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We review some recent results on discrete symmetries and topological order in spinor Bose-Einstein condensates (BECs) of $^{23}Na$. For spin one bosons with two-body scatterings dominated by a total spin equal to two channel, the BECs are…
We propose a novel numerical method of modelling Bose-Einstein correlations (BEC) observed among identical (bosonic) particles produced in multiparticle production reactions. We argue that the most natural approach is to work directly in…
Bose-Einstein condensate (BEC) is considered under conditions of Feshbach resonance in two-atom collisions due to a coupling of atomic pair and resonant molecular states. The association of condensate atoms can form a molecular BEC, and the…
We study the quantum coherent-tunneling between two Bose-Einstein condensates separated through an oscillating trap potential. The cases of slowly and rapidly varying in time trap potential are considered. In the case of a slowly varying…
In a two-mode approximation, Bose-Einstein condensates (BEC) in a double-well potential can be described by a many particle Hamiltonian of Bose-Hubbard type. We focus on such a BEC whose interatomic interaction strength is modulated…
We study the dynamics of matter waves in an effectively one-dimensional Bose-Einstein condensate in a double well potential. We consider in particular the case when one of the double wells confines excited states. Similarly to the known…
Instabilities resulting in Bose-Einstein condensation and/or modulation of "displacements" in a system of quantum particles described by a two-state Bose-Hubbard model (with an allowance for the interaction between particle displacements on…
We study the formation of quantum droplets in the mixture of a single-component Bose-Einstein condensate (BEC), and a two-species Fermi superfluid across a wide Feshbach resonance. With repulsive boson-boson and attractive boson-fermion…
We study the behavior of moving Bose-Bose mixtures in a weak disordered potential in the realm of the Bogoliubov-Huang-Meng theory. Corrections due to the quantum fluctuations, disorder effects and the relative motion of two fluids to the…
A correlated quantum many-body method is applied to describe resonance states of atomic Bose-Einstein condensates (BEC) in a realistic shallow trap (as opposed to infinite traps commonly used). The realistic van der Waals interaction is…
Dynamical evolution of quantum mechanical squeezing and entanglement in a two-mode Bose-Einstein condensate (TBEC) with an adiabatic, time-varying Raman coupling is studied by finding analytical expressions for these quantities. In…
The problem of understanding how a coherent, macroscopic Bose-Einstein condensate (BEC) emerges from the cooling of a thermal Bose gas has attracted significant theoretical and experimental interest over several decades. The pioneering…
We prove two equilibrium properties of a system of interacting atoms in three or higher dimensional continuous space. (i) If the particles interact via pair potentials of a nonnegative Fourier transform, their self-organization into…
In the last several years considerable efforts have been devoted to developing Bose-Einstein Condensate (BEC)-based devices for applications such as fundamental research, precision measurements and integrated atom optics. Such devices…
We investigate the dynamics of a homogenous Bose-Einstein condensate (BEC) following a sudden quench of the scattering length. Our focus is the time evolution of short-range correlations via the dynamical contact. We compute the dynamics…
We demonstrate that two coupled Bose-Einstein condensates (BEC) at zero temperature can be used to realize a qubit which is the counterpart of Josephson charge qubits. The two BEC are weakly coupled and confined in an asymmetric double-well…
We compare the dynamics of a Bose-Einstein condensate in two coupled potential wells with atoms diffracting from a standing light wave. The corresponding Hamiltonians have an identical appearance, but with a different set of commutation…
We investigate the relative phase coherence properties and the occurrence of demixing instabilities for two mutually interacting and time evolving Bose-Einstein condensates in traps. Our treatment naturally includes the additional…
We present an analytical description of the tunneling dynamics between two coupled Bose-Einstein condensates in the Josephson regime. The model relies on the classical analogy with a rigid pendulum and focuses on two dynamical modes of this…
We study the fidelity decay and its freeze for an initial coherent state of two-mode Bose-Einstein condensates in the Fock regime considering a Bose-Hubbard model that includes two-particle tunneling terms. By using linear-response theory…