We study a dilute gas of attractive bosons confined in a harmonic cylinder, i.e., under cylindric confinement due to a transverse harmonic potential. We introduce a many-body wavefunction which extends the Bethe ansatz proposed by McGuire (1964 J. Math. Phys. 5 622) by including a variational transverse Gaussian shape. We investigate the ground-state properties of the system comparing them with those of the one-dimensional (ID) attractive Bose gas. We find that the gas becomes ultra ID as a consequence of the attractive interaction: the transverse width of the Bose gas reduces by increasing the number of particles up to a critical width below which there is the collapse of the cloud. In addition, we derive a simple analytical expression for the symmetry-breaking solitonic density profile of the ground state, which generalizes the one deduced by Calogero and Degasperis (Calogero F and Degasperis A 1975 Phys. Rev. A 11265). This bright-soliton analytical solution shows near the collapse small deviations with respect to the three-dimensional (3D) mean-field numerical solution. Finally, we show that our variational Gauss-McGuire theory is always more accurate than the McGuire theory. In addition, we prove that, for small numbers of particles, the Gauss-McGuire theory is more reliable than the mean-field theory described by the 3D Gross-Pitaevskii equation.
Beyond mean-field theory for attractive bosons under transverse harmonic confinement
Salasnich L
2006
Abstract
We study a dilute gas of attractive bosons confined in a harmonic cylinder, i.e., under cylindric confinement due to a transverse harmonic potential. We introduce a many-body wavefunction which extends the Bethe ansatz proposed by McGuire (1964 J. Math. Phys. 5 622) by including a variational transverse Gaussian shape. We investigate the ground-state properties of the system comparing them with those of the one-dimensional (ID) attractive Bose gas. We find that the gas becomes ultra ID as a consequence of the attractive interaction: the transverse width of the Bose gas reduces by increasing the number of particles up to a critical width below which there is the collapse of the cloud. In addition, we derive a simple analytical expression for the symmetry-breaking solitonic density profile of the ground state, which generalizes the one deduced by Calogero and Degasperis (Calogero F and Degasperis A 1975 Phys. Rev. A 11265). This bright-soliton analytical solution shows near the collapse small deviations with respect to the three-dimensional (3D) mean-field numerical solution. Finally, we show that our variational Gauss-McGuire theory is always more accurate than the McGuire theory. In addition, we prove that, for small numbers of particles, the Gauss-McGuire theory is more reliable than the mean-field theory described by the 3D Gross-Pitaevskii equation.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
