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3He impurity in a Bose-Einstein condensate

P. Capuzzi, E. Susana Hernández, M. Barranco

Published Jan 1, 2000• 1 citation
OpenAlex

Abstract

We analyze a configuration consisting of a \n3\nHe\n droplet inmersed in a Bose-Einstein condensate at \nT\n≈\n0.\n We investigate the stationary density and oscillations of the condensate, as well as the dynamics of the droplet in the frame of a simple model. Our paper takes into account the actual interaction potential between the \n3\nHe\n and condensate atoms and reveals the stability of the dynamics of a small \n3\nHe\n droplet inside the condensate.

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3He impurity in a Bose-Einstein condensate

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We analyze a configuration consisting of a ${}^{3}\mathrm{He}$ droplet inmersed in a Bose-Einstein condensate at $T\ensuremath{\approx}0.$ We investigate the stationary density and oscillations of the condensate, as well as the dynamics of the droplet in the frame of a simple model. Our paper takes into account the actual interaction potential between the ${}^{3}\mathrm{He}$ and condensate atoms and reveals the stability of the dynamics of a small ${}^{3}\mathrm{He}$ droplet inside the condensate.

Physical Review A•Jul 13, 2000•5 citations

Dipolar droplet bound in a trapped Bose-Einstein condensate

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We study the statics and dynamics of a dipolar Bose-Einstein condensate (BEC) droplet bound by interspecies contact interaction in a trapped nondipolar BEC. Our findings are demonstrated in terms of stability plots of a dipolar ${}^{164}$Dy droplet bound in a trapped nondipolar ${}^{87}$Rb BEC with a variable number of ${}^{164}$Dy atoms and interspecies scattering length. A trapped nondipolar BEC of a fixed number of atoms can bind only a dipolar droplet containing fewer atoms than a critical number for the interspecies scattering length between two critical values. The shape and size (statics) as well as the small breathing oscillation (dynamics) of the dipolar BEC droplet are studied using numerical and variational solutions of a mean-field model. We also suggest an experimental procedure for achieving such a ${}^{164}$Dy droplet by relaxing the trap on the ${}^{164}$Dy BEC in a trapped binary ${}^{87}$Rb-${}^{164}$Dy mixture.

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Dynamics of quantum droplets in Bose–Einstein condensates with three-body loss and external feeding

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Abstract We consider quantum droplets in Bose–Einstein condensates with three-body recombination and external feeding in a spherically symmetric harmonic trap. A quantum droplet is a self-bound state which arises due to the delicate balance between the mean-field effect and quantum fluctuation. We find effective potentials for flat- and sharp-top droplets and show that the potentials in both cases are minimized for certain values of the width. The width of a droplet oscillates periodically with time and the oscillation amplitude depends sensitively on the initial width of a droplet around the minimum of the effective potential. The maximum width of a droplet decreases gradually with time due to the loss of atoms arising from the three-body recombination. It shows that this loss of atoms can be managed by appropriately feeding the condensate from an external source to generate stable droplets. We examine the stability of a droplet by fixed point analysis and find that the region of stability is affected with the change of external feeding and three-body loss.

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Collision of impurities with Bose–Einstein condensates

Fabio Lingua, Luca Lepori, F. Minardi +2 more

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.

arXiv:1707.09568•New Journal of Physics•Feb 22, 2018•12 citations

Mean-field theory of an atomic Bose–Einstein condensate

S. Geltman

Mean-field theory for an atomic Bose–Einstein condensate is re-examined and two new boundary conditions are introduced that take account of the impenetrability of the atomic cores. The dominant part of the resulting effective atom–atom interaction arises from the attractive part of the potential and it is seen to differ substantially from that (proportional to the scattering length) used in Gross–Pitaevskii theory. This difference is described in detail for the case of a 'hard-sphere plus attractive square-well' model potential. The consequences of the new interaction in the quantum dynamics of a rubidium condensate are studied and it is shown that, while a stable stationary S state does not exist, the condensate is contained in its trap in a state of quasi-equilibrium with small rapid variations in space and time.

Journal of Physics B Atomic Molecular and Optical Physics•Dec 17, 2003•13 citations

Dynamics of a 2D Bose-Einstein Condensate With an Impurity

Jonas Rønning

In this project we have studied the hydrodynamic forces that are acting on a small impurity submerged into a two-dimensional Bose-Einstein condensate at finite temperature. The condensate is modeled by the damped Gross-Pitaevskii equation which we have coupled to a repulsive Gaussian potential to model the interaction with the impurity. We have considered a weakly coupled impurity in an untrapped condensate. The perturbations away from the condensates ground-state, both the ones caused by the particle and those that are not, are assumed to be small. We therefore use linear perturbation analysis to find expressions for the hydrodynamic forces and compare these expressions to the classical Maxey-Riley equation. We find that the force caused by the perturbations that were in the fluid in the absence of the particle are proportional to the local condensate acceleration. This is analogous to the inertial term in the Maxey-Riley equation. The force due to the perturbations that were caused by the impurity takes, for slowly moving impurities in the steady-state, the form of the Stokes’ drag. The obtained expressions are then compared to numerical simulations.

•Jan 1, 2020•1 citation
We analyze a configuration consisting of a \n3\nHe\n droplet inmersed in a Bose-Einstein condensate at \nT\n≈\n0.\n We investigate the stationary density and oscillations of the condensate, as well as the dynamics of the droplet in the frame of a simple model. Our paper takes into account the actual interaction potential between the \n3\nHe\n and condensate atoms and reveals the stability of the dynamics of a small \n3\nHe\n droplet inside the condensate.
We analyze a configuration consisting of a 3He{}^{3}\mathrm{He}3He droplet inmersed in a Bose-Einstein condensate at $T\ensuremath{\approx}0.$ We investigate the stationary density and oscillations of the condensate, as well as the dynamics of the droplet in the frame of a simple model. Our paper takes into account the actual interaction potential between the 3He{}^{3}\mathrm{He}3He and condensate atoms and reveals the stability of the dynamics of a small 3He{}^{3}\mathrm{He}3He droplet inside the condensate.
We study the statics and dynamics of a dipolar Bose-Einstein condensate (BEC) droplet bound by interspecies contact interaction in a trapped nondipolar BEC. Our findings are demonstrated in terms of stability plots of a dipolar 164{}^{164}164Dy droplet bound in a trapped nondipolar 87{}^{87}87Rb BEC with a variable number of 164{}^{164}164Dy atoms and interspecies scattering length. A trapped nondipolar BEC of a fixed number of atoms can bind only a dipolar droplet containing fewer atoms than a critical number for the interspecies scattering length between two critical values. The shape and size (statics) as well as the small breathing oscillation (dynamics) of the dipolar BEC droplet are studied using numerical and variational solutions of a mean-field model. We also suggest an experimental procedure for achieving such a 164{}^{164}164Dy droplet by relaxing the trap on the 164{}^{164}164Dy BEC in a trapped binary 87{}^{87}87Rb-164{}^{164}164Dy mixture.
Abstract We consider quantum droplets in Bose–Einstein condensates with three-body recombination and external feeding in a spherically symmetric harmonic trap. A quantum droplet is a self-bound state which arises due to the delicate balance between the mean-field effect and quantum fluctuation. We find effective potentials for flat- and sharp-top droplets and show that the potentials in both cases are minimized for certain values of the width. The width of a droplet oscillates periodically with time and the oscillation amplitude depends sensitively on the initial width of a droplet around the minimum of the effective potential. The maximum width of a droplet decreases gradually with time due to the loss of atoms arising from the three-body recombination. It shows that this loss of atoms can be managed by appropriately feeding the condensate from an external source to generate stable droplets. We examine the stability of a droplet by fixed point analysis and find that the region of stability is affected with the change of external feeding and three-body loss.
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.
Mean-field theory for an atomic Bose–Einstein condensate is re-examined and two new boundary conditions are introduced that take account of the impenetrability of the atomic cores. The dominant part of the resulting effective atom–atom interaction arises from the attractive part of the potential and it is seen to differ substantially from that (proportional to the scattering length) used in Gross–Pitaevskii theory. This difference is described in detail for the case of a 'hard-sphere plus attractive square-well' model potential. The consequences of the new interaction in the quantum dynamics of a rubidium condensate are studied and it is shown that, while a stable stationary S state does not exist, the condensate is contained in its trap in a state of quasi-equilibrium with small rapid variations in space and time.
In this project we have studied the hydrodynamic forces that are acting on a small impurity submerged into a two-dimensional Bose-Einstein condensate at finite temperature. The condensate is modeled by the damped Gross-Pitaevskii equation which we have coupled to a repulsive Gaussian potential to model the interaction with the impurity. We have considered a weakly coupled impurity in an untrapped condensate. The perturbations away from the condensates ground-state, both the ones caused by the particle and those that are not, are assumed to be small. We therefore use linear perturbation analysis to find expressions for the hydrodynamic forces and compare these expressions to the classical Maxey-Riley equation. We find that the force caused by the perturbations that were in the fluid in the absence of the particle are proportional to the local condensate acceleration. This is analogous to the inertial term in the Maxey-Riley equation. The force due to the perturbations that were caused by the impurity takes, for slowly moving impurities in the steady-state, the form of the Stokes’ drag. The obtained expressions are then compared to numerical simulations.