Stable Quantum Resonances in Atom Optics

Abstract

A theory for stabilization of quantum resonances by a mechanism similar to one leading to classical resonances in nonlinear systems is presented. It explains recent surprising experimental results, obtained for cold cesium atoms when driven in the presence of gravity, and leads to further predictions. The theory makes use of invariance properties of the system allowing for separation into independent kicked rotor problems. The analysis relies on a fictitious classical limit where the small parameter is not Planck's constant, but rather the detuning from the frequency that is resonant in the absence of gravity.

Superballistic wavepacket spreading in double kicked rotors

“…For both the QKR and the DQKR with potential V S , the special case of = 2π+˜ (|˜ | 1) is of special interest because it allows one to analyze the system by a classical method [6,11]. This is known as the pseudoclassical limit theory [11], which maps the system onto a virtual classical system by assuming as a virtual Planck constant and taking the virtual classical limit of˜ → 0.…”

“…This is known as the pseudoclassical limit theory [11], which maps the system onto a virtual classical system by assuming as a virtual Planck constant and taking the virtual classical limit of˜ → 0. We find that the pseudoclassical limit theory is also valid in dealing with our DQKR models of non-KAM potentials.…”

“…Based on our understanding of the mechanism for the exponential spreading [6,10], our strategy here is to design variant QKR systems such that the superballistic diffusion can happen in the pseudoclassical limit [11]. Then we show and study the superballistic wavepacket spreading in the original systems, in particular its conditions and characteristics.…”

“…Then we show and study the superballistic wavepacket spreading in the original systems, in particular its conditions and characteristics. This method involves the concepts of quantum resonance [12], quantum antiresonance [12,13], pseudoclassical limit theory [11], Kolmogorov-Arnold-Moser (KAM) systems [14], etc. For recent progress in revealing the general wave propagation properties in quantum mechanics and the roles nonlinearities may play in matter wavepacket dynamics, we refer the reader to refs.…”

Controlling the momentum current of an off-resonant ratchet

“…It has revealed a wide variety of interesting effects including: dynamical localization [2], quantum resonances (QR) [2][3][4], quantum accelerator modes [5,6], and quantum ratchets [7][8][9][10][11][12][13][14][15]. The latter are quantum mechanical systems that display directed motion of particles in the absence of unbalanced forces.…”