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Wiley eBooks

The physics and chemistry of wave packets

John A. Yeazell, T. Uzer

Published Jan 1, 2000• 70 citations
OpenAlex

Abstract

Wave Packets: Past and Present (M. Nauenberg). Semiclassical Wave Packets (E. Heller). Excitation of Atomic Wave Packets (J. Yeazell). From Asteroids to Atoms: Quantum Wave Packets and the Restricted Three--Body Problem of Celestial Mechanics (E. Lee, et al.). Destruction of Quantum Coherence and Wave Packet Dynamics (G. Alber). Wave Packets and Half--Cycle Pulses (P. Bucksbaum). Exploring Phase Space with Wave Packets (F. Borondo & R. Benito). Wave Packet Dynamics in Small Molecules (M. Braun, et al.). Time Dependent and Time Independent Wave Packet Approaches to Reactive Scattering (S. Althorpe, et al.). Laser--Excited Wave Packets in Semiconductor Heterostructures (K. Leo & M. Koch). Index.

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Exploring multiple degrees of freedom in Rydberg wave packets.

Haidan Wen

Recent advances in the study of Rydberg atoms have focused on the control, manipulation and detection of Rydberg wave packets using novel external fields such as half-cycle pulses. The radial degree of freedom has been controlled and used to process information encoded in Rydberg states. However, these previous experiments make use of only a single degree of freedom, restricting the potential of other degrees of freedom for quantum computing in Rydberg atoms. In this dissertation, we explore the control and detection of other degrees of freedom in an electron wave packet, such as the angular momentum quantum number ℓ, the magnetic quantum number m and the electron spin; so that the full range of quantum numbers can participate in information processing. We first propose an interferometric control of the population of angular momentum states using two time-delayed phase-locked ultrafast laser pulses. The population of arbitrary angular momentum states can be greatly enhanced by optimizing the time delay and the relative phases between two laser pulses. We then qualitatively measure the evolution of angular momentum components in Stark wave packets by a weak half-cycle pulse (HCP). This measurement utilizes a time-delayed HCP and is proved to be effective for detecting various aspects of wave packet dynamics, particularly, the evolution of non-stationary states. The technique relies on the fact that the HCP redistributes the eigenstate populations and induced the population variation which reflects the evolution of eigenstate phases. Finally, we find that the dynamics of m-states could be highly correlated with the internal degree of freedom of the electron, the spin. We study the effect of spin-orbit coupling on the wave packet dynamics and observe the angular precession of a Rydberg wave packet. The population redistribution from p to s states is highly sensitive to the polarization of the HCP and changes with the precession of the electron orbit. We obtain the selection rules and give an intuitive classical interpretation of angular momentum redistribution by an HCP. In short, new dynamics involving multiple degrees of freedom of an electron wave packet are discovered, observed and understood.

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Because the de Broglie wavelength of ultracold molecules is very large, the cross sections for collisions of molecules at ultracold temperatures are always computed by the time-independent quantum scattering approach. Here, we report the first accurate time-dependent wave packet dynamics calculation for reactive scattering of ultracold molecules. Wave packet dynamics calculations can be applied to molecular systems with more dimensions and provide real-time information on the process of bond rearrangement and/or energy exchange in molecular collisions. Our work thus makes possible the extension of rigorous quantum calculations of ultracold reaction properties to polyatomic molecules and adds a new powerful tool for the study of ultracold chemistry.

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Nonlinear wave-packet dynamics for a generic one-dimensional time-independent system and its application to the hydrogen atom in a weak magnetic field

Karine Dupret, Dominique Delande

We study the time propagation of an initially localized wave packet for a generic one-dimensional time-independent system, using the ``nonlinear wave-packet dynamics'' [S. Tomsovic and E. J. Heller, Phys. Rev. Lett. 67, 664 (1991)], a semiclassical approximation using a local linearization of the wave packet in the vicinity of classical reference trajectories. Several reference trajectories are needed to describe the behavior of the full wave packet. The introduction of action-angle variables allows us to obtain a simple analytic expression for the autocorrelation function, and to show that a universal behavior (quantum collapses, quantum revivals, etc.) is obtained via interferences between the reference trajectories. A connection with the standard WKB approach is established. Finally, we apply the nonlinear wave-packet dynamics to the case of the hydrogen atom in a weak magnetic field, and show that the semiclassical expressions obtained by nonlinear wave-packet dynamics are extremely accurate. \textcopyright{} 1996 The American Physical Society.

Physical Review A•Mar 1, 1996•5 citations
Wave Packets: Past and Present (M. Nauenberg). Semiclassical Wave Packets (E. Heller). Excitation of Atomic Wave Packets (J. Yeazell). From Asteroids to Atoms: Quantum Wave Packets and the Restricted Three--Body Problem of Celestial Mechanics (E. Lee, et al.). Destruction of Quantum Coherence and Wave Packet Dynamics (G. Alber). Wave Packets and Half--Cycle Pulses (P. Bucksbaum). Exploring Phase Space with Wave Packets (F. Borondo & R. Benito). Wave Packet Dynamics in Small Molecules (M. Braun, et al.). Time Dependent and Time Independent Wave Packet Approaches to Reactive Scattering (S. Althorpe, et al.). Laser--Excited Wave Packets in Semiconductor Heterostructures (K. Leo & M. Koch). Index.
Recent advances in the study of Rydberg atoms have focused on the control, manipulation and detection of Rydberg wave packets using novel external fields such as half-cycle pulses. The radial degree of freedom has been controlled and used to process information encoded in Rydberg states. However, these previous experiments make use of only a single degree of freedom, restricting the potential of other degrees of freedom for quantum computing in Rydberg atoms. In this dissertation, we explore the control and detection of other degrees of freedom in an electron wave packet, such as the angular momentum quantum number ℓ, the magnetic quantum number m and the electron spin; so that the full range of quantum numbers can participate in information processing. We first propose an interferometric control of the population of angular momentum states using two time-delayed phase-locked ultrafast laser pulses. The population of arbitrary angular momentum states can be greatly enhanced by optimizing the time delay and the relative phases between two laser pulses. We then qualitatively measure the evolution of angular momentum components in Stark wave packets by a weak half-cycle pulse (HCP). This measurement utilizes a time-delayed HCP and is proved to be effective for detecting various aspects of wave packet dynamics, particularly, the evolution of non-stationary states. The technique relies on the fact that the HCP redistributes the eigenstate populations and induced the population variation which reflects the evolution of eigenstate phases. Finally, we find that the dynamics of m-states could be highly correlated with the internal degree of freedom of the electron, the spin. We study the effect of spin-orbit coupling on the wave packet dynamics and observe the angular precession of a Rydberg wave packet. The population redistribution from p to s states is highly sensitive to the polarization of the HCP and changes with the precession of the electron orbit. We obtain the selection rules and give an intuitive classical interpretation of angular momentum redistribution by an HCP. In short, new dynamics involving multiple degrees of freedom of an electron wave packet are discovered, observed and understood.
Because the de Broglie wavelength of ultracold molecules is very large, the cross sections for collisions of molecules at ultracold temperatures are always computed by the time-independent quantum scattering approach. Here, we report the first accurate time-dependent wave packet dynamics calculation for reactive scattering of ultracold molecules. Wave packet dynamics calculations can be applied to molecular systems with more dimensions and provide real-time information on the process of bond rearrangement and/or energy exchange in molecular collisions. Our work thus makes possible the extension of rigorous quantum calculations of ultracold reaction properties to polyatomic molecules and adds a new powerful tool for the study of ultracold chemistry.
We study the time propagation of an initially localized wave packet for a generic one-dimensional time-independent system, using the ``nonlinear wave-packet dynamics'' [S. Tomsovic and E. J. Heller, Phys. Rev. Lett. 67, 664 (1991)], a semiclassical approximation using a local linearization of the wave packet in the vicinity of classical reference trajectories. Several reference trajectories are needed to describe the behavior of the full wave packet. The introduction of action-angle variables allows us to obtain a simple analytic expression for the autocorrelation function, and to show that a universal behavior (quantum collapses, quantum revivals, etc.) is obtained via interferences between the reference trajectories. A connection with the standard WKB approach is established. Finally, we apply the nonlinear wave-packet dynamics to the case of the hydrogen atom in a weak magnetic field, and show that the semiclassical expressions obtained by nonlinear wave-packet dynamics are extremely accurate. \textcopyright{} 1996 The American Physical Society.