Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

Physics Reports

Numerical methods for atomic quantum gases with applications to Bose–Einstein condensates and to ultracold fermions

Anna Minguzzi

Published Apr 21, 2004• 141 citations
Publisher
DOI
10.1016/j.physrep.2004.02.001

Related papers

Bose–Einstein condensation

M. Inguscio, L. Fallani

Besides the enormous opportunities offered by spectroscopy and atom interferometry, laser cooling has opened up the possibility of experimentally realizing and manipulating quantum degenerate gases: Bose–Einstein condensates and degenerate Fermionic systems. This chapter starts with an illustration of key experimental techniques, such as magnetic trapping, evaporative cooling, and Feshbach resonances. It then turns to the physics of atomic Bose–Einstein condensates, discussing their superfluid behaviour, their coherence properties, and their application to precise measurements. It also describes the experimental investigation of ultracold Fermi gases and fermionic superfluidity, as well as ongoing research into ultracold polar molecules.

Oxford University Press eBooks•Sep 1, 2013•2 citations

Monte Carlo methods for impurity physics in ultracold Bose quantum gases

Luis A. Peña Ardila

Nature Reviews Physics•Mar 28, 2022•8 citations

Algebraic Bethe ansatz method for the exact calculation of energy spectra and form factors: applications to models of Bose Einstein condensates and metallic nanograins

Jon Links, Huan-Qiang Zhou, Ross H. McKenzie +1 more

In this review we demonstrate how the algebraic Bethe ansatz is used for the calculation of the energy spectra and form factors (operator matrix elements in the basis of Hamiltonian eigenstates) in exactly solvable quantum systems. As examples we apply the theory to several models of current interest in the study of Bose–Einstein condensates, which have been successfully created using ultracold dilute atomic gases. The first model we introduce describes Josephson tunnelling between two coupled Bose–Einstein condensates. It can be used not only for the study of tunnelling between condensates of atomic gases, but for solid state Josephson junctions and coupled Cooper pair boxes. The theory is also applicable to models of atomic–molecular Bose–Einstein condensates, with two examples given and analysed. Additionally, these same two models are relevant to studies in quantum optics. Finally, we discuss the model of Bardeen, Cooper and Schrieffer in this framework, which is appropriate for systems of ultracold fermionic atomic gases, as well as being applicable for the description of superconducting correlations in metallic grains with nanoscale dimensions. In applying all the above models to physical situations, the need for an exact analysis of small-scale systems is established due to large quantum fluctuations which render mean-field approaches inaccurate.

arXiv:nlin/0305049•Journal of Physics A Mathematical and General•Apr 29, 2003•143 citations

Efficient and spectrally accurate numerical methods for computing ground and first excited states in Bose–Einstein condensates

Weizhu Bao, I‐Liang Chern, Fong Yin Lim

Journal of Computational Physics•Jun 22, 2006•167 citations

A numerical study of the ground state and dynamics of atomic–molecular Bose–Einstein condensates

Wei Jiang, Hanquan Wang, Xiang‐Gui Li

Computer Physics Communications•Jun 10, 2013•4 citations

Feshbach resonances in ultracold gases

Cheng Chin, Rudolf Grimm, Paul S. Julienne +1 more

Feshbach resonances are the essential tool to control the interaction between atoms in ultracold quantum gases. They have found numerous experimental applications, opening up the way to important breakthroughs. This review broadly covers the phenomenon of Feshbach resonances in ultracold gases and their main applications. This includes the theoretical background and models for the description of Feshbach resonances, the experimental methods to find and characterize the resonances, a discussion of the main properties of resonances in various atomic species and mixed atomic species systems, and an overview of key experiments with atomic Bose-Einstein condensates, degenerate Fermi gases, and ultracold molecules.

arXiv:0812.1496•Reviews of Modern Physics•Apr 29, 2010•3,854 citations
Besides the enormous opportunities offered by spectroscopy and atom interferometry, laser cooling has opened up the possibility of experimentally realizing and manipulating quantum degenerate gases: Bose–Einstein condensates and degenerate Fermionic systems. This chapter starts with an illustration of key experimental techniques, such as magnetic trapping, evaporative cooling, and Feshbach resonances. It then turns to the physics of atomic Bose–Einstein condensates, discussing their superfluid behaviour, their coherence properties, and their application to precise measurements. It also describes the experimental investigation of ultracold Fermi gases and fermionic superfluidity, as well as ongoing research into ultracold polar molecules.
In this review we demonstrate how the algebraic Bethe ansatz is used for the calculation of the energy spectra and form factors (operator matrix elements in the basis of Hamiltonian eigenstates) in exactly solvable quantum systems. As examples we apply the theory to several models of current interest in the study of Bose–Einstein condensates, which have been successfully created using ultracold dilute atomic gases. The first model we introduce describes Josephson tunnelling between two coupled Bose–Einstein condensates. It can be used not only for the study of tunnelling between condensates of atomic gases, but for solid state Josephson junctions and coupled Cooper pair boxes. The theory is also applicable to models of atomic–molecular Bose–Einstein condensates, with two examples given and analysed. Additionally, these same two models are relevant to studies in quantum optics. Finally, we discuss the model of Bardeen, Cooper and Schrieffer in this framework, which is appropriate for systems of ultracold fermionic atomic gases, as well as being applicable for the description of superconducting correlations in metallic grains with nanoscale dimensions. In applying all the above models to physical situations, the need for an exact analysis of small-scale systems is established due to large quantum fluctuations which render mean-field approaches inaccurate.
Feshbach resonances are the essential tool to control the interaction between atoms in ultracold quantum gases. They have found numerous experimental applications, opening up the way to important breakthroughs. This review broadly covers the phenomenon of Feshbach resonances in ultracold gases and their main applications. This includes the theoretical background and models for the description of Feshbach resonances, the experimental methods to find and characterize the resonances, a discussion of the main properties of resonances in various atomic species and mixed atomic species systems, and an overview of key experiments with atomic Bose-Einstein condensates, degenerate Fermi gases, and ultracold molecules.