arXiv:cond-mat/9905101 · Physical review. B, Condensed matter

Structure of the Bose-Einstein condensate ground state

A. I. Solomon, Yu-Jie Feng, Vittorio Penna

Published Aug 1, 1999• 18 citations

Abstract

We construct a macroscopic wave function that describes the Bose-Einstein condensate and weakly excited states, using the $\mathrm{SU}(1,1)$ structure of the mean-field Hamiltonian, and compare this state with the experimental values of second- and third-order correlation functions.

DOI: 10.1103/physrevb.60.3044

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arXiv:cond-mat/9905101 · Physical review. B, Condensed matter

Structure of the Bose-Einstein condensate ground state

A. I. Solomon, Yu-Jie Feng, Vittorio Penna

Published Aug 1, 1999• 18 citations

arXiv HTML PDF

Abstract

We construct a macroscopic wave function that describes the Bose-Einstein condensate and weakly excited states, using the

\mathrm{SU}(1,1)

structure of the mean-field Hamiltonian, and compare this state with the experimental values of second- and third-order correlation functions.

DOI: 10.1103/physrevb.60.3044

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The Structure, State and Properties of Matter in Bose-Einstein Condensate

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Abstract: Shows the fundamental structure, state and properties of matter in Bose-Einstein condensate in a new perspective and according to a new theory of atomic structure.

Sep 1, 20150 citations

Variational Wave Function for Inhomogeneous Bose–Einstein Condensate with 3/2-Body Correlations

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We construct a variational wave function for inhomogeneous weakly interacting Bose--Einstein condensates beyond the mean-field approximation by incorporating $3/2$ -body correlations. From our numerical results calculated for a system trapped by a one-dimensional harmonic oscillator, the $3/2$ -body correlations give a contribution comparable to the mean- field energy toward lowering the ground-state energy.We construct a variational wave function for inhomogeneous weakly interacting Bose--Einstein condensates beyond the mean-field approximation by incorporating $3/2$-body correlations. From our numerical results calculated for a system trapped by a one-dimensional harmonic oscillator, the $3/2$-body correlations give a contribution comparable to the mean- field energy toward lowering the ground-state energy.

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We construct a variational wave function for the ground state of weakly interacting bosons that gives a lower energy than the mean-field Girardeau-Arnowitt (or Hartree-Fock-Bogoliubov) theory. This improvement is brought about by incorporating the dynamical 3/2-body processes where one of two colliding non-condensed particles drops into the condensate and vice versa. The processes are also shown to transform the one-particle excitation spectrum into a bubbling mode with a finite lifetime even in the long-wavelength limit. These 3/2-body processes, which give rise to dynamical exchange of particles between the non-condensate reservoir and condensate absent in ideal gases, are identified as a key mechanism for realizing and sustaining macroscopic coherence in Bose-Einstein condensates.We construct a variational wave function for the ground state of weakly interacting bosons that gives a lower energy than the mean-field Girardeau-Arnowitt (or Hartree-Fock-Bogoliubov) theory. This improvement is brought about by incorporating the dynamical 3/2-body processes where one of two colliding non-condensed particles drops into the condensate and vice versa. The processes are also shown to transform the one-particle excitation spectrum into a bubbling mode with a finite lifetime even in the long-wavelength limit. These 3/2-body processes, which give rise to dynamical exchange of particles between the non-condensate reservoir and condensate absent in ideal gases, are identified as a key mechanism for realizing and sustaining macroscopic coherence in Bose-Einstein condensates.

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We construct a variational ground-state wave function of weakly interacting M-component Bose-Einstein condensates beyond the mean-field theory by incorporating the dynamical 3/2-body processes, where one of the two colliding particles drops into the condensate and vice versa. Our numerical results with various masses and particle numbers show that the 3/2-body processes between different particles make finite contributions to lowering the ground-state energy, implying that many-body correlation effects between different particles are essential even in the weak-coupling regime of the Bose--Einstein condensates. We also consider the stability condition for $2$ -component miscible states using the new ground-state wave function. Through this calculation, we obtain the relation $U^{2}_{AB}/U_{AA}U_{BB}<1+α$ , where $U_{ij}$ is the effective contact potential between particles $i$ and $j$ and $α$ is the correction, which originates from the $3/2$ -body and $2$ -body processes.We construct a variational ground-state wave function of weakly interacting M-component Bose-Einstein condensates beyond the mean-field theory by incorporating the dynamical 3/2-body processes, where one of the two colliding particles drops into the condensate and vice versa. Our numerical results with various masses and particle numbers show that the 3/2-body processes between different particles make finite contributions to lowering the ground-state energy, implying that many-body correlation effects between different particles are essential even in the weak-coupling regime of the Bose--Einstein condensates. We also consider the stability condition for $2$-component miscible states using the new ground-state wave function. Through this calculation, we obtain the relation $U^{2}_{AB}/U_{AA}U_{BB}<1+α$, where $U_{ij}$ is the effective contact potential between particles $i$ and $j$ and $α$ is the correction, which originates from the $3/2$-body and $2$-body processes.

arXiv:1802.04937Journal of the Physical Society of JapanFeb 13, 20183 citations

We construct a macroscopic wave function that describes the Bose-Einstein condensate and weakly excited states, using the

\mathrm{SU}(1,1)

structure of the mean-field Hamiltonian, and compare this state with the experimental values of second- and third-order correlation functions.

We construct a variational wave function for inhomogeneous weakly interacting Bose--Einstein condensates beyond the mean-field approximation by incorporating

3/2

-body correlations. From our numerical results calculated for a system trapped by a one-dimensional harmonic oscillator, the

3/2

-body correlations give a contribution comparable to the mean- field energy toward lowering the ground-state energy.

2

-component miscible states using the new ground-state wave function. Through this calculation, we obtain the relation

U^{2}_{AB}/U_{AA}U_{BB}<1+α

, where

U_{ij}

is the effective contact potential between particles

i

and

j

and

α

is the correction, which originates from the

3/2

-body and

2

-body processes.