Application of potential harmonic expansion method to BEC: Thermodynamic properties of trapped 23 Na atoms
TL;DR: In this paper, the authors adopt the potential harmonics expansion method for anab initio solution of the many-body system in a Bose condensate containing interacting bosons.
Abstract: We adopt the potential harmonics expansion method for anab initio solution of the many-body system in a Bose condensate containing interacting bosons. Unlike commonly adopted mean-field theories, our method is capable of handling two-body correlation properly. We disregard three- and higher-body correlations. This simplification is ideally suited to dilute Bose Einstein condensates, whose number density is required to be so small that the interparticle separation is much larger than the range of two-body interaction to avoid three- and higher-body collisions, leading to the formation of molecules and consequent instability of the condensate. In our method we can incorporate realistic finite range interactions. We calculate energies of low-lying states of a condensate containing23Na atoms and some thermodynamical properties of the condensate.
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TL;DR: In this article, a modification of the potential harmonic expansion method (including a short range correlation function in the expansion basis) to solve the many-body Schr\"odinger equation was proposed.
Abstract: We investigate Bose-Einstein condensates (BEC) containing a large number of bosonic atoms interacting via a finite-range semirealistic interatomic interaction. Ground state properties for an increasing number of atoms in the condensate have been calculated using a modification of the potential harmonic expansion method (including a short range correlation function in the expansion basis) to solve the many-body Schr\"odinger equation. An improved numerical algorithm for the calculation of the potential matrix elements permits us to have up to 14 000 atoms in the condensate. Although our approach is approximate and justified for dilute condensates, our results agree well with available diffusion Monte Carlo results for the same case. The ground state energies also agree well with those by the Gross-Pitaevskii equation method for up to 100 particles in the trap and become gradually larger than the latter (up to 5% for 14 000 atoms). The difference is attributed to the effects of finite range interatomic interaction and two-body correlations. Our approach presents a clear physical picture of the condensate, being computationally economical at the same time.
36 citations
Dissertation•
01 Mar 2012
2 citations
Cites methods from "Application of potential harmonic e..."
...The PHEM is one of them....
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...The main concern in this chapter was the mathematical derivation of the PHEM and the IDEA....
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...But as A increases, one faces similar difficulties as in the PHEM....
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...We mention also the Quantum Monte Carlo Methods (QMC) [6, 10], Variational Methods [11, 12], the Cluster Reduction Method (CRM) [13, 14], the IntegroDifferential Equation Approach (IDEA) [15, 16, 17, 18, 19, 20] and the Potential Harmonic Expansion Method (PHEM) [21, 22, 23, 25, 27, 28, 29]....
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...But unlike in the case of the PHEM, once the Faddeev amplitude has been expanded, it is projected on the space of the coordinate rij ....
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TL;DR: In this paper, an approximate but ab initio many-body approach, viz., potential harmonics expansion method (PHEM), which includes two-body correlations for dilute Bose-Einstein condensates, is presented and examined.
Abstract: We present and examine an approximate but ab initio many-body approach, viz., potential harmonics expansion method (PHEM), which includes two-body correlations for dilute Bose-Einstein condensates. Comparing the total ground state energy for three trapped interacting bosons calculated in PHEM with the exact energy, the new method is shown to be very good in the low density limit which is necessary for achieving Bose-Einstein condensation experimentally.
1 citations
TL;DR: In this paper , the S-state energy of Coulombic three-body systems (N Z+ μ − e −) consisting of a positively charged nucleus of charge number Z, a negatively charged muon (μ −) and an electron (e −) was investigated in the framework of few-body (i.e., two-and threebody) cluster model approach.
Abstract: Lowest bound S-state energy of Coulombic three-body systems (N Z+ μ − e −) consisting of a positively charged nucleus of charge number Z (N Z+), a negatively charged muon (μ −) and an electron (e −), is investigated in the framework of few-body (i.e., two- and three-body) cluster model approach. For the three-body cluster model, we adopted the hyperspherical harmonics expansion (HHE) method. An approximated two-body model calculation is also performed for all the three-body systems considered here. A Yukawa-type screened Coulomb potential with an arbitrary screening parameter (λ) is chosen for the two-body subsystems of the three-body system. In the resulting Schrödinger equation (SE), the three-body relative wave function is expanded in the complete set of hyperspherical harmonics (HH). The use of the orthonormality of HH in the SE leads to a set of coupled differential equations (CDEs) which are solved numerically for a manageable basis size to get the energy (E). The pattern of convergence in energy relative to increasing basis size is also investigated. Results are compared with some of those found in the literature.
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46,339 citations
"Application of potential harmonic e..." refers background in this paper
...where wl(z) = (1iz)fi(1+z)fl is the weight function of the Jacobi polynomials [ 13 ]....
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...2K+l(`) is a function related to the Jacobi polynomial [ 13 ] and Y0(Di3) is the HH of order zero in 3(N i 1)-dimensional space....
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...[12], h fifl K is the norm of the Jacobi polynomial [ 13 ] and...
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TL;DR: In this article, the authors reviewed the Bose-Einstein condensation of dilute gases in traps from a theoretical perspective and provided a framework to understand the main features of the condensation and role of interactions between particles.
Abstract: 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.
4,782 citations
01 Jan 2001
TL;DR: In this paper, a unified introduction to the physics of ultracold atomic Bose and Fermi gases for advanced undergraduate and graduate students, as well as experimentalists and theorists is provided.
Abstract: Since an atomic Bose-Einstein condensate, predicted by Einstein in 1925, was first produced in the laboratory in 1995, the study of ultracold Bose and Fermi gases has become one of the most active areas in contemporary physics. This book explains phenomena in ultracold gases from basic principles, without assuming a detailed knowledge of atomic, condensed matter, and nuclear physics. This new edition has been revised and updated, and includes new chapters on optical lattices, low dimensions, and strongly-interacting Fermi systems. This book provides a unified introduction to the physics of ultracold atomic Bose and Fermi gases for advanced undergraduate and graduate students, as well as experimentalists and theorists. Chapters cover the statistical physics of trapped gases, atomic properties, cooling and trapping atoms, interatomic interactions, structure of trapped condensates, collective modes, rotating condensates, superfluidity, interference phenomena, and trapped Fermi gases. Problems are included at the end of each chapter.
3,534 citations
TL;DR: In this paper, a unified introduction to the physics of ultracold atomic Bose and Fermi gases for advanced undergraduate and graduate students, as well as experimentalists and theorists is provided.
Abstract: Since an atomic Bose-Einstein condensate, predicted by Einstein in 1925, was first produced in the laboratory in 1995, the study of ultracold Bose and Fermi gases has become one of the most active areas in contemporary physics. This book explains phenomena in ultracold gases from basic principles, without assuming a detailed knowledge of atomic, condensed matter, and nuclear physics. This new edition has been revised and updated, and includes new chapters on optical lattices, low dimensions, and strongly-interacting Fermi systems. This book provides a unified introduction to the physics of ultracold atomic Bose and Fermi gases for advanced undergraduate and graduate students, as well as experimentalists and theorists. Chapters cover the statistical physics of trapped gases, atomic properties, cooling and trapping atoms, interatomic interactions, structure of trapped condensates, collective modes, rotating condensates, superfluidity, interference phenomena, and trapped Fermi gases. Problems are included at the end of each chapter.
3,017 citations
TL;DR: In this paper, the authors present a tutorial review of some ideas that are basic to our current understanding of Bose-Einstein condensation in the dilute atomic alkali gases, with special emphasis on the case of two or more coexisting hyperfine species.
Abstract: The author presents a tutorial review of some ideas that are basic to our current understanding of the phenomenon of Bose-Einstein condensation (BEC) in the dilute atomic alkali gases, with special emphasis on the case of two or more coexisting hyperfine species. Topics covered include the definition of and conditions for BEC in an interacting system, the replacement of the true interatomic potential by a zero-range pseudopotential, the time-independent and time-dependent Gross-Pitaevskii equations, superfluidity and rotational properties, the Josephson effect and related phenomena, and the Bogoliubov approximation.
1,695 citations