Self-similar approximations for a trapped Bose-Einstein condensate

Abstract

An approximate solution to the Gross-Pitaevskii equation for Bose-Einstein condensate in a spherical harmonic trap is suggested, which is valid in the whole interval of the coupling parameter, correctly interpolating between weak-coupling and strong-coupling limits. This solution is shown to be more accurate than the optimized Gaussian approximation as well as the Thomas-Fermi approximation. The derivation of the solution is based on the self-similar approximation theory. The possibility of obtaining interpolation formulas in the case of nonspherical traps is discussed. 03.75.Fi

Route to turbulence in a trapped Bose-Einstein condensate

“…The possibility of generating strongly nonequilibrium BECs with vortices and other coherent topological modes by modulating the trapping potential was discussed earlier [16][17][18]. The prevailing creation of vortices by such a modulation owes to the fact that vortices with unit circulation are the most stable among all other topological modes.…”

Atomic squeezing under collective emission

“…Since the spin operators, employed for describing finite-level atoms, do not represent real spins, but rather are convenient mathematical tools, one also uses for atomic squeezing the names of dipole squeezing [1,4] or pseudospin squeezing [5]. Recently this type of pseudospin squeezing has been studied for Bose-condensed atoms with two internal states [13], for two-component mixtures [14], and for multimode BoseEinstein condensates [15][16][17]. There is a variety of possible practical applications of atomic squeezing, e.g., for atomic spectroscopy and atomic clocks [6], for atom interferometers [18], and for quantum information processing and quantum computation [19].…”

Kinetic Thomas–Fermi solutions of the Gross–Pitaevskii equation

“…An extension of Ref. [21] to the regime of significant collisional interaction is a difficult venture, which requires further research. In case of a stable KTF-solution, the fact that we can provide the appropriate time-dependent potential, which drives the required current density, is nevertheless a strong indication, that this KTF-solution can be efficiently excited.…”

“…Since we are interested in solutions ψ(x, y), for which the collisional energy gρ is on the same order as the kinetic energy, we cannot directly apply the theory of Ref. [21] to calculate the excitation efficiency. An extension of Ref.…”

“…Thus, temporary application of V mod (x, y, t) should be a means to excite the KTF-solution ψ(x, y), if Ω is adjusted to match the energy difference between ψ(x, y) and the ground state in the lattice potential V (x, y) [21]. Since we are interested in solutions ψ(x, y), for which the collisional energy gρ is on the same order as the kinetic energy, we cannot directly apply the theory of Ref.…”