Tunneling of Bose—Einstein condensate and interference effect in a harmonic trap with a Gaussian energy barrier

Abstract

The tunneling effect of Bose-Einstein condensate (BEC) in a harmonic trap with a Gaussian energy barrier is studied in this paper. The initial condensate evolves into two separate moving condensates after the tunneling time under certain conditions. The interference pattern between the two moving condensates is given as a comparison and as a further demonstration of the existence of the global phase.

Soliton breathers in spin-1 Bose—Einstein condensates

“…This bright soliton is similar to that illustrated in Ref. [34]. This verifies that when the condensates are trapped in a harmonic trap, stable solitons exist in a finite range of the scattering length.…”

Nonlinear tunneling through a strong rectangular barrier

“…On the other hand, the asymptotic behaviors of these two solutions are quite different when η → 0. For the supersonic solution (11), lim η→0 ρ sup = α 2 √ µ , which is just the downstream density in the linear tunneling case; while a divergence is found for the subsonic solution (12). Since we are looking for the solution that can be reduced to the linear one, only the supersonic solution (11), of a constant form, is studied further.…”

“…For the supersonic solution (11), lim η→0 ρ sup = α 2 √ µ , which is just the downstream density in the linear tunneling case; while a divergence is found for the subsonic solution (12). Since we are looking for the solution that can be reduced to the linear one, only the supersonic solution (11), of a constant form, is studied further. In other words, the superfluid solution does not have any linear counterpart when the chemical potential µ is smaller than the barrier height.…”

“…For restricted systems, such as BECs in a harmonic trap, in a double or triple well, or in an optical lattice, some numerical or theoretical methods have been employed to solve the Gross-Pitaevskii equation (GPE), for example, two-or three-mode approximation, the symplectic method, and the particle swarm optimization (PSO) algorithm. [8][9][10][11][12][13][14] For non-restricted systems, a few methods have been proposed to deal with the nonlinear tunneling problem from various aspects, for example, involving the nonlinear effect only within the barrier, [15] or gradually increasing nonlinear interaction as BECs approaching an atomic quantum dot in a waveguide. [16] The dispersive wave shocks, formed in the upstream when BECs collide with a potential, were suggested to be studied by hydromechanics methods (Riemann invariants).…”

Production and detection of ultracold Cs 2 molecules via four-photon adiabatic passage

“…In recent years, the preparation and quantum control of cold (T > 1 mK) and ultracold (T < 1 mK) molecules have captured much attention of researchers and been one of the most active research subjects in the atomic and molecular physics. [1][2][3][4][5][6] Ultracold molecules have been applied in many fields such as testing fundamental physical constants, [7] precision spectroscopy, [8] and quantum-information processing. [9] Particularly, highly dense samples of molecules in the ground rovibrational state (ν = 0, J = 0) are required in many applications.…”