Related papers: Eigenstates and excitations of the simple atom-mol…
Recent experiments have revealed the formation of stable droplets in dipolar Bose-Einstein condensates. This surprising result has been explained by the stabilization given by quantum fluctuations. We study in detail the properties of a BEC…
We study analytically and asymptotically as well as numerically ground states and dynamics of two-component spin-orbit-coupled Bose-Einstein condensates (BECs) modeled by the coupled Gross-Pitaevskii equations (CGPEs). In fact, due to the…
We study ground states of two-component Bose-Einstein condensates (BEC) with trapping potentials in $R^2$, where the intraspecies interaction $(-a_1,-a_2)$ and the interspecies interaction $-\beta$ are both attractive, $i.e,$ $a_1$, $a_2$…
In this paper, we propose a new numerical method to compute the ground state solution of trapped interacting Bose-Einstein condensation (BEC) at zero or very low temperature by directly minimizing the energy functional via finite element…
The achievement of Bose-Einstein condensation (BEC) in ultracold vapors of alkali atoms has given enormous impulse to the theoretical and experimental study of dilute atomic gases in condensed quantum states inside magnetic traps and…
In this paper, we systematically review mathematical models, theories and numerical methods for ground states and dynamics of spinor Bose-Einstein condensates (BECs) based on the coupled Gross-Pitaevskii equations (GPEs). We start with a…
The computation of the ground states of spin-$F$ Bose-Einstein condensates (BECs) can be formulated as an energy minimization problem with two quadratic constraints. We discretize the energy functional and constraints using the Fourier…
We analytically investigate the ground-state properties of two-component Bose-Einstein condensates with few ⁸⁷Rb atoms inside a high-quality cavity quantum electrodynamics. In the SU(2) representation for atom, this quantum…
We analyze the model of an atomic Bose-Einstein condensate (BEC) parametrically coupled to a molecular BEC via a photoassociation process. We show that an interplay of nonlinear inter- and intra-species interactions leads to the formation…
We investigate the spatial patterns of the ground state of two interacting Bose-Einstein condensates. We consider the general case of two different atomic species (with different mass and in different hyperfine states) trapped in a magnetic…
We have created a dark quantum superposition state of a Rb Bose-Einstein condensate (BEC) and a degenerate gas of Rb$_2$ ground state molecules in a specific ro-vibrational state using two-color photoassociation. As a signature for the…
We demonstrate that the ground state of a trapped spin-1 and spin-2 spinor ferromagnetic Bose-Einstein condensate (BEC) can be well approximated by a single decoupled Gross-Pitaevskii (GP) equation. Useful analytic models for the…
We show that both single-component and two-component Bose-Einstein condensates' (BECs) ground states can be simulated by deep convolutional neural networks of the same structure. We trained the neural network via inputting the coupling…
We identify all possible classes of solutions for two-component Bose-Einstein condensates (BECs) within the Thomas-Fermi (TF) approximation, and check these results against numerical simulations of the coupled Gross-Pitaevskii equations…
We study a three-mode Hamiltonian modelling a heteronuclear molecular Bose--Einstein condensate. Two modes are associated with two distinguishable atomic constituents, which can combine to form a molecule represented by the third mode.…
We study the effect of atom-molecule internal tunneling on the ground state of atom-molecule Bose-Einstein condensates in a double-well potential. In the absence of internal tunneling between atomic and molecular states, the ground state is…
We consider a two-dimensional self-bound quantum droplet, which consists of a mixture of two Bose-Einstein condensates. We start with the ground state, and then turn to the rotational response of this system, in the presence of an external…
We consider the ground state of a trapped Bose-Einstein condensate in two dimensions. In the mean-field approximation, the ground state density profile satisfies the Gross-Pitaevskii equation. We compute the leading quantum corrections to…
In this paper, we mainly review recent results on mathematical theory and numerical methods for Bose-Einstein condensation (BEC), based on the Gross-Pitaevskii equation (GPE). Starting from the simplest case with one-component BEC of the…
We consider a dilute atomic Bose-Einstein condensate with two non-degenerate internal energy levels. The presence of an external radiation field can result in new ground states for the condensate which result from the lowering of the…