Quasi one-dimensional Bose–Einstein condensate in a gravito-optical surface trap

Abstract

Abstract. We study both static and dynamic properties of a weakly interacting BoseEinstein condensate (BEC) in a quasi one-dimensional gravito-optical surface trap, where the downward pull of gravity is compensated by the exponentially decaying potential of an evanescent wave. First, we work out approximate solutions of the Gross-Pitaevskii equation for both a small number of atoms using a Gaussian ansatz and a larger number of atoms using the Thomas-Fermi limit. Then we confirm the accuracy of these analytical solutions by comparing them to numerical results. From there, we numerically analyze how the BEC cloud expands non-ballistically, when the confining evanescent laser beam is shut off, showing agreement between our theoretical and previous experimental results. Furthermore, we analyze how the BEC cloud expands non-ballistically due to gravity after switching off the evanescent laser field in the presence of a hard-wall mirror which we model by using a blue-detuned far-off-resonant sheet of light. There we find that the BEC shows significant self-interference patterns for a large number of atoms, whereas for a small number of atoms, a revival of the BEC wave packet with few matter-wave interference patterns is observed.

Retroreflection and diffraction of a Bose–Einstein condensate by evanescent standing wave potential

“…In the following considerations we assume ω y = 2π × 12.0 kHz , which fulfills the quasi two-dimensional condition ω y >> ω ⊥ for the ESWP experiment. As the BEC does not penetrate very far into the repulsive ESWP, it is hardly influenced by the Van-der-Waals potential, which follows from the above values of the GOST experiment 30 . In order to do the numerical simulation, we use the dimensionless equation as here, we consider dimensional spatial coordinates z = κz and x = κx , the dimensionless time t = t(mg)/ κ and the two-particle dimensionless interaction strength G = N2 √ 2πãk/ã y , here, ã = aκ being a dimensionless s-wave scattering length, ã y = a y κ is the dimensionless oscillator length along the y-axis, and k = 2 κ 3 /(g m 2 ) defines the dimensionless kinetic energy constant.…”

“…Previously, we have studied the behavior of Cs BEC in a quasi-1D GOST, we developed an analytical approximate solution of GOST and compared with numerical simulations and with Innsbruck experimental data 30 . The analytical solution of this complicated problem is only possible around GOST minimum harmonic potential 30 . However, the system gets quite complected when the anharmonicities started to play the role, therefore, it is not possible to solve this research problem analytically.…”

“…In order to have a concrete set-up in mind, we will use for our analysis the following parameter values which stem from the GOST experiment 20,30 . We denote the number N of Cs atoms, where the s-wave scattering length amounts to a = 440 a 0 with the Bohr radius a 0 .…”

Two-soliton molecule bouncing in a dipolar Bose–Einstein condensates under the effect of gravity

“…Figure 2 illustrates the parametric excitation of the two-soliton molecule. Ordinary differential equations (23) and (24) If the coefficient of nonlocal nonlinearity γ(t) = 2d 2 ρ(t) of a system vary periodically with time ρ(t) = 1 + ε sin(ω 0 t + ϕ 0 ), then an equilibrium position can be unstable, even if it stable for each fixed value of the parameter. This instability is what makes it possible for the parametric excitation of the two-siliton molecule to appear.…”

“…Mitschke's group described the first experimental demonstration of the existence of temporal optical soliton molecules. In recent experiment 14 with ultracold polar molecules, full control over the internal states of ultracold 23 Na 87 Rb polar molecules was obtained. The authors used the microwave spectroscopy to control the rotational and hyperfine states of ultracold ground state 23 Na 87 Rb polar molecules, which were created by them.…”