Fast transitionless expansion of cold atoms in optical Gaussian-beam traps

Abstract

We study fast expansions of cold atoms in a three-dimensional Gaussian-beam optical trap. Three different methods to avoid final motional excitation are compared: inverse engineering using Lewis-Riesenfeld invariants, which provides the best overall performance, a bang-bang approach, and a fast adiabatic approach. We analyze the excitation effect of anharmonic terms, radial-longitudinal coupling, and radial-frequency mismatch. In the inverse-engineering approach these perturbations can be suppressed or mitigated by increasing the laser beam waist.

Ehrenfest dynamics and frictionless cooling methods

“…These are exactly the forms obtained by Muga and collaborators [30] and despite the decoupling of the radial and axial coordinates, ω 2 r (t) and ω…”

“…We shall take the minimum Rayleigh length that permits paraxial approximation, z R = 2w 0 (typically z R is much larger, for example z R = 24w 0 in [30]). Also we choose the small beam waist of w 0 =20 and 200 harmonic oscillator lengths, based on the fact that the size of a typical beam waist can range from w 0 = 8µm (as in [30] which is of the order 53 harmonic oscillator lengths for 87 Rb atoms) to sizes of order 0.3 mm (corresponding to roughly 2, 000 harmonic oscillator lengths). Figure 3 shows the Π vs. ρ phase diagram, where the top row presents the phase space diagram for the radial variables Π r and ρ r and the bottom row is for the axial variables Π z and ρ z .…”

Shortcuts to adiabaticity: Fast-forward approach

“…Among other approaches let us mention (i) a transitionless tracking algorithm or "counterdiabatic" approach that adds to the original Hamiltonian extra terms to cancel transitions in the adiabatic or superadiabatic bases [8][9][10][11][12][13]; (ii) inverse engineering of the external driving [3,4,6,[21][22][23][24][25][26] based on Lewis-Riesenfeldt invariants [27], which has been applied in several expansion experiments [25,26]; (iii) optimal control (OC) methods [5,7,14,16], sometimes combined with other methods to enhance their performance [4,5,7]; (iv) the fast-forward (FF) approach advocated by Masuda and Nakamura [19,28]; (v) parallel adiabatic passage [29][30][31][32].…”

Fast and stable manipulation of a charged particle in a Penning trap

“…Torrontegui et al [15] studied the fast expansions of cold atoms in a three-dimensional Gaussian-beam optical trap. The radial and axial frequencies are coupled and as a consequence some shortcut schemes that work in 1D were in fact restricted to certain parameter domains, and others failed completely.…”