No Arabic abstract
We consider a trapped atomic ensemble of interacting bosons in the presence of a single trapped ion in a quasi one dimensional geometry. Our study is carried out by means of the newly developed multilayer-multiconfiguration time-dependent Hartree method for bosons, a numerical exact approach to simulate quantum many-body dynamics. In particular, we are interested in the scenario by which the ion is so strongly trapped that its motion can be effectively neglected. This enables us to focus on the atomic ensemble only. With the development of a model potential for the atom-ion interaction, we are able to numerically obtain the exact many-body ground state of the atomic ensemble in the presence of an ion. We analyse the influence of the atom number and the atom-atom interaction on the ground state properties. Interestingly, for weakly interacting atoms, we find that the ion impedes the transition from the ideal gas behaviour to the Thomas-Fermi limit. Furthermore, we show that this effect can be exploited to infer the presence of the ion both in the momentum distribution of the atomic cloud and by observing the interference fringes occurring during an expansion of the quantum gas. In the strong interacting regime, the ion modifies the fragmentation process in dependence of the atom number parity which allows a clear identification of the latter in expansion experiments. Hence, we propose in both regimes experimentally viable strategies to assess the impact of the ion on the many-body state of the atomic gas. This study serves as the first building block for systematically investigate many-body physics of such hybrid system.
We discuss the local density approximation approach to calculating the ground state energy of a one-dimensional Fermi gas containing a single impurity, and compare the results with exact numerical values that we have for up to 11 particles for general interaction strengths and up to 30 particles in the strongly interacting case. We also calculate the contact coefficient in the strongly interacting regime. The different theoretical predictions are compared to recent experimental results with few-atom systems. Firstly, we find that the local density approximation suffers from great ambiguity in the few-atom regime, yet it works surprisingly well for some models. Secondly, we find that the strong interaction theories quickly break down when the number of particles increase or the interaction strength decreases.
We report on controlled doping of an ultracold Rb gas with single neutral Cs impurity atoms. Elastic two-body collisions lead to a rapid thermalization of the impurity inside the Rb gas, representing the first realization of an ultracold gas doped with a precisely known number of impurity atoms interacting via s-wave collisions. Inelastic interactions are restricted to a single three-body recombination channel in a highly controlled and pure setting, which allows to determine the Rb-Rb-Cs three-body loss rate with unprecedented precision. Our results pave the way for a coherently interacting hybrid system of individually controllable impurities in a quantum many-body system.
A correlated many-body calculation is presented to characterize the Shannon information entropy of trapped interacting bosons. We reformulate the one-body Shannon information entropy in terms of the one-body probability density. The minimum limit of the entropy uncertainty relation (EUR) is approached by making $N$ very small in our numerical work. We examine the effect of correlations in the calculation of information entropy. Comparison with the mean-field result shows that the correlated basis function is indeed required to characterize the important features of the information entropies. We also accurately calculate the point of critical instability of an attractive BEC, which is in close agreement with the experimental value. Next we calculate two-body entropies in position and momentum spaces and study quantum correlations in the attractive BEC.
We explore the quantum dynamics of a one-dimensional trapped ultracold ensemble of bosonic atoms triggered by the sudden creation of a single ion. The numerical simulations are performed by means of the ab initio multiconfiguration time-dependent Hartree method for bosons which takes into account all correlations. The dynamics is analyzed via a cluster expansion approach, adapted to bosonic systems of fixed particle number, which provides a comprehensive understanding of the occurring many-body processes. After a transient during which the atomic ensemble separates into fractions which are unbound and bound with respect to the ion, we observe an oscillation in the atomic density which we attribute to the additional length and energy scale induced by the attractive long-range atom-ion interaction. This oscillation is shown to be the main source of spatial coherence and population transfer between the bound and the unbound atomic fraction. Moreover, the dynamics exhibits collapse and revival behavior caused by the dynamical build-up of two-particle correlations demonstrating that a beyond mean-field description is indispensable.
We present a variational calculation of the energy of an impurity immersed a double Fermi sea of non-interacting Fermions. We show that in the strong-coupling regime, the system undergoes a first order transition between polaronic and trimer states. Our result suggests that the smooth crossover predicted in previous literature for a superfluid background is the consequence of Cooper pairing and is absent in a normal system.