The stability of trapped interacting bosons with attractive interactions is studied using an approximate many-body calculation. Instead of using the traditional hyperspherical harmonics expansion method we prescribe a potential harmonics expansion method (PHEM). The justification of the use of PHEM in connection with dilute condensates is presented. The choice of a correlation function is justified as it correctly reproduces the short-range two-body correlation in the wavefunction as also the correct value of the s-wave scattering length (as). Applications to 7Li and 85Rb condensates with the realistic van der Waals interaction give good agreement with the Rice and JILA experiments, respectively. The JILA experiment used controlled collapse of the 85Rb condensate for different values of as. Our calculations agree with the experimental results within the experimental error bars. © 2007 IOP Publishing Ltd.

TAPAN DAS

Ancient Indian History and Culture

A KUNDU

B CHAKRABARTI

University of Calcutta (informally known as Calcutta University or CU) is a collegiate public state university located in Kolkata, West Bengal, India.&nbsp;Within India it is recognized as a &quot;Five-Star University&quot; and accredited &quot;A&quot; Grade by National Assessment and Accreditation Council.

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The University of Calcutta has secured the Fifth position among the Universities of India in the prestigious &quot;Indian University Ranking 2019&quot; list, released by the NIRF of the Ministry of Human Resource Development, Government of India.

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It was established on 24 January 1857, and was one of the first institutions in Asia to be established as a multidisciplinary and Western-style university. Its alumni and faculty include several heads of state, heads of government, social reformers, prominent artists, only academy award winner and Dirac medal winner in India, many Fellows of the Royal Society and five Nobel laureates as of 2019 which is highest in South Asia.

University Of Calcutta

An approximate many-body calculation for trapped bosons with attractive interaction

Journal of Physics B: Atomic, Molecular and Optical Physics

By using a correlated many body method and using the realistic van der Waals potential we study several statistical measures like the specific heat, transition temperature and the condensate fraction of the interacting Bose gas trapped in an anharmonic potential. As the quadratic plus a quartic confinement makes the trap more tight, the transition temperature increases which makes more favourable condition to achieve Bose-Einstein condensation (BEC) experimentally. BEC in 3D isotropic harmonic potential is also critically studied, the correction to the critical temperature due to finite number of atoms and also the correction due to inter-atomic interaction are calculated by the correlated many-body method. Comparison and discussion with the mean-field results are presented. © 2014 EDP Sciences, SIF, Springer-Verlag Berlin Heidelberg.

Fulltext

European Physical Journal D

Condensate fraction and critical temperature of interacting Bose gas in anharmonic trap

A two-body correlated basis set is used to develop a many-body theory which is valid for any number of bosons in the trap. The formalism incorporates the van der Waals interaction and two-body correlations in an exact way. The theory has successfully been applied to Bose-Einstein condensates - dilute weakly interacting and also dilute but having a large scattering length. Even in the extreme dilute condition, we observe the breakdown of the shape-independent approximation and the interatomic correlation plays an important role in the large particle-number limit. This correlated many-body calculation can handle, within the two-body correlation approximation, the entire range of atom number of experimentally achieved condensates. Next we successfully push the basis function for large scattering lengths where the mean-field results are manifestly bad. The sharp increase in correlation energy clearly shows the beyond-mean-field effect. We also calculate one-particle densities for various scattering lengths and particle numbers. Our many-body calculation exhibits the finite-size effect in the one-body density. © 2013 American Physical Society.

Physical Review A - Atomic, Molecular, and Optical Physics

Beyond mean-field ground-state energies and correlation properties of a trapped Bose-Einstein condensate

A simple method to calculate ground state energies for a typical condensates containing up to A ~ 107 atoms is presented. The method, based on the expansion of the wave function in terms of the Faddeev components, which in turn are expanded in terms of potential harmonics is numerically efficient. We obtain ground state results for condensates of 87Rb containing up to A → 108 atoms. The results agree very well with other methods in regions where the other methods are valid. © 2013 Springer-Verlag Wien.

Few-Body Systems

A Few-Body Approach to Bose-Einstein Condensation

We report exact numerical calculations of the chemical potential, condensate fraction and specific heat of N non-interacting bosons confined in an isotropic harmonic oscillator trap in one, two and three dimensions, as also for interacting bosons in a 3D trap. Quasi phase transitions (QPT) are observed in all these cases, including in one-dimension, as shown by a rapid change of several thermodynamic quantities at the transition point. The change becomes more rapid as N increases in 2D and 3D cases. However with increase in N, the sudden change in the nature of specific heat, gets gradually wiped out in 1D, while it becomes more drastic in 2D and 3D. But the sudden changes in the condensate fraction and chemical potential become more drastic as N increases, even in 1D. This shows that a QPT is possible in 1D also. We define the transition exponent, which characterizes the nature of a thermodynamic quantity at the transition point of a quasi phase transition, and evaluate them by careful numerical calculations, very near the transition temperature. These exponents are found to be independent of the size of the system. They are also the same for interacting and non-interacting bosons. These demonstrate the universality property of the transition exponents. © 2013 Springer Science+Business Media New York.

Journal of Low Temperature Physics

Thermodynamic properties of ultracold bose gas: Transition exponents and universality

A correlated many-body calculation is presented to characterize the Shannon information entropy of trapped interacting bosons. We reformulate the one-body Shannon information entropy in terms of the one-body probability density. The minimum limit of the entropy uncertainty relation is approached by making N very small in our numerical work. We examine the effect of correlations in the calculation of information entropy. Comparison with the mean-field result shows that the correlated basis function is indeed required to characterize the important features of the information entropies. We also accurately calculate the point of critical instability of an attractive BEC, which is in close agreement with the experimental value. Next, we calculate two-body entropies in position and momentum spaces and study quantum correlations in the attractive BEC. © 2013 American Physical Society.

Correlated many-body calculation to study characteristics of Shannon information entropy for ultracold trapped interacting bosons

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 Schrödinger equation. An improved numerical algorithm for the calculation of the potential matrix elements permits us to have up to 14000 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 14000 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. © 2007 The American Physical Society.

Behavior of a Bose-Einstein condensate containing a large number of atoms interacting through a finite-range interatomic interaction

We consider a finite number of trapped interacting bosons and present an approximate but ab initio many-body calculation including two-body correlations. The adopted approximation is very well justified for the actual conditions necessary for achieving Bose-Einstein condensation experimentally. The ground state energy is in good agreement with the diffusion Monte Carlo calculation, which is an essentially exact calculation. However, our method is both simple and relatively fast. © 2005 IOP Publishing Ltd.

A finite number of trapped interacting bosons: An approximate many-body calculation

The T=0 properties of a Bose-Einstein condensate (BEC), consisting of A atoms (bosons) trapped by an external field, were investigated. An ab initio treatment of the Schrödinger equation involves 3(A-1) degrees of freedom for the relative motion. The potential matrix elements involved integrals over only three angle variables, leading to an immense reduction in the complexity of the numerical procedure for A particles. It was noticed that many-body results converged towards the mean field results as the particle number increased.

Journal	Data powered by TypesetJournal of Physics B: Atomic, Molecular and Optical Physics
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ISSN	0953-4075