We estimate the changes in the condensate ground state energy induced by one or more "sizable" impurities. By "sizable", we mean an impurity whose size is within a few orders of magnitude of the trap size and not necessarily atomic in scale. A sizable impurity will "drill" a hole in the condensate wave function and alter the condensate energy. The question is whether this microscopic change can be detected macroscopically because of the Bose-Einstein condensation effect. We discuss the effect of impurity expulsion, condensate interactions, and the induced interaction between two impurities.
We estimate the changes in the condensate ground state energy induced by one or more "sizable" impurities. By "sizable", we mean an impurity whose size is within a few orders of magnitude of the trap size and not necessarily atomic in scale. A sizable impurity will "drill" a hole in the condensate wave function and alter the condensate energy. The question is whether this microscopic change can be detected macroscopically because of the Bose-Einstein condensation effect. We discuss the effect of impurity expulsion, condensate interactions, and the induced interaction between two impurities.
Bose-Einstein condensates have been, by now, observed in as many as nine different atomic assemblies of bosons. Such a condensate is quantum mechanical interacting system whose ground state properties can be studied theoretically by solving the appropriate non-linear Gross-Pitaevskii-Ginzburg GPG equation. One can now study the change in the behavior of Bose-Einstein condensate by introducing a localized impurity which interacts with the condensate as a function of position of impurity in the condensate. The introduction of such an impurity can be mimicked by simply allowing an intensely focused laser beam to interact with the condensate. This would lead to alteration of ground state properties of the condensate as it would now interact with a potential of type V Sech2(r/w) where, V and w are amplitude and width of the impurity potential, respectively. The modified GPG equation in the presence of localized impurity potential as function of position in the condensate, has been numerically solved to obtain its various ground state properties as function of position, such as total energy per particle, chemical potential, kinetic, harmonic trap potential and two-body interaction energies per particle in addition to energy associated with impurity potential, correlation length, healing length etc. We have studied the behavior of the above-mentioned ground state properties as the position of localized impurity is changed in the condensate from core to peripheral position. While the total, harmonic oscillator potential and impurity energies decrease as the position of localized impurity is displaced from core of the condensate to its periphery, the value of two-body inter-particle interaction energy increases. Further, the values of chemical potential and total energy per particle shows decrease by ~ 9% and ~ 17% respectively, leading to the inference that the stability of condensate increases as the localized impurity is moved away from the core of the condensate.
Quantum dynamics of impurities in a bath of bosons is a long-standing problem in solid-state, plasma, and atomic physics. Recent experimental and theoretical investigations with ultracold atoms have focused on this problem, studying atomic impurities immersed in an atomic Bose–Einstein condensate (BEC) and for various relative coupling strengths tuned by the Fano−Feshbach resonance technique. Here, we report extensive numerical simulations on a closely related problem: the collision between a bosonic impurity consisting of a few 41 K atoms and a BEC of 87 Rb atoms in a quasi one-dimensional configuration and under a weak harmonic axial confinement. For small values of the inter-species interaction strength (regardless of its sign), we find that the impurity, which starts from outside the BEC, simply causes the BEC cloud to oscillate back and forth, but the frequency of oscillation depends on the interaction strength. For intermediate couplings, after a few cycles of oscillation the impurity is captured by the BEC, and strongly changes its amplitude of oscillation. In the strong interaction regime, if the inter-species interaction is attractive, a local maximum (bright soliton) in the BEC density occurs where the impurity is trapped; if, instead, the inter-species interaction is repulsive, the impurity is not able to enter the BEC cloud and the reflection coefficient is close to one. However, if the initial displacement of the impurity is increased, the impurity is able to penetrate the cloud, leading to the appearance of a moving hole (dark soliton) in the BEC.
Motivated by recent experiments, we investigate a single 133Cs impurity in the center of a trapped 87Rb Bose-Einstein condensate (BEC). Within a zero-temperature mean-field description we provide a one-dimensional physical intuitive model which involves two coupled differential equations for the condensate and the impurity wave function, which we solve numerically. With this we determine within the equilibrium phase diagram spanned by the intra- and interspecies coupling strength whether the impurity is localized at the trap center or expelled to the condensate border. In the former case we find that the impurity induces a bump or dip on the condensate for an attractive or a repulsive Rb-Cs interaction strength, respectively. Conversely, the condensate environment leads to an effective mass of the impurity which increases quadratically for small interspecies interaction strength. Afterwards, we investigate how the impurity imprint upon the condensate wave function evolves for two quench scenarios. At first we consider the case that the harmonic confinement is released. During the resulting time-of-flight expansion it turns out that the impurity-induced bump in the condensate wave function starts decaying marginally, whereas the dip decays with a characteristic time scale which decreases with increasing repulsive impurity-BEC interaction strength. Second, once the attractive or repulsive interspecies coupling constant is switched off, we find that white-shock waves or bisolitons emerge which both oscillate within the harmonic confinement with a characteristic frequency.
We study the ground-state properties of a trapped Bose-Einstein condensate with a neutral impurity. By varying the strength of the attractive atom-impurity interactions, the degree of localization of the impurity at the trap center can be controlled. As the impurity becomes more strongly localized, the peak condensate density, which can be monitored experimentally, grows markedly. For strong enough attraction, the impurity can make the condensate unstable by strongly deforming the atom density in the neighborhood of the impurity. This 'collapse' can possibly be investigated in bosenova-type experiments.
We study the ground-state properties of a trapped Bose-Einstein condensate with a neutral impurity. By varying the strength of the attractive atom-impurity interactions, the degree of localization of the impurity at the trap center can be controlled. As the impurity becomes more strongly localized, the peak condensate density, which can be monitored experimentally, grows markedly. For strong enough attraction, the impurity can make the condensate unstable by strongly deforming the atom density in the neighborhood of the impurity. This ``collapse'' can possibly be investigated in bosenova-type experiments.
This paper examines the dynamics of two impurities in a quasi-one-dimensional Bose-Einstein condensate, considering the effect of interaction amplitude and the initial state of the impurity on the coupled dynamics of the impurities and condensate. We consider the interaction between impurities only through the condensate neglecting any direct interactions. By changing the initial parameters of the impurities, the contribution of the condensate density to the trajectory of the impurities is demonstrated. The results show that the trajectory of the impurities strongly depends on their initial position, leading to irregular trajectories due to the deformation of the condensate density at a sufficiently strong attractive interaction between the condensate and impurities.