scholarly journals STABILITY OF BOSE–EINSTEIN CONDENSATES CONFINED IN TRAPS

2000 ◽  
Vol 14 (07) ◽  
pp. 655-719 ◽  
Author(s):  
TAKEYA TSURUMI ◽  
HIROFUMI MORISE ◽  
MIKI WADATI
Keyword(s):  
Time Development ◽  
Theoretical Research ◽  
Einstein Condensation ◽  
Pitaevskii Equation ◽  
Static Properties ◽  
Atomic Vapors ◽  
Dilute Gas ◽  
Two Component ◽  
The Stability ◽  
Bose Einstein

Bose–Einstein condensation has been realized as dilute atomic vapors. This achievement has generated immense interest in this field. This article review of recent theoretical research into the properties of trapped dilute-gas Bose–Einstein condensates. Among these properties, stability of Bose–Einstein condensates confined in traps is mainly discussed. Static properties of the ground state are investigated by using the variational method. The analysis is extended to the stability of two-component condensates. Time-development of the condensate is well-described by the Gross–Pitaevskii equation which is known in nonlinear physics as the no nlinear Schrödinger equation. For the case that the inter-atomic potential is effectively attractive, a singularity of the solution emerges in a finite time. This phenomenon which we call collapse explains the upper bound for the number of atoms in such condensates under traps.

Systems with Condensates and Pairing

2018 ◽  
Author(s):  
Klaus Morawetz
Keyword(s):  
Critical Parameters ◽  
Einstein Condensation ◽  
Cooper Pairs ◽  
Pair Breaking ◽  
Systematic Theory ◽  
Bose Einstein Condensation ◽  
T Matrix ◽  
The Stability ◽  
Bose Einstein

The Bose–Einstein condensation and appearance of superfluidity and superconductivity are introduced from basic phenomena. A systematic theory based on the asymmetric expansion of chapter 11 is shown to correct the T-matrix from unphysical multiple-scattering events. The resulting generalised Soven scheme provides the Beliaev equations for Boson’s and the Nambu–Gorkov equations for fermions without the usage of anomalous and non-conserving propagators. This systematic theory allows calculating the fluctuations above and below the critical parameters. Gap equations and Bogoliubov–DeGennes equations are derived from this theory. Interacting Bose systems with finite temperatures are discussed with successively better approximations ranging from Bogoliubov and Popov up to corrected T-matrices. For superconductivity, the asymmetric theory leading to the corrected T-matrix allows for establishing the stability of the condensate and decides correctly about the pair-breaking mechanisms in contrast to conventional approaches. The relation between the correlated density from nonlocal kinetic theory and the density of Cooper pairs is shown.

BOSE-EINSTEIN CONDENSATION OF ATOMS WITH ATTRACTIVE INTERACTION

1999 ◽  
Vol 13 (05n06) ◽  
pp. 625-631 ◽  
Author(s):  
N. AKHMEDIEV ◽  
M. P. DAS ◽  
A. V. VAGOV
Keyword(s):  
Statistical Physics ◽  
Scattering Length ◽  
Stationary Solutions ◽  
Attractive Potential ◽  
Einstein Condensation ◽  
Pitaevskii Equation ◽  
Bose Einstein Condensation ◽  
Three Body ◽  
Negative Scattering Length ◽  
Bose Einstein

We suggest that crucial effect on Bose-Einstein condensation in systems with attractive potential is three-body interaction. We investigate stationary solutions of the Gross-Pitaevskii equation with negative scattering length and a higher-order stabilising term in presence of an external parabolic potential. Stability properties of the condensate are similar to those for thermodynamic systems in statistical physics which have first order phase transitions. We have shown that there are three possible type of stationary solutions corresponding to stable, metastable and unstable phases. Results are discussed in relation to recently observed 7 Li condensate.

Dynamic vortex evolution of harmonically trapped coupled Bose–Einstein condensate with quintic nonlinearity

2021 ◽  
Author(s):  
Yunsong Guo ◽  
Yubin Jiao ◽  
Xiaoning Liu ◽  
Xiangbo Zhu ◽  
Ying Wang
Keyword(s):  
Periodic Breathing ◽  
Oscillation Period ◽  
Angular Frequency ◽  
Equation Model ◽  
Einstein Condensate ◽  
Pitaevskii Equation ◽  
Atomic Systems ◽  
Bose Einstein Condensate ◽  
Two Component ◽  
Bose Einstein

In this study, we investigate the evolution of vortex in harmonically trapped two-component coupled Bose–Einstein condensate with quintic-order nonlinearity. We derive the vortex solution of this two-component system based on the coupled quintic-order Gross–Pitaevskii equation model and the variational method. It is found that the evolution of vortex is a metastable state. The radius of vortex soliton shrinks and expands with time, resulting in periodic breathing oscillation, and the angular frequency of the breathing oscillation is twice the value of the harmonic trapping frequency under infinitesimal nonlinear strength. At the same time, it is also found that the higher-order nonlinear term has a quantitative effect rather than a qualitative impact on the oscillation period. With practical experimental setting, we identify the quasi-stable oscillation of the derived vortex evolution mode and illustrated its features graphically. The theoretical results developed in this work can be used to guide the experimental observation of the vortex phenomenon in ultracold coupled atomic systems with quintic-order nonlinearity.

scholarly journals Bose-Einstein Condensation of Confined Atomic Gases at Ultra Low Temperatures

2017 ◽  
Vol 9 (5) ◽  
pp. 96
Author(s):  
M. Serhan
Keyword(s):  
Low Temperatures ◽  
Chemical Potential ◽  
Scattering Length ◽  
Einstein Condensation ◽  
Pitaevskii Equation ◽  
Atomic Gases ◽  
Bose Einstein Condensation ◽  
Gaussian Type ◽  
Negative Scattering Length ◽  
Bose Einstein

In this work I solve the Gross-Pitaevskii equation describing an atomic gas confined in an isotropic harmonic trap by introducing a variational wavefunction of Gaussian type. The chemical potential of the system is calculated and the solutions are discussed in the weakly and strongly interacting regimes. For the attractive system with negative scattering length the maximum number of atoms that can be put in the condensate without collapse begins is calculated.

NEW INSIGHT ON THE CHAIN STATES AND BOSE-EINSTEIN CONDENSATE IN LIGHT NUCLEI

2008 ◽  
Vol 17 (10) ◽  
pp. 2150-2154 ◽  
Author(s):  
S. YU. TORILOV ◽  
K. A. GRIDNEV ◽  
W. GREINER
Keyword(s):  
Cluster Model ◽  
Einstein Condensate ◽  
Light Nuclei ◽  
Einstein Condensation ◽  
Pitaevskii Equation ◽  
Deformed Nuclei ◽  
Bose Einstein Condensation ◽  
Bose Einstein Condensate ◽  
Alpha Cluster ◽  
Bose Einstein

The simple alpha-cluster model was used for the consideration of the chain states and Bose-Einstein condensation in the light self-conjugated nuclei. Obtained results were compared with predictions of the shell-model for the deformed nuclei, with calculations based on Gross-Pitaevskii equation and with recent experimental results.

EXCITONS IN A HIGH MAGNETIC FIELD

1996 ◽  
Vol 10 (07) ◽  
pp. 729-775 ◽  
Author(s):  
ANDREI V. KOROLEV ◽  
MICHAEL A. LIBERMAN
Keyword(s):  
Magnetic Field ◽  
Binding Energy ◽  
High Magnetic Field ◽  
Bose Condensate ◽  
Einstein Condensation ◽  
Interacting Electrons ◽  
New States ◽  
The Stability ◽  
Bose Einstein ◽  
Quantization Representation

A high magnetic field, such that the distance between the Landau levels exceeds the binding energy of an exciton, gives an opportunity to create various new states of matter, i.e. exciton crystal, molecular compexes, Bose–Einstein condensation an exciton gas in a semiconductor, depending on the dimensionality of the system. We consider the problem of excitonic interaction in a semiconductor in its multi-electron formulation, starting from the second-quantization representation of the Hamiltonian of interacting electrons and holes in a high magnetic field. A system of excitons in its ground state in a high magnetic field is similar to a weakly non-ideal Bose gas; whereas the excited states may be strongly bounded. It is shown that different types of exciton complexes in a quasi-one-dimensional semiconductor quantum wire, from crystals to molecular chains, can be obtained both by varying the direction and intensity of the magnetic field and by changing the exciton density. The existence and the stability of the Bose condensate in a bulk semiconductor due to an essential decrease of the interaction between excitons and an increase of their binding energy in a high magnetic field are established at a high density of excitons. Existence of the built-in condensate of excitons in a broad density range significantly changes the excitation spectrum of coupled excitons and photons in a high magnetic field and results in a number of interesting optical phenomena.

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