron formation typically requires strong impurity interactions beyond the validity of more commonly used weak-coupling approaches that lead to local Yukawa-type interactions. We predict that the bipolarons are observable in present experiments and describe a procedure to probe their properties.
In this work we present numerical study of a trapped Bose-Einstein condensate perturbed by an alternating potential. The relevant physical situation has been recently realized in experiment, where the trapped condensate of $^{87}$Rb, being strongly perturbed, exhibits the set of spatial structures. Firstly, regular vortices are detected. Further, increasing either the excitation amplitude or modulation time results in the transition to quantum vortex turbulence, followed by a granular state. Numerical simulation of the nonequilibrium Bose-condensed system is based on the solution of the time-dependent 3D nonlinear Schr{o}dinger equation within the static and dynamical algorithms. The damped gradient step and time split-step Fourier transform methods are employed. We demonstrate that computer simulations qualitatively reproduce the experimental picture, and describe well the main experimental observables.
The presence of strong interactions in a many-body quantum system can lead to a variety of exotic effects. Here we show that even in a comparatively simple setup consisting of a charged impurity in a weakly interacting bosonic medium the competition of length scales gives rise to a highly correlated mesoscopic state. Using quantum Monte Carlo simulations, we unravel its vastly different polaronic properties compared to neutral quantum impurities. Moreover, we identify a transition between the regime amenable to conventional perturbative treatment in the limit of weak atom-ion interactions and a many-body bound state with vanishing quasi-particle residue composed of hundreds of atoms. In order to analyze the structure of the corresponding states we examine the atom-ion and atom-atom correlation functions which both show nontrivial properties. Our findings are directly relevant to experiments using hybrid atom-ion setups that have recently attained the ultracold regime.
The ground state of a Bose-Einstein condensate in a two-dimensional trap potential is analyzed numerically at the infinite-particle limit. It is shown that the anisotropy of the many-particle position variance along the $x$ and $y$ axes can be opposite when computed at the many-body and mean-field levels of theory. This is despite the system being $100%$ condensed, and the respective energies per particle and densities per particle to coincide.
We realized a quantum geometric charge pump for a Bose-Einstein condensate (BEC) in the lowest Bloch band of a novel bipartite magnetic lattice. Topological charge pumps in filled bands yield quantized pumping set by the global -- topological -- properties of the bands. In contrast, our geometric charge pump for a BEC occupying just a single crystal momentum state exhibits non-quantized charge pumping set by local -- geometrical -- properties of the band structure. Like topological charge pumps, for each pump cycle we observed an overall displacement (here, not quantized) and a temporal modulation of the atomic wavepackets position in each unit cell, i.e., the polarization.
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