Abstract We study the ground-state entanglement between two atoms in a two-dimensional isotropic harmonic trap. We consider a finite-range soft-core interaction that can be applied to simulate various atomic systems. We provide detailed results on the dependence of the correlations on the parameters of the system. Our investigations show that in the hardcore limit, the wave function can be approximated as the product of the radial and angular components regardless of the interaction range. This implies that the radial and angular correlations are independent of one another. However, correlations within the radial and angular components persist and are heavily influenced by the interaction range. The radial correlations are generally weaker than the angular correlations. When soft-core interactions are considered, the correlations exhibit more complex behavior.
We study the ground-state correlations between two atoms in a two-dimensional isotropic harmonic trap. We consider a finite-range soft-core interaction that can be applied to simulate various atomic systems. We provide detailed results on the dependence of the correlations on the parameters of the system. Our investigations show that in the hardcore limit, the wave function can be approximated as the product of the radial and angular components regardless of the interaction range. This implies that the radial and angular correlations are independent of one another. However, correlations within the radial and angular components persist and are heavily influenced by the interaction range. The radial correlations are generally weaker than the angular correlations. When soft-core interactions are considered, the correlations exhibit more complex behavior.
Trapped Bose-Einstein condensates (BECs) differ considerably from the standard textbook example of a uniform Bose gas. In an isotropic harmonic potential V(r) = ½Mω2 r 2, the single-particle ground state introduces a new intrinsic scale of length [the ground-state size d = √ℏ/(Mω)] and energy [the ground-state energy E 0 =
23 ℏω]. When the trap rotates at a low angular velocity, the behavior of a single vortex illustrates the crucial role of discrete quantized vorticity. For more rapid rotation, the condensate contains a vortex array. The resulting centrifugal forces expand the condensate radially and shrink it axially; thus, the condensate becomes effectively two dimensional. If the external rotation speed approaches the frequency of the radial harmonic confining potential, the condensate enters the “lowest-Landau-level” regime, and a simple description again becomes possible. Eventually, the system is predicted to make a quantum phase transition to a highly correlated state analogous to the fractional quantum Hall states of electrons in a strong magnetic field.