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Physical Review Letters

Angular Focusing, Squeezing, and Rainbow Formation in a Strongly Driven Quantum Rotor

Ilya Sh. Averbukh, Robert Arvieu

Published Sep 28, 2001• 186 citations
Publisher

Abstract

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.

DOI
10.1103/physrevlett.87.163601

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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.
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.
We consider deflection of polarizable molecules by inhomogeneous optical fields and analyze the role of molecular orientation and rotation in the scattering process. It is shown that molecular rotation induces spectacular rainbowlike features in the distribution of the scattering angle. Moreover, by preshaping molecular angular distribution with the help of short and strong femtosecond laser pulses, one may efficiently control the scattering process, manipulate the average deflection angle and its distribution, and reduce substantially the angular dispersion of the deflected molecules. We study the problem both classically and quantum mechanically and arrive at the same conclusions in both treatments. The effects of strong deflecting field on the scattering of rotating molecules are considered by the means of the adiabatic invariants formalism. The suggested control scheme opens new ways for many applications involving molecular focusing, guiding, and trapping by optical and static fields.
Some quantum optical models possessing a transition from regular to chaotic dynamics and influence of `quantum chaos' to squeezing are investigated. Particular cases of semiclassical dynamics of a single atom and cooperative system of these atoms with (2j + 1)--equidistant levels interacting with a quantized photon mode in an ideal cavity were considered. Corresponding equations of motion are received without the rotation-wave approximation. Chaotic behavior and squeezing degree time dependence were obtained in computer simulations for coupling constant values or order of the atomic frequency.
Squeezed optical fields are a powerful resource for a variety of investigations in basic research and technology. However, the generation of intense squeezed light is challenging. Here, we show that intense squeezed light can be produced using strongly laser driven atoms and the so far unrelated process of high harmonic generation. We demonstrate that when the intensity of the driving field significantly depletes the ground state of the atoms, leading to dipole moment correlations, the quantum state of the driving field and the generated high harmonics are entangled and squeezed. Furthermore, we analyze how the resulting quadrature squeezing of the fundamental laser mode after the interaction can be controlled. The findings open the way for the generation of high intensity squeezed light states for a wide range of applications.
We report a theoretical study of the optical centrifuge acceleration of an asymmetric top molecule interacting with an electric static field by solving the time-dependent Schr\"odinger equation in the rigid rotor approximation. A detailed analysis of the mixing of the angular momentum in both the molecular and the laboratory fixed frames allows us to deepen the understanding of the main features of the acceleration process, for instance, the effective angular frequency of the molecule at the end of the pulse. For the case of the SO2{\mathrm{SO}}_{2}SO2​ molecular super-rotor, we show numerically that it rotates around one internal axis and that its dynamics is confined to the plane defined by the polarization axis of the laser, in agreement with experimental findings. Furthermore, we consider the orientation patterns induced by the dc field, showing the characteristics of their structure as a function of the strength of the static field and the initial configuration of the fields.