Ballistic and Localized Transport for the Atom Optics Kicked Rotor in the Limit of a Vanishing Kicking Period

Abstract

We present mean energy measurements for the atom optics kicked rotor as the kicking period tends to zero. A narrow resonance is observed marked by quadratic energy growth, in parallel with a complete freezing of the energy absorption away from the resonance peak. Both phenomena are explained by classical means, taking proper account of the atoms' initial momentum distribution.

Experimental verification of a one-parameter scaling law for the quantum and “classical” resonances of the atom-optics kicked rotor

“…For the experiments reported here, the effect of the finite width of the kicking pulses [19,22] turns out to be negligible, since fairly small numbers of kicks (less than 20) and low kicking strengths are used. In the case where the τ → 0 limit is being investigated experimentally, the δ-kick assumption is clearly not valid [13,21]. This restricts us to a minimum period τ = 330 ns, for τ p = 240 ns, in our study of the "classical" resonance peaks.…”

“…This phenomenon is a classical effect in a system with a regular phase space, and has been observed in [13] for the first time. It is distinct from dynamical localization which is the quantum suppression of momentum diffusion for a chaotic phase space [4,12].…”

“…The typical momentum spread of the atomic sample lies between 4 and 8 two-photon recoils. The shape of the initial momentum distribution is well approximated by a Gaussian with standard deviation σ p ≃ (4 − 8) × 2 k L , centered at zero momentum [19], although significant non-Gaussian tails can exist [13]. The width is measured in units of two-photon recoils, corresponding to the wavelength of the kicking laser λ L = 2π/k L .…”

“…The corresponding fitted values of σ p were 5 and 5.2 two-photon recoils respectively which differ from the measured values of 4.53 ± 0.02 and 4.3 ± 0.2. This difference is due to the systematic error involved in determining σ p from the experimental initial momentum distribution (as discussed in [13]). In particular this distribution may have noisy exponential wings [19] which must truncated in order to reliably extract the second moment leading to an underestimation of the true initial momentum spread.…”

“…Since τ → 0, all quasi-momentum subclasses contribute now similarly to the energy growth, and the averaged energy is given only by the initial conditions within the principal nonlinear resonance island (see [13] for details):…”