Related papers: Optimization using Bose-Einstein condensation and …
We consider the theory of feedback control of a Bose-Einstein condensate (BEC) confined in a harmonic trap under a continuous measurement constructed via non-destructive imaging. A filtering theory approach is used to derive a stochastic…
We discuss the mean-field approximation for a trapped weakly-interacting Bose-Einstein condensate (BEC) and its connection with the exact many-body problem by deriving the Gross-Pitaevskii action of the condensate. The mechanics of the BEC…
Ensembles of particles governed by quantum mechanical laws exhibit fascinating emergent behavior. Atomic quantum gases, liquid helium, and electrons in quantum materials all show distinct properties due to their composition and…
An efficient multigrid method is proposed to compute the ground state solution of Bose-Einstein condensations by the finite element method based on the combination of the multigrid method for nonlinear eigenvalue problem and an efficient…
A numerical framework is proposed and analyzed for computing the ground state of Bose--Einstein condensates. A gradient flow approach is developed, incorporating both a Lagrange multiplier to enforce the $L^2$ conservation and a free energy…
We give an overview on current experiments on Bose-Einstein condensation (BEC) in a one-dimensional (1D) optical lattice. We introduce measurements of ground state, tunnelling and dynamical properties as well as investigations of atom…
Resonant absorption imaging is a common technique for detecting the two-dimensional column density of ultracold atom systems. In many cases, the system's thickness along the imaging direction greatly exceeds the imaging system's depth of…
In this paper, we prove the energy diminishing of a normalized gradient flow which provides a mathematical justification of the imaginary time method used in physical literatures to compute the ground state solution of Bose-Einstein…
The paper considers Bose-Einstein condensation (BEC) of light in a cavity with medium. In the framework of two-level model we show the effect of gaseous medium on the critical temperature of light condensation in the system. Transition of…
We study the Bose-Einstein condensation (BEC) of a free Bose gas under rigid rotation. The aim is to explore the impact of rotation on the thermodynamic quantities associated with BEC, including the Bose-Einstein (BE) transition temperature…
We consider a special nonconvex quartic minimization problem over a single spherical constraint, which includes the discretized energy functional minimization problem of non-rotating Bose-Einstein condensates (BECs) as one of the important…
Bose-Einstein condensates of ultracold atoms serve as low-entropy sources for a multitude of quantum-science applications, ranging from quantum simulation and quantum many-body physics to proof-of-principle experiments in quantum metrology…
We consider a Bose gas consisting of $N$ particles in $\mathbb{R}^3$, trapped by an external field and interacting through a two-body potential with scattering length of order $N^{-1}$. We prove that low energy states exhibit complete…
We propose a preconditioned nonlinear conjugate gradient method coupled with a spectral spatial dis-cretization scheme for computing the ground states (GS) of rotating Bose-Einstein condensates (BEC), modeled by the Gross-Pitaevskii…
Attempts to create quantum degenerate gases without evaporative cooling have been pursued since the early days of laser cooling, with the consensus that polarization gradient cooling (PGC, also known as "optical molasses") alone cannot…
Applications of Bose-Einstein Condensates (BEC) often require that the condensate be prepared in a specific complex state. Optimal control is a reliable framework to prepare such a state while avoiding undesirable excitations, and, when…
We propose and analyze a new numerical method for computing the ground state of the modified Gross-Pitaevskii equation for modeling the Bose-Einstein condensate with a higher order interaction by adapting the density function formulation…
A new method of cooling positronium down is proposed to realize Bose-Einstein condensation of positronium. We perform detail studies about three processes (1) thermalization processes between positronium and silica walls of a cavity, (2)…
Bose-Einstein condensates (BECs) of neutral atoms constitute an important quantum system for fundamental research and precision metrology. Many applications require short preparation times of BECs, for example, for optimized data…
Squeezed, nonclassical states are an integral tool of quantum metrology due to their ability to push the sensitivity of a measurement apparatus beyond the limits of classical states. While their creation in light has become a standard…