We investigated the tunnelling dynamics of a zero-temperature Bose-Einstein condensate (BEC) in configuration of four potential wells arranged in a loop. We found three interesting dynamic regimes: (a) flows of matter with small amplitude, (b) steady flow and (c) forced flow of matter for large amplitudes. The regime of quantum self-confinement has been studied and a new variant of it has been found for this system.
In the large-$N$, classical limit, the Bose-Hubbard dimer undergoes a transition to chaos when its tunnelling rate is modulated in time. We use exact and approximate numerical simulations to determine the features of the dynamically evolving state that are correlated with the presence of chaos in the classical limit. We propose the statistical distance between initially similar number distributions as a reliable measure to distinguish regular from chaotic behaviour in the quantum dynamics. Besides being experimentally accessible, number distributions can be efficiently reconstructed numericall…
Ultracold quantum gases confined in three-dimensional bubble traps are promising tools for exploring many-body effects on curved manifolds. As an alternative to the conventional technique of radio-frequency dressing, we propose to create such shell-shaped Bose-Einstein condensates in microgravity based on dual-species atomic mixtures and we analyze their properties as well as the feasibility to realize symmetrically filled shells. Beyond similarities with the radio-frequency dressing method as in the collective-excitation spectrum, our approach has several natural advantages like the robustnes…
We consider the dynamical properties of density fluctuations in the cigar-shaped Bose-Einstein condensate described by the logarithmic wave equation with a constant nonlinear coupling by using the Thomas-Fermi and linear approximations. It is shown that the propagation of small density fluctuations along the long axis of a condensed lump in a strongly anisotropic trap is essentially one-dimensional, while the trapping potential can be disregarded in the linear regime. Depending on the sign of nonlinear coupling, the fluctuations either take the form of translationally symmetric pulses and stan…
We observe experimentally the spontaneous formation of star-shaped surface patterns in driven Bose-Einstein condensates. Two-dimensional star-shaped patterns with $l$-fold symmetry, ranging from quadrupole ($l=2$) to heptagon modes ($l=7$), are parametrically excited by modulating the scattering length near the Feshbach resonance. An effective Mathieu equation and Floquet analysis are utilized, relating the instability conditions to the dispersion of the surface modes in a trapped superfluid. Identifying the resonant frequencies of the patterns, we precisely measure the dispersion relation of …
A Faraday-wave-like parametric instability is investigated via mean-field and Floquet analysis in immiscible binary Bose-Einstein condensates. The condensates form a so-called \textit{ball-shell} structure in a two-dimensional harmonic trap. To trigger the dynamics, the scattering length of the core condensate is periodically modulated in time. We reveal that in the dynamics the interface becomes unstable towards the formation of oscillating patterns. The interface oscillates sub-harmonically exhibiting an $m$-fold rotational symmetry that can be controlled by maneuvering the amplitude and the…
We show that the critical point of the two-dimensional Bose-Hubbard model can be easily found through studies of either on-site atom number fluctuations or the nearest-neighbor two-point correlation function (the expectation value of the tunnelling operator). Our strategy to locate the critical point is based on the observation that the derivatives of these observables with respect to the parameter that drives the superfluid-Mott insulator transition are singular at the critical point in the thermodynamic limit. Performing the quantum Monte Carlo simulations of the two-dimensional Bose-Hubbard…
Ultra-cold atoms in light-shaped potentials open up new ways to explore mesoscopic physics: Arbitrary trapping potentials can be engineered with only a change of the laser field. Here, we propose using ultracold atoms in light-shaped potentials to feasibly realize a cold atom device to study one of the fundamental problems of mesoscopic physics, the Aharonov-Bohm effect: The interaction of particles with a magnetic field when traveling in a closed loop. Surprisingly, we find that the Aharonov-Bohm effect is washed out for interacting bosons, while it is present for fermions. We show that our a…
We study fingering instabilities and pattern formation at the interface of an oppositely polarized two-component Bose-Einstein condensate with strong dipole-dipole interactions in three dimensions. It is shown that the rotational symmetry is spontaneously broken by fingering instability when the dipole-dipole interactions are strengthened. Frog-shaped and mushroom-shaped patterns emerge during the dynamics due to the dipolar interactions. We also demonstrate the spontaneous density modulation and domain growth of a two-component dipolar BEC in the dynamics. Bogoliubov analyses in the two-dimen…
We revisit here the Kibble-Zurek mechanism for superfluid bosons slowly driven across the transition towards the Mott-insulating phase. By means of a combination of the Time-Dependent Variational Principle and a Tree-Tensor Network, we characterize the current flowing during annealing in a ring-shaped one-dimensional Bose-Hubbard model with artificial classical gauge field on up to 32 lattice sites. We find that the superfluid current shows, after an initial decrease, persistent oscillations which survive even when the system is well inside the Mott insulating phase. We demonstrate that the am…
