Zero-temperature Properties of Attractive Bose-Einstein Condensate by Correlated Many-body Approach (original) (raw)
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Physical Review A, 1996
The physical properties and stability of a trapped Bose{Einstein condensate are strongly in uenced by the presence of a net attractive interaction between the particles. In this Letter we describe the spatial distribution, stability, collisional loss rates, and lifetimes for this situation in a weakly interacting trapped atomic gas in the context of mean eld theory. The experimentally important case of 7 Li is discussed in some detail. We show how the condensate contracts and the mean eld becomes unstable as the number of atoms in the condensate are increased. We further show how the number of atoms is limited by the rapid increase in collisional loss rates associated with the contraction of the condensed atomic cloud. PACS numbers: 03.75.Fi, Typeset using REVT E X
Bose-Einstein Condensation of Molecules
Science, 2003
We report on the Bose-Einstein condensation of more than 10 5 Li 2 molecules in an optical trap starting from a spin mixture of fermionic lithium atoms. During forced evaporative cooling, the molecules are formed by three-body recombination near a Feshbach resonance and finally condense in a long-lived thermal equilibrium state. We measured the characteristic frequency of a collective excitation mode and demonstrated the magnetic field–dependent mean field by controlled condensate spilling.
Collective collapse of a Bose-Einstein condensate with attractive interactions
The sixteenth international conference on atomic physics, 1999
Bose-Einstein condensation (BEC) of atoms with attractive interactions is profoundly di erent from BEC of atoms with repulsive interactions, in several respects. We describe experiments with Bose condensates of 7 Li atoms, which are weakly attracting at ultralow temperature. We measure the distribution of condensate occupation numbers occurring in the gas, which shows that the number is limited and demonstrates the dynamics of condensate growth and collapse.
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The stability of a Bose-Einstein condensed state of trapped ultra-cold atoms is investigated under the assumption of an attractive two-body and a repulsive three-body interaction. The Ginzburg-Pitaevskii-Gross (GPG) nonlinear Schrödinger equation is extended to include an effective potential dependent on the square of the density and solved numerically for the s-wave. The lowest collective mode excitations are determined and their dependences on the number of atoms and on the strength of the three-body force are studied. The addition of three-body dynamics can allow the number of condensed atoms to increase considerably, even when the strength of the three-body force is very small compared with the strength of the two-body force. We study in detail the first-order liquid-gas phase transition for the condensed state, which can happen in a critical range of the effective three-body force parameter.
The physics of trapped dilute-gas Bose–Einstein condensates
Physics Reports, 1998
Contents 1. Introduction 4 1.1. The experiments 4 1.2. The theory 7 1.3. Outline 7 2. Ground state properties of dilute-gas Bose-Einstein condensates in traps 8 2.1. Hamiltonian: binary collision model 8 2.2. Mean-field theory 9 2.3. Ground state properties of a condensate with repulsive interactions 10 2.4. Ground state properties of a condensate with attractive interactions 14 2.5. Vortex states 16 2.6. Condensate lifetime 18 2.7. Binary mixtures of Bose-Einstein condensates 19 2.8. Beyond mean-field theory: quantum properties of trapped condensates 20 3. Elementary excitations of a trapped Bose-Einstein condensate 29 3.1. Collective excitations of a trapped Bose-Einstein condensate (at ¹"0) 30 3.2. Propagation of sound in a Bose-Einstein condensate 34 3.3. Decay of collective excitations 35 3.4. Collective excitations of trapped double condensates 36 3.5. Finite temperature excitations 37 4. Light scattering from a Bose-Einstein condensate 40 4.1. Coherent light scattering 40 4.2. Incoherent light scattering 42 4.3. Manipulation of the scattering length via light scattering 47 4.4. Nonlinear atom optics 47 4.5. Interaction with quantised cavity radiation fields 48 5. Broken gauge symmetry in pairs of condensates 48 5.1. Interference of two Bose-Einstein condensates and measurement-induced phase 48 5.2. Collapses and revivals of the interference pattern visibility 54 5.3. Pumping of twin-trap condensates 55 5.4. Detection of broken gauge symmetry via light scattering 56 5.5. Pumping of double condensates via light scattering 58 5.6. Establishment of relative phase via light scattering 59 6. Quantum dynamics of a Bose-Einstein condensate in a double-well potential 60 6.1. Coherent quantum tunnelling 60 6.2. Quantum phase between tunnelling Bose-Einstein condensates 62 7. The atom laser 63 7.1. What is an ''atom laser"? 6 3 7.2. Proposed models 64 7.3. An atom laser based on evaporative cooling 65 7.4. An atom laser based on optical cooling 68 7.5. Output couplers for Bose-Einstein condensates 70 7.6. Higher-order coherence of Bose-Einstein condensates 71 8. Conclusions 72 Appendix A. Bose-Einstein condensation in a weakly interacting gas: Bogoliubov theory 73 A.1. Elimination of the condensate mode 74 A.2. Bogoliubov transformation 74 References 76
Theory of Bose-Einstein condensation in trapped gases
Reviews of Modern Physics, 1999
The phenomenon of Bose-Einstein condensation of dilute gases in traps is reviewed from a theoretical perspective. Mean-field theory provides a framework to understand the main features of the condensation and the role of interactions between particles. Various properties of these systems are discussed, including the density profiles and the energy of the ground state configurations, the collective oscillations and the dynamics of the expansion, the condensate fraction and the thermodynamic functions. The thermodynamic limit exhibits a scaling behavior in the relevant length and energy scales. Despite the dilute nature of the gases, interactions profoundly modify the static as well as the dynamic properties of the system; the predictions of mean-field theory are in excellent agreement with available experimental results. Effects of superfluidity including the existence of quantized vortices and the reduction of the moment of inertia are discussed, as well as the consequences of coherence such as the Josephson effect and interference phenomena. The review also assesses the accuracy and limitations of the mean-field approach.
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Ground state properties of Bose-Einstein condensate of 20000 23 Na atoms confined in isotropic and highly anisotropic magnetic traps in the presence of three-body interaction, in addition to the two-body and hard-core interactions, have been theoretically studied by solving modified highly non-linear Gross-Pitaevskii-Ginzburg (GPG) equation. There is increasingly significant change in the chemical potential, total and differential energies per particle as the aspect ratio, λ, is increased from 0.1 to 1.0, with respect to the corresponding values when only two-body and hard-core interactions are considered. The condensate order parameter changes drastically and becomes quasi 1-dimensional, as λ is varied from 1 to 0.1.