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Quantum Electronics and Laser Science Conference

Squeezing of atoms in a pulsed optical lattice

M. Leibscher, Ilya Sh. Averbukh

Published Jun 25, 2003• 1 citation
Publisher

Abstract

Summary form only given. Recently, we have proposed an aperiodic kicked-rotor excitation strategy leading to unlimited angular squeezing of rotational wave packets. It has been pointed out that this approach should be useful in several contexts, but it is in the setting of a pulsed optical lattice that we discuss in the present paper. We consider both classical and quantum regimes of preparing ultra-narrow (squeezed) atomic spatial distribution by a proper sequence of laser pulses forming the optical lattice. It is shown that after a linear focusing phenomenon caused by a single pulse, the rainbow-like structures appear in atomic spatial density.

DOI
10.1109/qels.2002.1031140

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Summary form only given. Recently, we have proposed an aperiodic kicked-rotor excitation strategy leading to unlimited angular squeezing of rotational wave packets. It has been pointed out that this approach should be useful in several contexts, but it is in the setting of a pulsed optical lattice that we discuss in the present paper. We consider both classical and quantum regimes of preparing ultra-narrow (squeezed) atomic spatial distribution by a proper sequence of laser pulses forming the optical lattice. It is shown that after a linear focusing phenomenon caused by a single pulse, the rainbow-like structures appear in atomic spatial density.
Semiclassical catastrophes in the dynamics of a quantum rotor (molecule) driven by a strong time-varying field are considered. We show that for strong enough fields, a sharp peak in the rotor angular distribution can be achieved via a time-domain focusing phenomenon, followed by the formation of rainbowlike angular structures. A strategy leading to the enhanced angular squeezing is proposed that uses a specially designed sequence of pulses. The predicted effects can be observed in many processes, ranging from molecular alignment (orientation) by laser fields to heavy-ion collisions, and the trapping of cold atoms by a standing light wave.
We present a detailed theory of spectacular semiclassical catastrophes happening during the time evolution of a kicked quantum rotor [Phys. Rev. Lett. 87, 163601 (2001)]. Both two- and three-dimensional rotational systems are analyzed. It is shown that the wave function of the rotor develops a cusp at certain delay after a kick, which results in a sharply focused rotational wave packet. The cusp is followed by a fold-type catastrophe manifested in the rainbow-type moving singularities. In the three-dimensional case, the rainbows are accompanied by additional singular features similar to the glory structures known in the wave optics. These catastrophes in the time-dependent angular wave function are well described by the appropriate tools of the quasiclassical wave mechanics, i.e., by Airy and Bessel approximations and Pearcey's functions. A scenario of ``cumulative squeezing'' is also presented in which a specially designed train of short kicks produces an unlimited narrowing of the rotor angular distribution. This scenario is relevant to the molecular alignment by short laser pulses, and also to the atom lithography schemes in which cold atoms are focused by an optical standing wave.
We examine the effect of the initial atomic momentum distribution on the dynamics of the atom-optical realisation of the quantum kicked rotor. The atoms are kicked by a pulsed optical lattice, the periodicity of which implies that quasi-momentum is conserved in the transport problem. We study and compare experimentally and theoretically two resonant limits of the kicked rotor: in the vicinity of the quantum resonances and in the semiclassical limit of vanishing kicking period. It is found that for the same experimental distribution of quasi-momenta, significant deviations from the kicked rotor model are induced close to quantum resonance, while close to the classical resonance (i.e. for small kicking period) the effect of the quasi-momentum vanishes.
Motivated by recent experimental progress achieved with ultracold atoms in kilohertz-driven optical lattices, we provide a theoretical discussion of mechanisms governing the response of a particle in a cosine lattice potential to strong forcing pulses with smooth envelope. Such pulses effectuate adiabatic motion of a wave packet's momentum distribution on quasienergy surfaces created by spatiotemporal Bloch waves. Deviations from adiabaticity can then be deliberately exploited for exerting coherent control and for reaching target states which may not be accessible by other means. As one particular example, we consider an analog of the $\ensuremath{\pi}$ pulses known from optical resonance. We also suggest adapting further techniques previously developed for controlling atomic and molecular dynamics by laser pulses to the coherent control of matter waves in shaken optical lattices.
For a series of incoherent and ultracold atoms with an orbital angular momentum (or vortices) released from an optical lattice, we consider the density-density correlation of this freely expanding ultracold gases. Because of the unique phase structure originating from the quantized angular momentum, it is shown that the phase structure plays an important role in the distribution of the density-density correlation through the appearance of crescent-shaped peaks accompanying the ordinary round-shaped peaks. In particular, it is found that the orientation of the crescent-shaped peaks corresponds with the rotation direction of the atoms prepared in the optical lattices.