. Therefore, it can be interpreted as an effective three-body repulsion that stabilizes the gas, preventing collapse and leading to a finite-density solution. We also show that the same effect plays a crucial role in the binding of strongly elongated dipolar droplets under harmonic confinement.

DOI: 10.48550/arxiv.2405.15433

Related papers

Dipolar droplets at the crossover from three dimensions to one dimension

Maciej Pylak, Mariusz Gajda, Paweł Zin

We investigate beyond-mean-field corrections to the energy of an elongated homogeneous Bose gas strongly confined in two directions, with dipoles aligned along the long axis of the system. When the dipolar interaction reaches its critical strength, the mean-field approach predicts instability. However, similar to the free-space case, beyond-mean-field effects significantly alter the ground state of the system, leading to the formation of a self-bound atomic cloud known as a quantum droplet. Our analysis demonstrates that the beyond-mean-field contribution to the energy in the quasi-one-dimensional region, in addition to the confinement-induced shift of the mean-field energy, is proportional to the third power of the density approximately equal to ${n}^{3}$ . Therefore, it can be interpreted as an effective three-body repulsion that stabilizes the gas, preventing collapse and leading to a finite-density solution. We also show that the same effect plays a crucial role in the binding of strongly elongated dipolar droplets under harmonic confinement.We investigate beyond-mean-field corrections to the energy of an elongated homogeneous Bose gas strongly confined in two directions, with dipoles aligned along the long axis of the system. When the dipolar interaction reaches its critical strength, the mean-field approach predicts instability. However, similar to the free-space case, beyond-mean-field effects significantly alter the ground state of the system, leading to the formation of a self-bound atomic cloud known as a quantum droplet. Our analysis demonstrates that the beyond-mean-field contribution to the energy in the quasi-one-dimensional region, in addition to the confinement-induced shift of the mean-field energy, is proportional to the third power of the density approximately equal to ${n}^{3}$. Therefore, it can be interpreted as an effective three-body repulsion that stabilizes the gas, preventing collapse and leading to a finite-density solution. We also show that the same effect plays a crucial role in the binding of strongly elongated dipolar droplets under harmonic confinement.

Physical Review ADec 23, 20243 citations

Quantum droplets in a dipolar Bose gas at a dimensional crossover

Paweł Zin, Maciej Pylak, Tomasz Wasak +2 more

Abstract We study the beyond-mean-field corrections to the energy of a dipolar Bose gas confined to two dimensions by a box potential with dipoles oriented in plane such that their interaction is anisotropic in the two unconfined dimensions. At a critical strength of the dipolar interaction the system becomes unstable on the mean field level. We find that the ground state of the gas is strongly influenced by the corrections, leading to formation of a self-bound droplet, in analogy to the free space case. Properties of the droplet state can be found by minimizing the extended Gross–Pitaevskii energy functional. In the limit of strong confinement we show analytically that the correction can be interpreted as an effective three-body repulsion which stabilizes the gas at finite density.Abstract We study the beyond-mean-field corrections to the energy of a dipolar Bose gas confined to two dimensions by a box potential with dipoles oriented in plane such that their interaction is anisotropic in the two unconfined dimensions. At a critical strength of the dipolar interaction the system becomes unstable on the mean field level. We find that the ground state of the gas is strongly influenced by the corrections, leading to formation of a self-bound droplet, in analogy to the free space case. Properties of the droplet state can be found by minimizing the extended Gross–Pitaevskii energy functional. In the limit of strong confinement we show analytically that the correction can be interpreted as an effective three-body repulsion which stabilizes the gas at finite density.

arXiv:1911.02384Journal of Physics B Atomic Molecular and Optical PhysicsAug 18, 202112 citations

Supersolid droplets in two-dimensional dipolar Bose gases

Abdelâali Boudjemâa

We calculate analytically the quantum and thermal fluctuations corrections of a dilute quasi-two-dimensional Bose-condensed dipolar gas. We show that these fluctuations may change their character from repulsion to attraction in the density-temperature plane owing to the striking momentum dependence of the dipole-dipole interactions. The dipolar instability is halted by such unconventional beyond mean field corrections leading to the formation of a droplet phase. The equilibrium features and coherence properties exhibited by such droplets are deeply discussed. At finite temperature, we find that the equilibrium density crucially depends on the temperature and on the confinement strength and thus, a stable droplet can exist only at ultralow temperature due to the strong thermal fluctuations.We calculate analytically the quantum and thermal fluctuations corrections of a dilute quasi-two-dimensional Bose-condensed dipolar gas. We show that these fluctuations may change their character from repulsion to attraction in the density-temperature plane owing to the striking momentum dependence of the dipole-dipole interactions. The dipolar instability is halted by such unconventional beyond mean field corrections leading to the formation of a droplet phase. The equilibrium features and coherence properties exhibited by such droplets are deeply discussed. At finite temperature, we find that the equilibrium density crucially depends on the temperature and on the confinement strength and thus, a stable droplet can exist only at ultralow temperature due to the strong thermal fluctuations.

Sep 20, 20170 citations

Two-dimensional quantum droplets in dipolar Bose gases

Abdelâali Boudjemâa

Abstract We calculate analytically the quantum and thermal fluctuations corrections of a dilute quasi-two-dimensional Bose-condensed dipolar gas. We show that these fluctuations may change their character from repulsion to attraction in the density-temperature plane owing to the striking momentum dependence of the dipole–dipole interactions. The dipolar instability is halted by such unconventional beyond mean field corrections leading to the formation of a droplet phase. The equilibrium features and coherence properties exhibited by such droplets are deeply discussed. At finite temperature, we find that the equilibrium density crucially depends on the temperature and on the confinement strength and thus, a stable droplet can exist only at ultralow temperature due to the strong thermal fluctuations.Abstract We calculate analytically the quantum and thermal fluctuations corrections of a dilute quasi-two-dimensional Bose-condensed dipolar gas. We show that these fluctuations may change their character from repulsion to attraction in the density-temperature plane owing to the striking momentum dependence of the dipole–dipole interactions. The dipolar instability is halted by such unconventional beyond mean field corrections leading to the formation of a droplet phase. The equilibrium features and coherence properties exhibited by such droplets are deeply discussed. At finite temperature, we find that the equilibrium density crucially depends on the temperature and on the confinement strength and thus, a stable droplet can exist only at ultralow temperature due to the strong thermal fluctuations.

arXiv:1709.07088New Journal of PhysicsAug 30, 201922 citations

Beyond-mean-field crossover from one dimension to three dimensions in quantum droplets of binary mixtures

L. Lavoine, Thomas Bourdel

The existence of quantum droplets in binary Bose-Einstein condensate mixtures relies on beyond-mean-field effects, competing with mean-field effects. Interestingly, the beyond-mean-field effects change from repulsive in three dimensions (3D) to attractive in 1D leading to drastically different behaviors. We quantitatively model quantum droplets in the beyond-mean-field crossover from 1D to 3D in the relevant case of an elongated harmonic trap and give realistic numbers for experimental realizations. We identify and quantify two main limiting factors: three-body losses and tiny energy scales. The crossover region is appealing as it offers a trade-off between these two main limitations opening the possibility of observing stable flat-top density profiles, a yet unobserved, characteristic feature of quantum droplets. It would permit testing of beyond-mean-field theories to an unprecedented precision.The existence of quantum droplets in binary Bose-Einstein condensate mixtures relies on beyond-mean-field effects, competing with mean-field effects. Interestingly, the beyond-mean-field effects change from repulsive in three dimensions (3D) to attractive in 1D leading to drastically different behaviors. We quantitatively model quantum droplets in the beyond-mean-field crossover from 1D to 3D in the relevant case of an elongated harmonic trap and give realistic numbers for experimental realizations. We identify and quantify two main limiting factors: three-body losses and tiny energy scales. The crossover region is appealing as it offers a trade-off between these two main limitations opening the possibility of observing stable flat-top density profiles, a yet unobserved, characteristic feature of quantum droplets. It would permit testing of beyond-mean-field theories to an unprecedented precision.

Physical Review AMar 15, 202133 citations

Quantum Fluctuations in Quasi-One-Dimensional Dipolar Bose-Einstein Condensates

Daniel Edler, Chinmayee Mishra, F. Wächtler +3 more

Recent experiments have revealed that beyond-mean-field corrections are much more relevant in weakly interacting dipolar condensates than in their nondipolar counterparts. We show that in quasi-one-dimensional geometries quantum corrections in dipolar and nondipolar condensates are strikingly different due to the peculiar momentum dependence of the dipolar interactions. The energy correction of the condensate presents not only a modified density dependence, but it may even change from attractive to repulsive at a critical density due to the surprising role played by the transversal directions. The anomalous quantum correction translates into a strongly modified physics for quantum-stabilized droplets and dipolar solitons. Moreover, and for similar reasons, quantum corrections of three-body correlations, and hence of three-body losses, are strongly modified by the dipolar interactions. This intriguing physics can be readily probed in current experiments with magnetic atoms.Recent experiments have revealed that beyond-mean-field corrections are much more relevant in weakly interacting dipolar condensates than in their nondipolar counterparts. We show that in quasi-one-dimensional geometries quantum corrections in dipolar and nondipolar condensates are strikingly different due to the peculiar momentum dependence of the dipolar interactions. The energy correction of the condensate presents not only a modified density dependence, but it may even change from attractive to repulsive at a critical density due to the surprising role played by the transversal directions. The anomalous quantum correction translates into a strongly modified physics for quantum-stabilized droplets and dipolar solitons. Moreover, and for similar reasons, quantum corrections of three-body correlations, and hence of three-body losses, are strongly modified by the dipolar interactions. This intriguing physics can be readily probed in current experiments with magnetic atoms.

arXiv:1610.09176Physical Review LettersAug 2, 2017115 citations

\sim n^3

{n}^{3}