Related papers: The NLS limit for bosons in a quantum waveguide
There is great interest in generating and controlling entanglement in Bose-Einstein condensates and similar ensembles for use in quantum computation, simulation, and sensing. One class of entangled states useful for enhanced metrology are…
We study two-body correlations in a many-boson system with a hyperspherical approach, where we can use arbitrary scattering length and include two-body bound states. As a special application we look on Bose-Einstein condensation and…
A hydrodynamic description is used to study the normal modes of a vortex in a zero-temperature Bose-Einstein condensate. In the Thomas-Fermi (TF) limit, the circulating superfluid velocity far from the vortex core provides a small…
We study the stability of a Bose-Einstein condensate of harmonically trapped atoms with negative scattering length, specifically lithium 7. Our method is to solve the time-dependent nonlinear Schrodinger equation numerically. For an…
As a formal approximation, the nonlinear Schr\"{o}dinger (NLS) equation can be derived to describe the evolution of the envelopes of small oscillating wave packets-like solutions to the Euler-Poisson system. In this paper we rigorously…
In this work, we consider a Bose-Einstein condensate in the self-focusing regime, confined transversely by a funnel-like potential and axially by a double-well potential formed by the combination of two inverted P\"oschl-Teller potentials.…
As a genuine many-body entanglement, spin squeezing (SS) can be used to realize the highly precise measurement beyond the limit constrained by classical physics. Its generation has attracted much attention recently. It was reported that $N$…
We study the cubic-quartic nonlinear Schr\"odinger equation (NLS) in two and three spatial dimension. This equation arises in the mean-field description of Bose-Einstein condensates with Lee-Huang-Yang correction. We first prove global…
We propose a unified description of two important phenomena: color confinement in large-$N$ gauge theory, and Bose-Einstein condensation (BEC). We focus on the confinement/deconfinement transition characterized by the increase of the…
Starting from first principle many-body quantum dynamics, we show that the dynamics of Bose-Einstein condensates can be approximated by the time-dependent nonlinear Gross-Pitaevskii equation, giving a bound on the rate of the convergence.…
We consider the dynamics of a 2D Bose gas with an interaction potential of the form $N^{2\beta-1}w(N^\beta\cdot)$ for $\beta\in (0,3/2)$. The interaction may be chosen to be negative and large, leading to the instability regime where the…
We theoretically examine the vortex states of a gas of trapped quasi-two-dimensional ultracold bosons subject to a density-dependent gauge potential, realizing an effective nonlinear rotation of the atomic condensate, which we also show is…
We analyze the possibility that due to their superfluid properties some compact astrophysical objects may contain a significant part of their matter in the form of a Bose-Einstein condensate. To study the condensate we use the…
We study the time evolution of a quantum particle in a Gaussian random environment. We show that in the weak coupling limit the Wigner distribution of the wave function converges to a solution of a linear Boltzmann equation globally in…
We consider a non-relativistic quantum gas of $N$ bosonic atoms confined to a box of volume $\Lambda$ in physical space. The atoms interact with each other through a pair potential whose strength is inversely proportional to the density,…
We consider the cubic nonlinear Schr\"odinger equation (NLS) in any spatial dimension, which is a well-known example of an infinite-dimensional Hamiltonian system. Inspired by the knowledge that the NLS is an effective equation for a system…
For $N$ hard-core bosons on an arbitrary lattice with $d$ sites and independent of additional interaction terms we prove that the hard-core constraint itself already enforces a universal upper bound on the Bose-Einstein condensate given by…
The existence and stability of solitonic states in one-dimensional repulsive Bose-Einstein condensates is investigated within a fully many-body framework by considering the limit of infinite repulsion (Tonks-Girardeau gas). A class of…
We demonstrate the existence of bright solitons in a repulsively interacting, harmonically trapped quasi-one-dimensional Bose-Einstein condensate described by the Gross-Pitaevskii equation. Using a neural-network quantum state (NNQS)…
We study the time evolution of the Nelson model in a mean-field limit in which N non-relativistic bosons weakly couple (w.r.t. the particle number) to a positive or zero mass quantized scalar field. Our main result is the derivation of the…