Direct measurement of wave-packet dynamics

Antonio Boulhosa Nassar

A new quantum mechanical description of the dynamics of wave packet under continuous measurement is formulated via Bohmian mechanics. The solution to this equation is found through a wave packet approach which establishes a direct correlation between a classical variable with a quantum variable describing the dynamics of the center of mass and the width of the wave packet. The approach presented in this paper gives a comparatively clearer picture than approaches using restrited path integrals and master equation approaches. This work shows how the extremely irregular character of classical chaos can be reconciled with the smooth and wavelike nature of phenomena on the atomic scale. It is demonstrated that a wave packet under continuous quantum measurement displays both chaotic and non-chaotic features. The Lyapunov characteristic exponents for the trajectories of classical particle and the quantum wave packet center of mass are calculated and their chaoticities are demonstrated to be about the same. Nonetheless, the width of the wave packet exhibits a non-chaotic behavior and allows for the possibility to beat the standard quantum limit by means of transient, contractive states.

Rajendran Saravanan, Aniruddha Chakraborty

William Goldshlag

High resolution quantum beat spectroscopy has been realized to study atomic wave packet dynamics. Wave packets comprising pairs of low quantum number (n = 5 - 8) electronic states were formed in Rb vapor with ultrafast laser pulses, and their dynamics was observed by an all-optical technique of parametric four wave mixing (PFWM). The experimental apparatus designed, constructed and automated for this work provided unprecedented signal intensity that enabled time-frequency-resolved analysis of wave packet dynamics with picosecond temporal resolution over the course of 1100 ps. Both time-resolved and non-time-resolved discrete Fourier methods were applied to measure the concurrent formation of multiple wave packets. Many novel effects and interactions have been measured either for the first time or with greatly improved signal-to-noise ratio. Among them were the formation of the 8S1/2 - 6D5/2 wave packet that was not directly excited by the ultrafast radiation, formation and relative dynamics of quantum beating harmonics up to 73 THz, and quantum beating revivals. The effects of vapor number density and temperature were analyzed experimentally. Interference between the 7S1/2 - 5D5/2 and 8S1/2 - 6D5/2 wave packets (frequencies of 18.225 THz and 10.73 THz, respectively) has been observed for the first time and will be described in detail.

Ángel S. Sanz, Salvador Miret-Artés

Nikolay Leonidovich Chuprikov

We consider an oblique incidence on a uniform dielectric layer of the plane monochromatic TE- and TM-waves, as well as TE- and TM-polarized wave packets consisting of waves with the same angle of incidence. For each polarization the stationary model is presented, which allows one to uniquely restore the dynamics of the transmitted and reflected components of the incident wave packet at all stages of scattering. On this basis we introduce the concepts of ``true group-delay time"\/ and ``false group-delay time"\/ (the corresponding quantities for transmission and reflection are the same). The former is defined as the difference of two instants in the evolution of the same wave packet, one of which cannot be measured directly. Conversely, the latter is defined as the difference of two instants in the evolution of different wave packets, both can be measured directly. The false group-delay time does not in itself have a physical sense, but plays a key role for an indirect measurement of the true group-delay times of both polarizations.