Dynamical localization of ultracold sodium atoms

Abstract

We report a study of atomic motion in time-dependent optical potentials. We measure momentum transfer in parameter regimes for which the classical dynamics are chaotic, and observe the quantum suppression of chaos by dynamical localization. The high degree of control over the experimental parameters enables detailed comparisons with theoretical predictions, and opens new avenues for investigating quantum chaos.

Can quantum fractal fluctuations be observed in an atom-optics kicked rotor experiment?

“…In this work, however, we scan a different parameter than the one used in [12], which corresponded to quasimomentum. Here we use the kicking period τ as control parameter, which can be much better controlled in state-of-the-art experiments [10,14,17,18] than the initial value of momentum [11,18,27,28,29]. On the other hand, the use of τ confronts us with a new problem which is discussed in the following section.…”

“…Control over the kicking strength k is granted with a precision of a few percent [11,14]. Anyway, table 1 tells us that a variation of k of the order up to 25% is not crucial.…”

“…In such experiments the cross-over between mixed and completely chaotic classical dynamics can be scanned easily [9,10,11], and hence fractal transmission probabilities could be measured in a regime where classical or semiclassical arguments do not apply.…”

“…Let us call k L the wave number of the optical lattice,τ the flashing period ("kicking" period),p the momentum of the single atom,x its centre-of-mass position, V 0 the maximum potential depth, and M is the atomic mass. It is convenient to adopt rescaled units by noting that p R = k L is the photon recoil momentum and E R = ( k L ) 2 / 2M is the recoil energy [9,11,14]. So we define p =p / 2p R , x =x / 2k L , τ =τ · 8E R / .…”

“…The derivation of the one-period evolution operator exploits the spatial periodicity of the potential by Bloch's theorem [11,16]. This defines quasimomentum β as a constant of the motion, the value of which is the fractional part of the physical momentum p in dimensionless units p = n + β (n ∈ N).…”