Propagation of guided cold atoms

Abstract

In this article we focus on the propagation of a beam of particles guided by a transversely confining potential. We consider different regimes. In the classical regime, we describe the beam by means of a set of hydrodynamic-like equations. We apply this formalism in order to investigate two practical ways for increasing the collision rate: by using a constriction or by tilting the guide. A high enough collision rate is indeed the most crucial prerequisite for reaching the quantum degenerate regime by means of evaporative cooling. In the quantum regime, we study the propagation of bosonic atoms through a constriction in two opposite regimes: the collision-less one and the Thomas-Fermi one.

On a Hyperbolic Solution to the Nonlinear Schrödinger Equation for a Square Well Potential Coupled to a Contact Impurity at the Delocalization Threshold

“…14,15 These solutions are found in terms of Jacobi elliptic functions. 2 A local modification in a transverse waveguide, such as a constriction [16][17][18][19] or a local curvature [20][21][22] can be treated by a quasi 1D defect potential. The defect potential will have a number of atoms trapped as a wave-packet goes through the defect.…”

A moving magnetic mirror to slow down a bunch of atoms

“…In the latter techniques, the longitudinal velocity dispersion increases, while the mean velocity decreases [14] since the Liouville theorem applied to a continuous beam dictates in one-dimension the conservation of the productv∆v of the mean velocity of the beam by its dispersion. The thermalization time between transverse and longitudinal degrees of freedom is then drastically increased by this large mismatch in dispersion velocities.…”

“…A longer propagation time in the guide requires a priori an injection at lower velocity, which can be done only at the expense of an increase of τ delay , and therefore of a reduction of the flux. To overcome this limitation, two strategies have been proposed in [14] and experimentally demonstrated in [7]. They consist in slowing down the beam, either by increasing the strength of the transverse confinement with a tapered section, or by implementing an upward slope in the guide.…”

How to reach the collisional regime on a magnetically guided atomic beam

“…In this case, the phase space density and the enthalpy remain constant through the constriction, and the collision rate γ as well as N c increase significantly. Upon compression, the temperature T and the thermal velocity v th = (k B T 0 /m) 1/2 increase, while the velocity of the beam decreases by up to a factor 2 √ 2 [15]. The initial injection velocity should be chosen such that the thermal velocity remains lower than the mean velocity during the compression: M ≡ v b /v th > 1.…”

“…We stress that evaporation during compression could be beneficial, since it enhances the ratio M , allowing for an even lower injection velocity. However, if the optimal injection ratio M is higher due to experimental limitations in the injection region, we still have the possibility to locally tilt the guide in order to increase N c [15].…”