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The Journal of Physical Chemistry A

Suppressing the Spreading of Continuum Wave Packets via Chirped Laser Pulses

Corneliu Manescu, Jeffrey L. Krause, Klaus B. Møller, Niels E. Henriksen

Published May 28, 2004• 5 citations
Publisher

Abstract

We investigate the focusing, that is, the reversing of spreading of continuum wave packets created with chirped laser pulses in the weak-field limit. Focusing can be accomplished when a negative position−momentum correlation is created in the wave packet. Specializing to constant and linear (repulsive) potentials, we show analytically that in a constant potential wave packet spreading can be compensated with positively chirped laser pulses, whereas in the linear potential negatively chirped laser pulses are required, in the short-pulse limit. The analytical results for the linear potential are supported by numerical simulations. The results are discussed in the context of a classical model for wave packet focusing.

DOI
10.1021/jp049077q

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We discuss electronic population transfer in diatomic molecules. By analyzing time-dependent wave packets on electronic potential-energy surfaces, we investigate the efficiency and robustness of population transfer with intense, chirped laser pulses. Recently, the magnitude of the population transfer was observed to have a remarkable dependence on the sign of the chirp [J. Cao, C. J. Bardeen, and K. R. Wilson, Phys. Rev. Lett. 80, 1406 (1998)]. In this work we explain the reason for this asymmetry, and show how the frequency detuning, intensity, and chirp rate affect the results. In particular, we demonstrate efficient, robust population transfer for both positive and negative chirps. A Landau-Zener model of multiple avoided crossings is invoked to model the results.
We consider the time evolution of a special class of wave packets representing the motion of a free particle along a line. In order to make contact with an earlier work on s-waves in two or higher dimensions we confine ourselves to wave packets with a probability density that is symmetric with respect to the origin. Here we concentrate on the phenomenon that an appropriately prepared wave packet is focusing before it displays its familiar behavior of spreading. We derive the condition on the wave packet for this effect to occur: the probability density at the origin has to be concave. The translation of this requirement into Wigner phase space reads: the average of the kinetic energy along the momentum axis has to be negative. In this way we identify the origin of this focusing effect of the wave packet as quantum interference.
Linearly chirped femtosecond laser pulses are used to excite ro-vibrational wave packets in lithium dimers from a single well-prepared launch state. Two-photon resonant Raman transitions excite a manifold of rotational states in a coherent superposition. Excitation with positively chirped laser pulses is shown to enhance a quantum beat involving states with lower rotational quantum numbers, whereas negatively chirped pulses enhance a quantum beat between states with higher rotational quantum numbers, thus steering the rotational coherences to higher or lower rotational states. Time-dependent perturbation theory calculations verify the magnitudes and directions of the enhancement as a function of the applied chirp. The quantitative calculations and experimental results demonstrate that excitation with chirped pulses is an effective method for enhancing specific rotational coherences involving higher or lower rotational states.
In this article we discuss possibilities for manipulating a matter wave with time-dependent potentials. Assuming a specific setup on an atom chip, we explore how one can focus, accelerate, reflect, and stop an atomic wave packet, with, for example, electric fields from an array of electrodes. We also utilize this method to initiate coherent splitting or an arbitrary wave form. Special emphasis is put on the robustness of the control schemes. We begin with the wave packet of a single atom and extend this to a Bose-Einstein condensate in the Gross-Pitaevskii picture. In analogy to laser pulse shaping with its wide variety of applications, we expect this work to form the base for more complex time-dependent potentials, eventually leading to matter-wave pulse shaping with numerous applications.
We demonstrate the ability to coherently control ultracold atomic Rb collisions using frequency-chirped light on the nanosecond time scale. For certain center frequencies of the chirp, the rate of inelastic trap-loss collisions induced by negatively chirped light is dramatically suppressed compared to the case of a positive chirp. We attribute this to a fundamental asymmetry in the system: an excited wave packet moves inward on the attractive molecular potential. For a positive chirp, the resonance condition moves outward in time, while for a negative chirp, it moves inward, in the same direction as the excited wave packet; this allows multiple interactions between the wave packet and the light, enabling the wave packet to be returned coherently to the ground state. Classical and quantum calculations support this interpretation.