We study the ground state pair-correlation properties of a weakly interacting trapped Bose gas in three dimensions by using a correlated many-body method. The use of the van der Waals interaction potential and an external trapping potential shows realistic features. We also test the validity of shape-independent approximation in the calculation of correlation properties. © 2010 American Institute of Physics.

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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

Journal of Chemical Physics

We study the ground-state and the low-lying excitations of a trapped Bose gas in an isotropic harmonic potential for very small (∼ 3) to very large (∼ 10 7) particle numbers. We use the two-body correlated basis functions and the shape-dependent van der Waals interaction in our many-body calculations. We present an exhaustive study of the effect of inter-atomic correlations and the accuracy of the mean-field equations considering a wide range of particle numbers. We calculate the ground-state energy and the one-body density for different values of the van der Waals parameter C6. We compare our results with those of the modified Gross–Pitaevskii results, the correlated Hartree hypernetted-chain equations (which also utilize the two-body correlated basis functions), as well as of the diffusion Monte Carlo for hard sphere interactions. We observe the effect of the attractive tail of the van der Waals potential in the calculations of the one-body density over the truly repulsive zero-range potential as used in the Gross–Pitaevskii equation and discuss the finite-size effects. We also present the low-lying collective excitations which are well described by a hydrodynamic model in the large particle limit. © 2017, Springer Science+Business Media New York.

Journal of Low Temperature Physics

Use of Two-Body Correlated Basis Functions with van der Waals Interaction to Study the Shape-Independent Approximation for a Large Number of Trapped Interacting Bosons

We report the effects of interaction on thermodynamic properties of a repulsive Bose-Einstein condensate confined in a harmonic trap by using the correlated potential harmonics expansion method. This many-body technique permits the use of a realistic interactomic interaction, which gives rise to the effective long-range interaction of the condensate in terms of the s-wave scattering length. We have computed temperature (T) dependence of the chemical potential, specific heat, condensate fraction, entropy, pressure, and the average energy per particle of a system containing a large number (A) of 87Rb atoms in the Joint Institute for Laboratory Astrophysics (JILA) trap. The repulsion among the interacting bosons results in a small but measurable drop of condensate fraction and critical temperature (Tc), compared to those of a noninteracting condensate. These are in agreement with the experiment. Although all thermodynamic quantities have a strong dependence on A and to a smaller extent on the interatomic interaction, our numerical calculation appears to show that a thermodynamic quantity per particle follows a universal behavior as a function of T/Tc. This shows the importance of Tc for all thermodynamic properties of the condensate. As expected, for T&gt;T c, these properties follow those of a trapped noncondensed Bose gas. © 2013 American Physical Society.

Physical Review A - Atomic, Molecular, and Optical Physics

Effects of interaction on thermodynamics of a repulsive Bose-Einstein condensate

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.

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

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 study coherence of a trapped bosonic cloud with attractive finite-range interaction in a tight harmonic trap. One-body density and pair-distribution function in the ground state for different trap sizes are calculated. We also calculate healing length and the correlation length which signify the presence of high spatial coherence in a very tight trap leading to the destruction of the condensate for a fixed particle number. This is in marked variance with the usual collapse of the attractive metastable condensate when N&gt;Ncr. Thus we investigate the critical frequency and critical size of the trap for the existence of attractive Bose-Einstein condensation. The finite-range interaction gives a nonlocal effect in the effective many-body potential, and we observe a high-density stable branch besides the known metastable branch. Moreover, the new branch shows universal behavior even in the very tight trap. © 2011 American Physical Society.

Destruction of attractive bosonic cloud due to high spatial coherence in tight trap

We present a quantum many body approach with van der Waal type of interaction to achieve 85Rb Bose-Einstein condensate with tunable interaction which has been produced by magnetic field induced Feshbach resonance in the JILA experiment. © 2008 Elsevier B.V. All rights reserved.

Physics Letters, Section A: General, Atomic and Solid State Physics

85Rb Bose-Einstein condensate with tunable interaction: A quantum many body approach

We study the properties of Bose-Einstein condensates with the realistic van der Waals two-body interaction for large numbers of trapped atoms, solving the many-body Schrödinger equation by the potential harmonic expansion method. The effect of different C6 parameters has been critically examined, starting from very few to 14000 atoms to analyze and justify the idea of a shape-independent approximation. It is found that the condensate properties almost remain unchanged when the number of atoms are quite small (∼100), in good agreement with earlier results of Blume and Greene [Phys. Rev. A 63, 063601 (2001)], but we observe the appreciable effect of a long attractive tail when N is large, even in the low-density limit. The above reference considered only 20 atoms which is far from a real experimental situation. Our calculation gives a realistic scenario which justifies the use of a shape-dependent two-body interaction in many-body theories. © 2008 The American Physical Society.

Shape-independent approximation for Bose-Einstein condensates interacting through a van der Waals potential

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

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	Journal of Chemical Physics
Publisher	AMER INST PHYSICS
ISSN	0021-9606
Open Access	Yes