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Physical Review A

Quantum control of Rydberg wave packets in the strong-response regime

Luı́s E. E. de Araujo, Ian A. Walmsley

Published Jan 4, 2001• 5 citations
Publisher

Abstract

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.

DOI
10.1103/physreva.63.023401

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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.
A simple analytic formula is derived for the impulse that will produce approximately, for arbitrarily large population transfer, a specified wave packet in a Rydberg atom. This solution to the nonlinear control problem is obtained in the limit that the duration of the pulsed control field is less than the Kepler period of the system. The validity of our solution is tested by comparison with a direct numerical integration of Schr\"odinger's equation, and it is found to yield the target state and population transfer with very high fidelity.
We derive a simple approximate analytic solution for the driving field that will generate a desired target vibrational wavepacket in a diatomic molecule. This solution is valid for arbitrary population transfer from the initial to the final electronic states. Analytic solutions to the control problem are possible when the control field is of shorter duration than the characteristic time scale of the system being manipulated. For target states that are localized wavepackets, our technique yields multiple solutions for the control field. We describe a procedure to choose from the set of solutions one that achieves both the target state and population transfer with high accuracy, for a large class of target states. The fidelity of each solution is tested by comparing the state obtained from a direct numerical integration of Schrödinger's equation using the analytic solution with the specified target state.
In this article, we review a different approach to controlling quantum systems. We show that the quantum control problem can be greatly simplified by limiting the duration of the driving force to less than one characteristic period of the system. (For an atomic-electron Rydberg wavepacket this would be the Kepler period, for example, or the vibrational period in the case of a molecule.) If the target state is a bound state of the system, then for times less than the characteristic period, the particle does not have the opportunity to reach the system's boundary and acts essentially as a classical free particle. Such a restriction on the duration of the driving field allows an analytic solution to be found, even in the nonperturbative regime, helping clarify some of the differences between the perturbative and the nonperturbative regimes of excitation. We also show that our solution is nonunique, and the quantum controller has a multiplicity of solutions to chose from.
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.
Photoionization of Rydberg atoms is considered in the framework of the quasiclassical (WKB) approach. Distribution of the photoelectron density in space and time is found and analyzed. This distribution is shown to consist of two main parts: the temporary population, which exists only as long as the light field is on; and the population corresponding to irreversible ionization. The irreversible-ionization wave packets are shown to experience the effect referred to as Coulomb narrowing. An origin of this effect and the conditions of its existence are discussed. In a strong field, rather simple analytical expressions are found for the partial probabilities of above-threshold ionization and for the total probability of ionization. In contrast to many earlier works, in the present theory neither the rotating-wave nor ``pole'' approximations are used, and the results are derived for an arbitrary pulse shape. Strong-field interference stabilization of Rydberg atoms is confirmed to occur at pulse durations shorter than the Kepler period. The arising regimes of interference stabilization are analyzed in comparison with the predictions of earlier works.