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Physical Review A

Dynamics of interfering wave packets

Xin Chen, John A. Yeazell

Published Apr 1, 1997• 18 citations
Publisher

Abstract

We examine the dynamics of two or more interfering wave packets. Via an analytical expression for the interfering wave packets, the redistribution of population and the evolution of the wave packets are studied. This analysis is in agreement with recent experimental investigations of interfering wave packets including the excitation of a Schr\"odinger cat state. The analysis is extended to multiple pulses and offers a simple formula for predicting their behavior.

DOI
10.1103/physreva.55.3264

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We examine the dynamics of two or more interfering wave packets. Via an analytical expression for the interfering wave packets, the redistribution of population and the evolution of the wave packets are studied. This analysis is in agreement with recent experimental investigations of interfering wave packets including the excitation of a Schr"odinger cat state. The analysis is extended to multiple pulses and offers a simple formula for predicting their behavior.
A general analytical formalism is described for the design of the excitation pulse (in the weak-field limit) that will excite a specified target wave packet. These analytical formulas (accurate to third order in the phase) provide multiple solutions for a class of target wave packets and provide a basis for choosing between these solutions. In addition, the possibility of independent compensation of the second- and third-order phase terms offers flexibility in the creation of exotic wave packets. A concrete design example is given for the generation of a well-localized Rydberg atomic wave packet at a specific target time.
In this paper, the analytic solution of the time-dependent Schrödinger equation is obtained for the wave packet in two-dimensional oscillator potential. The quantum dynamics of the wave packet is investigated based on this analytic solution. To our knowledge, this is the first time we solve, analytically and exactly this kind of time-dependent Schrödinger equation in a two-dimensional system, in which the Gaussian parameters satisfy the coupled nonlinear differential equations. The coherent states and their rotations of the system are discussed in detail. We find also that this analytic solution includes four kinds of modes of the evolutions for the wave packets: rigid, rotational, vibrational states and a combination of the rotation and vibration without spreading.
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.
Interference is one of the most fundamental features which characterizes quantum systems. Here we provide an exhaustive analysis of the interfere dynamics associated with wave-packet superpositions from both the standard quantum-mechanical perspective and the Bohmian one. From this analysis, clear and insightful pictures of the physics involved in these kind of processes are obtained, which are of general validity (i.e., regardless of the type of wave packets considered) in the understanding of more complex cases where interference is crucial (e.g., scattering problems, slit diffraction, quantum control scenarios or, even, multipartite interactions). In particular, we show how problems involving wave-packet interference can be mapped onto problems of wave packets scattered off potential barriers.
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.
In this article, we describe an analytic approach to the quantum control of wave-packet dynamics. In particular, we show that the field that will produce a specified wave packet in a Rydberg atom can be found approximately from a simple analytic formula. This analytic solution is shown to hold even in the regime of strong excitation, and is found by limiting the duration of the pulsed control field to less than one Kepler period of the system. Comparison with a direct numerical integration of Schr\"odinger's equation shows that our solution yields the target state and population transfer with very high fidelity. The possibility of ionization to the continuum is also included in the model. The solution provides some insight into the multiplicity of solutions to the control problem and the relative complexity of the control-field shapes in the weak- and strong-response regimes.