We report on the realization of a trapped one-dimensional Bose gas and its characterization by means of measuring its lowest lying collective excitations. The quantum degenerate Bose gas is prepared in a 2D optical lattice, and we find the ratio of the frequencies of the lowest compressional (breathing) mode and the dipole mode to be (omega(B)/omega(D))(2) approximately 3.1, in accordance with the Lieb-Liniger and mean-field theory. For a thermal gas we measure (omega(B)/omega(D))(2) approximately 4. By heating the quantum degenerate gas, we have studied the transition between the two regimes. For the lowest number of particles attainable in the experiment the kinetic energy of the system is similar to the interaction energy, and we enter the strongly interacting regime.We report on the realization of a trapped one-dimensional Bose gas and its characterization by means of measuring its lowest lying collective excitations. The quantum degenerate Bose gas is prepared in a 2D optical lattice, and we find the ratio of the frequencies of the lowest compressional (breathing) mode and the dipole mode to be (omega(B)/omega(D))(2) approximately 3.1, in accordance with the Lieb-Liniger and mean-field theory. For a thermal gas we measure (omega(B)/omega(D))(2) approximately 4. By heating the quantum degenerate gas, we have studied the transition between the two regimes. For the lowest number of particles attainable in the experiment the kinetic energy of the system is similar to the interaction energy, and we enter the strongly interacting regime.

arXiv:cond-mat/0307607Physical Review LettersDec 18, 2003533 citations

A study of trapped Bose gas beyond mean-field theory

Arup Banerjee, Manoranjan P. Singh

We study the ground-state properties of dilute Bose gas confined to both isotropic and anisotropic traps to assess the accuracy of Gross-Pitaevskii (GP) theory. To go beyond GP approximation we use Huang-Yang theory of interatomic interaction energy for hard-sphere Bose gas and use a variational method to solve the resulting modified GP equation. We also make an analytic estimate of the corrections due to higher-order terms in the interatomic interaction energy. We find that the corrections are of the order of 1 percent. However, there is a qualitative change in the density profile due to presence of logarithimic term in the interaction energy for large N (number of atoms)We study the ground-state properties of dilute Bose gas confined to both isotropic and anisotropic traps to assess the accuracy of Gross-Pitaevskii (GP) theory. To go beyond GP approximation we use Huang-Yang theory of interatomic interaction energy for hard-sphere Bose gas and use a variational method to solve the resulting modified GP equation. We also make an analytic estimate of the corrections due to higher-order terms in the interatomic interaction energy. We find that the corrections are of the order of 1 percent. However, there is a qualitative change in the density profile due to presence of logarithimic term in the interaction energy for large N (number of atoms)

arXiv:cond-mat/0009023Sep 2, 20000 citations

Ground-state properties of a trapped Bose gas beyond the mean-field approximation

Arup Banerjee, Manoranjan P. Singh

We study the effect of interatomic correlations beyond the mean-field approximation on the ground-state properties of a trapped Bose gas interacting through a repulsive potential. To this end we employ a variational procedure that is based on the energy functional derived, in the local-density approximation, using the low-density expansion for the ground-state energy of the homogeneous gas. We also make analytic estimates of the corrections due to the higher-order terms in the expansion. We find that corrections are of the order of $1%.$ However, there is a qualitative change in the density profile for large N (number of atoms) due to presence of a logarithmic term in the expansion.We study the effect of interatomic correlations beyond the mean-field approximation on the ground-state properties of a trapped Bose gas interacting through a repulsive potential. To this end we employ a variational procedure that is based on the energy functional derived, in the local-density approximation, using the low-density expansion for the ground-state energy of the homogeneous gas. We also make analytic estimates of the corrections due to the higher-order terms in the expansion. We find that corrections are of the order of $1%.$ However, there is a qualitative change in the density profile for large N (number of atoms) due to presence of a logarithmic term in the expansion.

Physical Review ANov 9, 200123 citations

Interaction energy of a Bose gas in a harmonic trap

Mingzhe Li, Haixiang Fu, You-Hua Luo +1 more

Physics Letters AAug 1, 20022 citations

1%.

However, there is a qualitative change in the density profile for large N (number of atoms) due to presence of a logarithmic term in the expansion.